From 795a88d8505ce36103912f97d74fdd92cfdff71e Mon Sep 17 00:00:00 2001 From: nam Date: Wed, 10 Sep 2014 16:01:53 +0900 Subject: [PATCH 01/26] chap5, chap6 work with siunitx --- thesis/chapters/chap5_alcap_setup.tex | 228 +++++++++++++------------- thesis/chapters/chap6_analysis.tex | 111 ++++++------- thesis/mythesis.sty | 7 +- thesis/thesis.tex | 4 +- 4 files changed, 177 insertions(+), 173 deletions(-) diff --git a/thesis/chapters/chap5_alcap_setup.tex b/thesis/chapters/chap5_alcap_setup.tex index 638aa6b..5672daa 100644 --- a/thesis/chapters/chap5_alcap_setup.tex +++ b/thesis/chapters/chap5_alcap_setup.tex @@ -2,10 +2,40 @@ \label{cha:the_alcap_run_2013} \thispagestyle{empty} The first run of the AlCap experiment was performed at the $\pi$E1 beam line -area, PSI (Figure~\ref{fig:psi_exp_hall_all}) from November 26 to December 23, +area, PSI from November 26 to December 23, 2013. The goal of the run was to measure protons rate and spectrum following muon capture on aluminium. +\section{Experimental set up} +\label{sec:experimental_set_up} +The low energy muons from the $\pi$E1 beam line were stopped in thin aluminium +and silicon targets, and charged particles emitted were measured by two pairs +of silicon detectors inside of a vacuum vessel +(\cref{fig:alcap_setup_detailed}). A stopped muon event is defined by +a group of upstream detectors and a muon veto plastic scintillator. +The number of stopped muons is monitored by a germanium detector placed outside +of the vacuum chamber. In addition, several plastic scintillators were used to +provide veto signals for the silicon and germanium detectors. Two liquid +scintillators for neutron measurements were also tested in this run. +\begin{figure}[btp] + \centering + \includegraphics[width=0.55\textwidth]{figs/alcap_setup_detailed} + \caption{AlCap detectors: two silicon packages inside the vacuum vessel, + muon beam detectors including plastic scintillators and a wire chamber, + germanium detector and veto plastic scintillators.} + \label{fig:alcap_setup_detailed} +\end{figure} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Muon beam and vacuum chamber} +Muons in the $\pi$E1 beam line are decay products of pions created +as a \SI{590}{\mega\electronvolt} proton beam hits a thick carbon target +(E-target in \cref{fig:psi_exp_hall_all}). The beam line was designed to +deliver muons with momenta ranging from +\SIrange{10}{500}{\mega\electronvolt\per\cc} and +momentum spread from \SIrange{0.26}{8.0}{\percent}. These parameters can be +selected by changing various magnets and slits shown in +\cref{fig:psi_piE1_elements}~\cite{Foroughli.1997}. + \begin{figure}[p] \centering \includegraphics[height=0.85\textheight]{figs/psi_exp_hall_all} @@ -15,37 +45,7 @@ muon capture on aluminium. \label{fig:psi_exp_hall_all} \end{figure} -\section{Experimental set up} -\label{sec:experimental_set_up} -The low energy muons from the $\pi$E1 beam line were stopped in thin aluminium -and silicon targets, and charged particles emitted were measured by two pairs -of silicon detectors inside of a vacuum vessel -(Figure~\ref{fig:alcap_setup_detailed}). A stopped muon event is defined by -a group of upstream detectors and a muon veto plastic scintillator. -The number of stopped muons is monitored by a germanium detector placed outside -of the vacuum chamber. In addition, several plastic scintillators were used to -provide veto signals for the silicon and germanium detectors. Two liquid -scintillators for neutron measurements were also tested in this run. -\begin{figure}[htbp] - \centering - \includegraphics[width=0.65\textwidth]{figs/alcap_setup_detailed} - \caption{AlCap detectors: two silicon packages inside the vacuum vessel, - muon beam detectors including plastic scintillators and a wire chamber, - germanium detector and veto plastic scintillators.} - \label{fig:alcap_setup_detailed} -\end{figure} - -\subsection{Muon beam and vacuum chamber} -Muons in the $\pi$E1 beam line are decay products of pions created -as a 590~\mega\electronvolt\ proton beam hit a thick carbon target -(E-target in Figure~\ref{fig:psi_exp_hall_all}). The beam line was designed to -deliver muons with momenta ranging from 10 to 500~\mega\electronvolt\per\cc\ -and -momentum spread from 0.26 to 8.0\%. These parameters can be selected by -changing various magnets and slits shown in -Figure~\ref{fig:psi_piE1_elements}~\cite{Foroughli.1997}. - -\begin{figure}[htb] +\begin{figure}[btp] \centering \includegraphics[width=0.7\textwidth]{figs/psi_piE1_elements} \caption{The $\pi$E1 beam line} @@ -54,16 +54,17 @@ Figure~\ref{fig:psi_piE1_elements}~\cite{Foroughli.1997}. One of the main requirements of the AlCap experiment was a low energy muon beam with narrow momentum bite in order to achieve a high fraction of stopping muons -in the very thin targets. In this Run 2013, muons from 28 to -45~\mega\electronvolt\per\cc\ and momentum spread of 1\% and 3\%were used. +in the very thin targets. In this Run 2013, muons from +\SIrange{28}{45}{\mega\electronvolt\per\cc} and momentum spread of 1\% and +3\%were used. For part of the experiment the target was replaced with one of the silicon detector packages allowed an accurate momentum and range calibration %(via range-energy relations) -of the beam at the target. Figure~\ref{fig:Rates} shows the measured muon rates +of the beam at the target. \Cref{fig:Rates} shows the measured muon rates as a function of momentum for two different momentum bites. -Figure~\ref{fig:Beam} shows an example of the resulting energy spectra. -\begin{figure}[htbp] +\Cref{fig:Beam} shows an example of the resulting energy spectra. +\begin{figure}[btp] \centering \includegraphics[width=0.6\textwidth]{figs/Rates.png} \caption{Measured muon rate (kHz) at low momenta. Momentum bite of 3 and 1 \% @@ -71,18 +72,18 @@ Figure~\ref{fig:Beam} shows an example of the resulting energy spectra. \label{fig:Rates} \end{figure} -\begin{figure}[htbp] +\begin{figure}[btp] \centering \includegraphics[width=0.9\textwidth]{figs/beam.pdf} - \caption{Energy deposition at 36.4 MeV/c incident muon beam in an - 1500-\micron-active - target. The peak at low energy is due to beam electrons, the - peaks at higher energies are due to muons. Momentum bite of 1 and 3\% FWHM - on left and right hand side, respectively.} \label{fig:Beam} + \caption{Energy deposition at \SI{36.4}{/c} incident muon beam in an + \SI{1500}{\micro\meter}-thick active target. The peak at low energy is due + to beam electrons, the peaks at higher energies are due to muons. Momentum + bite of 1 and 3\% FWHM on left and right hand side, respectively.} + \label{fig:Beam} \end{figure} The targets and charged particle detectors are installed inside the vacuum -chamber as shown in Figure~\ref{fig:alcap_setup_detailed}. The muon beam enters +chamber as shown in \cref{fig:alcap_setup_detailed}. The muon beam enters from the right of the image and hits the target, which is placed at the centre of the vacuum chamber and orientated at 45 degrees to the beam axis. The side walls and bottom flange of the vessel provide several @@ -91,7 +92,7 @@ scintillator detectors inside the chamber. In addition, the chamber is equipped with several lead collimators %so that muons that are not captured in the target would quickly decay. to quickly capture muons that do not stop in the actual target. -%\begin{figure}[htbp] +%\begin{figure}[btp] %\centering %\includegraphics[width=0.55\textwidth]{figs/SetupOverview.jpg} %\caption{Vacuum chamber in beam line} @@ -102,22 +103,25 @@ to quickly capture muons that do not stop in the actual target. %a silicon detector in the low vacuum region of $10^{-3}$ mbar. %An interlock mechanism was installed to prevent the bias of the %silicon detectors from being applied before the safe vacuum level. -For a safe operation of the silicon detector, a vacuum of $<10^{-4}$\,mbar was -necessary. With the help of the vacuum group of PSI, we could consistently -reach $10^{-4}$\,mbar within 45 minutes after closure of the chamber's top -flange. +For a safe operation of the silicon detector, a vacuum of \SI{e-4}{\milli\bar} +was necessary. With the help of the vacuum group of PSI, we could consistently +reach the required vacuum level within 45 minutes after closure of the +chamber's top flange. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Silicon detectors} The main detectors for proton measurement in the Run 2013 were four large area silicon detectors. The silicon detectors were grouped into two detector packages located symmetrically at 90 degrees of the nominal muon beam path, SiL -and SiR in Figure~\ref{fig:alcap_setup_detailed}. Each arm consists of: one -$\Delta$E counter, a 65-\micro\meter-thick silicon detector, divided into -4 quadrants; one E counter made from 1500-\micron-thick silicon; and one -plastic scintillator to identify electrons or high energy protons that pass -through the silicon. The area of each of these silicon detectors and the -scintillators is $50\times50 \textrm{mm}^2$. +and SiR in \cref{fig:alcap_setup_detailed}. Each arm consists of: one +$\Delta$E counter, a \SI{65}{\micro\meter}-thick silicon detector, divided into +4 quadrants; one E counter made from \SI{1500}{\micro\meter}-thick silicon; and +one plastic scintillator to identify electrons or high energy protons that +pass through the silicon. The area of each of these silicon detectors and the +scintillators is $50\times50 \textrm{mm}^2$. There is a dead layer of +\SI{0.5}{\micro\meter} on each side of the silicon detectors according to the +manufacturer Micron Semiconductor +\footnote{\url{http://www.micronsemiconductor.co.uk/}}. The detectors were named according to their positions relative to the muon view: the SiL package contains the thin @@ -129,11 +133,11 @@ SiR1-4. Bias for the four silicon detectors was supplied by an ORTEC 710 NIM module, which has a vacuum interlock input to prevent biasing before the safe vacuum level has been reached. Typical voltage to fully depleted the detectors were --300~\volt\ and -10~\volt\ for the thick and thin silicon detectors +\SI{-300}{\volt} and \SI{-10}{\volt} for the thick and thin silicon detectors respectively. The leakage currents at the operating voltages are less than -1.5~\micro\ampere\ for the thick detectors, and about 0.05~\micro\ampere\ -for the thin ones (see Figure~\ref{fig:si_leakage}). -\begin{figure}[htb] +\SI{1.5}{\micro\ampere} for the thick detectors, and about +\SI{0.05}{\micro\ampere} for the thin ones (see \cref{fig:si_leakage}). +\begin{figure}[btp] \centering \includegraphics[width=0.85\textwidth]{figs/si_leakage} \caption{Leakage currents of the silicon detectors under bias.} @@ -146,8 +150,8 @@ output pulse height on an oscilloscope. One would expect that the maximum pulse height increases as the bias is raised until the voltage of fully depleted. The effect can also be seen on the pulse height spectrum as in -Figure~\ref{fig:sir2_bias_alpha}. -\begin{figure}[htb] +\cref{fig:sir2_bias_alpha}. +\begin{figure}[btp] \centering \includegraphics[width=0.75\textwidth]{figs/sir2_bias_alpha} \caption{$^{241}\textrm{Am}$ spectra in cases of fully depleted (top), and @@ -195,12 +199,12 @@ Figure~\ref{fig:sir2_bias_alpha}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Upstream counters} \label{sub:upstream_counters} -The upstream detector consists of three counters: a 500~$\mu$m thick -scintillator muon trigger counter ($\mu$SC); a muon anti-coincidence counter -($\mu$SCA) surrounding the trigger counter with a hole -of 35 \milli\meter\ in diameter to define the beam radius; and a multi-wire -proportional chamber ($\mu$PC) that uses 24 X wires and 24 Y wires at -2~\milli\meter~intervals. +The upstream detector consists of three counters: a \SI{500}{\micro\meter}-thick +scintillator muon trigger counter (\Pmu{}SC); a muon anti-coincidence counter +(\Pmu{}SCA) surrounding the trigger counter with a hole +of 35 \si{\milli\meter}\ in diameter to define the beam radius; and a multi-wire +proportional chamber (\Pmu{}PC) that uses 24 X wires and 24 Y wires at +2~\si{\milli\meter}~intervals. The upstream detectors provide signal of an incoming muon as coincident hits on the muon trigger and the wire chamber in anti-coincident with the muon @@ -214,7 +218,7 @@ ready to be used in our run without any modification. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Germanium detector} -%\begin{figure}[htbp] +%\begin{figure}[btp] %\centering %\includegraphics[width=0.9\textwidth]{figs/neutron.png} %\caption{Setup of two @@ -225,9 +229,9 @@ We used a germanium detector to normalise the number of stopped muons by measuring characteristics muon X-rays from the target material. The primary X-rays of interest are the 346.828~keV line for aluminium targets, and the 400.177 line for silicon targets. The energies and intensities of the X-rays -listed in Table~\ref{tab:xray_ref} follow measurement results from +listed in \cref{tab:xray_ref} follow measurement results from Measday and colleagues~\cite{MeasdayStocki.etal.2007}. -\begin{table}[htb] +\begin{table}[btp] \begin{center} \begin{tabular}{c l l l l } \toprule @@ -250,11 +254,11 @@ The germanium detector is a GMX20P4-70-RB-B-PL, n-type, coaxial high purity germanium detector produced by ORTEC. The detector was optimised for low energy gamma and X-rays measurement with an ultra-thin entrance window of 0.5-mm-thick beryllium and -a 0.3-\micron-thick ion implanted contact (Figure~\ref{fig:ge_det_dimensions}). +a 0.3-\si{\micro\meter}-thick ion implanted contact (\cref{fig:ge_det_dimensions}). This detector is equipped with a transistor reset preamplifier which, according to the producer, enables it to work in an ultra-high rate environment -up to $10^6$ counts\per\second~ at 1~\mega\electronvolt. -\begin{figure}[htb] +up to $10^6$ counts\si{\per\second} at \SI{1}{\mega\electronvolt}. +\begin{figure}[btp] \centering \includegraphics[width=0.9\textwidth]{figs/ge_det_dimensions} \caption{Dimensions of the germanium detector} @@ -288,12 +292,12 @@ carried out. \section{Front-end electronics and data acquisition system} The front-end electronics of the AlCap experiment was simple since we employed a trigger-less read out system with waveform digitisers and flash ADCs -(FADCs). As shown in Figure~\ref{fig:alcapdaq_scheme}, all plastic +(FADCs). As shown in \cref{fig:alcapdaq_scheme}, all plastic scintillators signals were amplified by PMTs, then fed into the digitisers. The signals from silicon and germanium detectors were preamplified, and subsequently shaped by spectroscopy amplifiers and timing filter amplifiers (TFAs) to provide energy and timing information. -\begin{figure}[htbp] +\begin{figure}[btp] \centering \includegraphics[width=0.99\textwidth]{figs/alcapdaq_scheme} \caption{Schematic diagram of the electronics and DAQ used in the Run 2013} @@ -304,21 +308,21 @@ The germanium detector has its own transistor reset preamplifier installed very close to the germanium crystal. Two ORTEC Model 142 preamplifiers were used for the thick silicon detectors. The timing outputs of the preamplifiers were fed into three ORTEC Model 579 TFAs. -We used an ORTEC Model 673 to shape the germanium signal with 6~\micro\second +We used an ORTEC Model 673 to shape the germanium signal with 6~\si{\micro\second} shaping time. A more modern-style electronics was used for thin silicon detectors where the preamplifier, shaping and timing amplifiers were implemented on one compact package, namely a Mesytec MSI-8 box. This box has 8 channels, each channel consists of one preamplifier board and one shaper-and-timing filter board which -can be fine-tuned independently. The shaping time was set to 1~\micro\second\ +can be fine-tuned independently. The shaping time was set to 1~\si{\micro\second}\ for all channels. The detector system produced signals that differs significantly in time scale, -ranging from very fast (about 40~\nano\second\ from scintillators) to very slow -(several \micro\second\ from shaping outputs of semiconductor detectors). This -lead to the use of several sampling frequencies from 17~\mega\hertz\ to -250~\mega\hertz, and three types of digitisers were employed: +ranging from very fast (about 40~\si{\nano\second}\ from scintillators) to very slow +(several \si{\micro\second}\ from shaping outputs of semiconductor detectors). This +lead to the use of several sampling frequencies from 17~\si{\mega\hertz}\ to +250~\si{\mega\hertz}, and three types of digitisers were employed: \begin{itemize} \item custom-built 12-bit 170-MHz FADCs which was designed for the MuCap experiment. Each FADC board has dimensions the same as those of @@ -328,10 +332,10 @@ lead to the use of several sampling frequencies from 17~\mega\hertz\ to Ethernet-level protocol. The protocol only allows detecting incomplete data transfers but no retransmitting is possible due to the limited size of the module's output buffer. The FADCs accept clock signal - at the frequency of 50~\mega\hertz\ then multiply that internally up to - 170~\mega\hertz. Each channel on one board can run at different sampling + at the frequency of 50~\si{\mega\hertz}\ then multiply that internally up to + 170~\si{\mega\hertz}. Each channel on one board can run at different sampling frequency not dependent on other channels. The FADC has 8 single-ended - LEMO inputs with 1~\volt pp dynamic range. + LEMO inputs with 1~\si{\volt} pp dynamic range. \item a 14-bit 100-MS/s CAEN VME FADC waveform digitiser model V1724. The module houses 8 channels with 2.25~Vpp dynamic range on single-ended MCX coaxial inputs. The digitiser features an optical link for transmission of @@ -347,7 +351,7 @@ lead to the use of several sampling frequencies from 17~\mega\hertz\ to proprietary binary drivers and libraries. \end{itemize} All digitisers were driven by external clocks which were derived from the same -500-\mega\hertz\ master clock, a high precision RF signal generator Model SG382 +500-\si{\mega\hertz}\ master clock, a high precision RF signal generator Model SG382 of Stanford Research System. The silicon detectors were read out by FADC boards feature network-based data @@ -355,14 +359,14 @@ readout interface. To maximize the data throughput, each of the four FADC boards was read out through separate network adapter. The CAEN digitisers were used to read out the germanium detector (timing and energy, slow signals) or scintillator -detectors (fast signals). For redundancy, all beam monitors ($\mu$SC, $\mu$SCA -and $\mu$PC) were also read out by a CAEN time-to-digital converter (TDC) +detectors (fast signals). For redundancy, all beam monitors (\Pmu{}SC, \Pmu{}SCA +and \Pmu{}PC) were also read out by a CAEN time-to-digital converter (TDC) model V767 which was kindly provided by the MuSun experiment. The Data Acquisition System (DAQ) of the AlCap experiment, so-called AlCapDAQ, provided the readout of front-end electronics, event assembling, data logging, hardware monitoring and control, and the run database of the experiment -(Figure~\ref{fig:alcapdaq_pcs}). It was based on MIDAS framework~\footnote{ +(\cref{fig:alcapdaq_pcs}). It was based on MIDAS framework~\footnote{ MIDAS is a general purpose DAQ software system developed at PSI and TRIUMF:\\ \url{http://midas.triumf.ca}} and consisted of two circuits, {\em i}) a detector circuit for synchronous data readout from the front-end electronics @@ -375,7 +379,7 @@ running Linux operating system and connected into a private subnetwork. %\hl{TODO: storage and shift monitor} -\begin{figure}[htb] +\begin{figure}[btp] \centering \includegraphics[width=0.95\textwidth]{figs/alcapdaq_pcs} \caption{AlCapDAQ in the Run 2013. The {\ttfamily fe6} front-end is @@ -397,10 +401,10 @@ correlation between detectors would be established in the analysis stage. At the beginning of each block, the time counter in each digitiser is reset to ensure time alignment across all modules. The period of 110~ms was chosen to be: -{\em i} long enough compares to the time scale of several \micro\second\ of the +{\em i} long enough compares to the time scale of several \si{\micro\second}\ of the physics of interest, {\em ii} short enough so that there is no timer rollover -on any digitiser (a FADC runs at its maximum speed of 170~\mega\hertz\ could -handle up to about 1.5 \second\ with its 28-bit time counter). +on any digitiser (a FADC runs at its maximum speed of \SI{170}{\mega\hertz} could +handle up to about \SI{1.5}{\second} with its 28-bit time counter). To ease the task of handling data, the data collecting period was divided into short runs, each run stopped when the logger had recorded 2 GB of data. @@ -431,14 +435,14 @@ different targets were carried out for silicon targets: As the emitted protons deposit a significant amount of energy in the target material, thin targets and thus excellent momentum resolution of the low energy -muon beam are critical. Aluminium targets of 50-\micro\meter\ and -100~\micron\ thick were used. Although a beam with low momentum spread of +muon beam are critical. Aluminium targets of 50-\si{\micro\meter}\ and +100~\si{\micro\meter}\ thick were used. Although a beam with low momentum spread of 1\% is preferable, it was used for only a small portion of the run due to the -low beam rate (see Figure~\ref{fig:Rates}). The beam momentum for each target +low beam rate (see \cref{fig:Rates}). The beam momentum for each target was chosen to maximise the number of stopped muons. The collected data sets are -shown in Table~\ref{tb:stat}. +shown in \cref{tb:stat}. -\begin{table}[htb!] +\begin{table}[btp!] \begin{center} \vspace{0.15cm} \begin{tabular}{l c c c} @@ -446,16 +450,16 @@ shown in Table~\ref{tb:stat}. \textbf{Target} &\textbf{Momentum} & \textbf{Run time} & \textbf{Number}\\ \textbf{and thickness}&\textbf{scaling factor} & \textbf{(h)} &\textbf{of muons}\\ \midrule - Si 1500 \micro\meter& 1.32& 3.07& $2.78\times 10^7$\\ + Si 1500 \si{\micro\meter}& 1.32& 3.07& $2.78\times 10^7$\\ & 1.30& 12.04& $2.89 \times 10^8$\\ & 1.10& 9.36& $1.37 \times 10^8$ \\ \midrule - Si 62 \micro\meter & 1.06& 10.29& $1.72 \times 10^8$\\ + Si 62 \si{\micro\meter} & 1.06& 10.29& $1.72 \times 10^8$\\ \midrule - Al 100 \micro\meter& 1.09& 14.37&$2.94 \times 10^8$\\ + Al 100 \si{\micro\meter}& 1.09& 14.37&$2.94 \times 10^8$\\ & 1.07& 2.56& $4.99 \times 10^7$\\ \midrule - Al 50 \micro\meter m & 1.07& 51.94& $8.81 \times 10^8$\\ + Al 50 \si{\micro\meter} m & 1.07& 51.94& $8.81 \times 10^8$\\ \bottomrule \end{tabular} \end{center} @@ -473,11 +477,11 @@ Since the AlCapDAQ is a trigger-less system, it stored all waveforms of the hits occured in 100-ms-long blocks without considering their physics significance The analysis code therefore must be able to extract parameters of the waveforms, then organises the pulses into physics events correlated to -stopped muons (Figure~\ref{fig:muon_event}). In addition, the analyser is +stopped muons (\cref{fig:muon_event}). In addition, the analyser is intended to be usable as a real-time component of a MIDAS DAQ, where simple analysis could be done online for monitoring and diagnostic during the run. -\begin{figure}[htb] +\begin{figure}[btp] \centering \includegraphics[width=0.9\textwidth]{figs/muon_event.pdf} \caption{Concept of the AlCap analysis code: pulses from individual detector @@ -520,7 +524,7 @@ algorithm that takes the pulse parameters from the peak of the waveform. In parallel, a pulse finding and template fitting code is being developed because it would provide more accurate pulse information. The first iteration of this code has been completed and is being tested. -\begin{figure}[htb] +\begin{figure}[btp] \centering \includegraphics[width=0.85\textwidth]{figs/analysis_scheme} \caption{Concept of the analysis framework in \rootana{}} @@ -545,7 +549,7 @@ detectors. These particle hits are still stored in the time-ordered tree corresponds to the 110 ms block length from the AlCapDAQ. By iterating through the tree to find stopped muons and taking any hits within a certain window around this muon from every detector, a stopped-muon-centred tree shown in -Figure~\ref{fig:muon_event} can be produced. This will make it much easier to +\cref{fig:muon_event} can be produced. This will make it much easier to look for coincidences and apply cuts, thereby bringing the end goal of particle numbers and energy distributions. @@ -558,8 +562,8 @@ The online analyser was developed and proved to be very useful during the run. A few basic modules were used to produce plots for diagnostic purposes including: persistency view of waveforms, pulse height spectra, timing correlations with respect to the upstream counters. The -modules and their purposes are listed in Table~\ref{tab:online_modules}. -\begin{table}[htb] +modules and their purposes are listed in \cref{tab:online_modules}. +\begin{table}[btp] \begin{center} \begin{tabular}{l p{6cm}} \toprule @@ -604,7 +608,7 @@ groups such as upstream counters, silicon arms. It could also periodically update the plots to reflect real-time status of the detector system. %Screen %shots of the {\ttfamily online-display} with several plots are shown in -%Figure~\ref{fig:online_display}. +%\cref{fig:online_display}. %\hl{Screen shots} \subsection{Offline analyser} @@ -612,15 +616,15 @@ update the plots to reflect real-time status of the detector system. Some offline analysis modules has been developed during the beam time and could provide quick feedback in confirming and guiding the decisions at the time. For example, the X-ray spectrum analysis was done to confirm that we could observe -the muon capture process (Figure~\ref{fig:muX}), and to help in choosing optimal +the muon capture process (\cref{fig:muX}), and to help in choosing optimal momenta which maximised the number of stopped muons. -\begin{figure}[htbp] +\begin{figure}[btp] \centering \includegraphics[width=0.7\textwidth]{figs/muX.png} \caption{Germanium detector spectra in the range of 300 - 450 keV with different setups: no - target, 62-\micron-thick silicon target, and 100-\micron-thick aluminium - target. The ($2p-1s$) lines from + target, 62-\si{\micro\meter}-thick silicon target, and + 100-\si{\micro\meter}-thick aluminium target. The ($2p-1s$) lines from aluminium (346.828 keV) and silicon (400.177 keV) are clearly visible, the double peaks at 431 and 438 keV are from the lead shield, the peak at 351~keV is a background gamma ray from $^{211}$Bi.} diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index 75f46bb..cc50dfe 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -4,7 +4,7 @@ \section{Analysis modules} \label{sec:analysis_modules} A full analysis has not been completed yet, but initial analysis -based on the existing modules (Table~\ref{tab:offline_modules}) is possible +based on the existing modules (\cref{tab:offline_modules}) is possible thanks to the modularity of the analysis framework. \begin{table}[htb] @@ -30,16 +30,16 @@ thanks to the modularity of the analysis framework. \end{table} The MakeAnalysedPulses module takes a raw waveform, calculates the pedestal -from a predefined number of first samples, subtracts this pedestal, takes +from a predefined number of first samples, subtracts this pedestal taking pulse polarity into account, then calls another module to extract pulse parameters. At the moment, the simplest module, so-called MaxBinAPGenerator, for pulse information calculation is in use. The module looks for the sample that has the maximal deviation from the baseline, takes the deviation as pulse amplitude and the time stamp of the sample as pulse time. The procedure is -illustrated on Figure~\ref{fig:tap_maxbin_algo}. This module could not detect +illustrated on \cref{fig:tap_maxbin_algo}. This module could not detect pile up or double pulses in one \tpulseisland{} in -Figure~\ref{fig:tap_maxbin_bad}. +\cref{fig:tap_maxbin_bad}. \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/tap_maxbin_algo} @@ -82,7 +82,7 @@ the beam rate was generally less than \SI{8}{\kilo\hertz}. %candidate: a prompt hit on the target in $\pm 200$ \si{\nano\second}\ around the %time of the $\mu$Sc pulse. The number comes from the observation of the %time correlation between hits on the target and the $\mu$Sc -%(Figure~\ref{fig:tme_sir_prompt_rational}). +%(\cref{fig:tme_sir_prompt_rational}). %\begin{figure}[htb] %\centering %\includegraphics[width=0.85\textwidth]{figs/tme_sir_prompt_rational} @@ -97,7 +97,7 @@ rate, time correlation to hits on $\mu$Sc, \ldots on each channel during the data collecting period. Runs with significant difference from the nominal values were further checked for possible causes, and would be discarded if such discrepancy was too large or unaccounted for. Examples of such trend plots are -shown in Figure~\ref{fig:lldq}. +shown in \cref{fig:lldq}. \begin{figure}[htb] \centering \includegraphics[width=0.47\textwidth]{figs/lldq_noise} @@ -131,15 +131,10 @@ During data taking period, electrons in the beam were were also used for energy calibration of thick silicon detectors where energy deposition is large enough. The muons at different momenta provided another mean of calibration in the beam tuning period. -%Typical pulse height spectra of the silicon detectors are shown -%in Figure~\ref{fig:si_eg_spectra}. -According to Micron Semiconductor -\footnote{\url{http://www.micronsemiconductor.co.uk/}}, the -manufacturer of the silicon detectors, the nominal thickness of the dead layer on -each side is 0.5~\si{\micro\meter}. The alpha particles from the source would deposit -about 66~keV in this layer, and the peak would appear at 5418~keV -(Figure~\ref{fig:toyMC_alpha}). +The alpha particles from the source would deposit +about 66~keV in the \SI{0.5}{\micro\meter}-thick dead layer, and the peak would +appear at 5418~keV (\cref{fig:toyMC_alpha}). \begin{figure}[htb] \centering \includegraphics[width=0.6\textwidth]{figs/toyMC_alpha} @@ -149,7 +144,7 @@ about 66~keV in this layer, and the peak would appear at 5418~keV \end{figure} The calibration coefficients for the silicon channels are listed in -Table~\ref{tab:cal_coeff}. +\cref{tab:cal_coeff}. \begin{table}[htb] \begin{center} \begin{tabular}{l c r} @@ -183,7 +178,7 @@ source\footnote{Energies and intensities of gamma rays are taken from the X-ray and Gamma-ray Decay Data Standards for Detector Calibration and Other Applications, which is published by IAEA at \\ \url{https://www-nds.iaea.org/xgamma_standards/}}, the -recorded pulse height spectrum is shown in Figure~\ref{fig:ge_eu152_spec}. The +recorded pulse height spectrum is shown in \cref{fig:ge_eu152_spec}. The source was placed at the target position so that the absolute efficiencies can be calibrated. The relation between pulse height in ADC count and energy is found to be: @@ -197,7 +192,7 @@ worse at 3.1~\si{\kilo\electronvolt}~for the annihilation photons at The absolute efficiencies for the $(2p-1s)$ lines of aluminium (346.828~\si{\kilo\electronvolt}) and silicon (400.177~\si{\kilo\electronvolt}) are -presented in Table~\ref{tab:xray_eff}. In the process of efficiency calibration, +presented in \cref{tab:xray_eff}. In the process of efficiency calibration, corrections for true coincidence summing and self-absorption were not applied. The true coincidence summing probability is estimated to be very small, about \sn{5.4}{-6}, thanks to the far geometry of the calibration. The @@ -263,7 +258,7 @@ polyethylene is less than \sn{4}{-4} for a 100~\si{\kilo\electronvolt}\ photon. %detector was placed perpendicular to the nominal beam path, after an oval %collimator. The beam momentum scaling factor was scanned from 1.10 to 1.60, %muon momenta and energies in the measured points are listed in -%Table~\ref{tab:mu_scales}. +%\cref{tab:mu_scales}. %\begin{table}[htbp] %\begin{center} %\begin{tabular}{c c c c} @@ -301,7 +296,7 @@ polyethylene is less than \sn{4}{-4} for a 100~\si{\kilo\electronvolt}\ photon. \label{sec:charged_particles_from_muon_capture_on_silicon_thick_silicon} This analysis was done on a subset of the active target runs 2119 -- 2140 because of the problem of wrong clock frequency found in the data quality -checking shown in Figure~\ref{fig:lldq}. The data set contains \sn{6.43}{7} +checking shown in \cref{fig:lldq}. The data set contains \sn{6.43}{7} muon events. %64293720 @@ -316,7 +311,7 @@ Because of the active target, a stopped muon would cause two coincident hits on the muon counter and the target. The energy of the muon hit on the active target is also well-defined as a narrow momentum spread beam was used. The correlation between the energy and timing of all the hits on the active target -is shown in Figure~\ref{fig:sir2f_Et_corr}. The most intense spot at zero time +is shown in \cref{fig:sir2f_Et_corr}. The most intense spot at zero time and about 5 MeV energy corresponds to stopped muons in the thick target. The band below 1 MeV is due to electrons, either in the beam or from muon decay in orbits, or emitted during the cascading of muon to the muonic 1S state. The @@ -341,7 +336,7 @@ particles from the stopped muons: It can be seen that there is a faint stripe of muons in the time larger than 1200~ns region, they are scattered muons by other materials without hitting the muon counter. The electrons in the beam caused the constant band below 1 MeV and -$t > 5000$ ns (see Figure~\ref{fig:sir2_1us_slices}). +$t > 5000$ ns (see \cref{fig:sir2_1us_slices}). \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/sir2_sir2f_amp_1us_slices} @@ -401,8 +396,8 @@ hits: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Number of charged particles with energy above 2~MeV} \label{sub:number_of_charged_particles_with_energy_from_8_10_mev} -As shown in Figure~\ref{fig:sir2_1us_slices} and illustrated by MC simulation -in Figure~\ref{fig:sir2_mc_pdfs}, there are several components in +As shown in \cref{fig:sir2_1us_slices} and illustrated by MC simulation +in \cref{fig:sir2_mc_pdfs}, there are several components in the energy spectrum recorded by the active target: \begin{enumerate} \item charged particles from nuclear muon capture, this is the signal we are @@ -484,7 +479,7 @@ The number of nuclear captures can be inferred from the number of recorded muonic X-rays. The reference values of the parameters needed for the calculation taken from Suzuki et al.~\cite{SuzukiMeasday.etal.1987} and Measday et al.~\cite{MeasdayStocki.etal.2007} are -listed in Table~\ref{tab:mucap_pars}. +listed in \cref{tab:mucap_pars}. \begin{table}[htb] \begin{center} \begin{tabular}{l l l} @@ -505,7 +500,7 @@ listed in Table~\ref{tab:mucap_pars}. \end{table} The muonic X-ray spectrum emitted from the active target is shown in -Figure~\ref{fig:sir2_xray}. The $(2p-1s)$ line is seen at +\cref{fig:sir2_xray}. The $(2p-1s)$ line is seen at 399.5~\si{\kilo\electronvolt}, 0.7~\si{\kilo\electronvolt}\ off from the reference value of 400.177~\si{\kilo\electronvolt}. This discrepancy is within our detector's resolution, and the calculated efficiency is @@ -552,7 +547,7 @@ corrected for several effects: pulse time, and (b) the reset pulses of the transistor reset preamplifier. The effects of the two dead time could be calculated by examining the interval between two consecutive pulses on the germanium detector in - Figure~\ref{fig:sir2_ge_deadtime}. + \cref{fig:sir2_ge_deadtime}. \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/sir2_ges_self_tdiff} @@ -592,7 +587,7 @@ corrected for several effects: \end{itemize} The number of X-rays after applying all above corrections is 3293.5. The X-ray -intensity in Table~\ref{tab:mucap_pars} was normalised to the number of stopped +intensity in \cref{tab:mucap_pars} was normalised to the number of stopped muons, so the number of stopped muons is: \begin{align} @@ -602,9 +597,9 @@ muons, so the number of stopped muons is: &= 9.03\times10^6 \nonumber \end{align} where $\epsilon_{(2p-1s)}$ is the calibrated absolute efficiency of the -detector for the 400.177~keV line in Table~\ref{tab:xray_eff}, and +detector for the 400.177~keV line in \cref{tab:xray_eff}, and $I_{(2p-1s)}$ is the probability of emitting this X-ray per stopped muon -(80.3\% from Table~\ref{tab:mucap_pars}). +(80.3\% from \cref{tab:mucap_pars}). Taking the statistical uncertainty of the peak area, and systematic uncertainties from parameters of muon capture, the number of stopped muons @@ -621,7 +616,7 @@ The number of nuclear captured muons is: \label{eqn:sir2_Ncapture} \end{equation} where the $f_{\textrm{cap.Si}}$ is the probability of nuclear capture per -stopped muon from Table~\ref{tab:mucap_pars}. +stopped muon from \cref{tab:mucap_pars}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Emission rate of charged particles} \label{sub:emission_rate_of_charged_particles} @@ -633,7 +628,7 @@ nuclear muon capture in~\eqref{eqn:sir2_Ncapture}: = \frac{149.9\times10^4}{7.25\times10^6} = 0.252 \end{equation} Uncertainties of this rate calculation are listed in -Table~\ref{tab:sir2_uncertainties}, including: +\cref{tab:sir2_uncertainties}, including: \begin{itemize} \item uncertainties from number of charged particles, both statistical and systematic (from spectrum shape and fitting) ones are absorbed in the @@ -690,7 +685,7 @@ So, the emission rate is: %\label{fig:sobottka_spec} %\end{figure} %The spectrum measured by Sobottka and Wills~\cite{SobottkaWills.1968} is -%reproduced in Figure~\ref{fig:sobottka_spec}, the spectral integral in the +%reproduced in \cref{fig:sobottka_spec}, the spectral integral in the %energy region from 8 to 10~\si{\mega\electronvolt}\ is $2086.8 \pm 45.7$. %The authors obtained the spectrum in a 4~\si{\micro\second}\ gate period which began %1~\si{\micro\second}\ after a muon stopped, which would take 26.59\% of the emitted @@ -769,11 +764,11 @@ within a coincidence window of $\pm 0.5$~\si{\micro\second}\ around the thick silicon hit, the two hits are considered to belong to one particle with $\Delta$E being the energy of the thin hit, and total E being the sum energy of the two hits. Particle identification is done using correlation between -$\Delta$E and E. Figure~\ref{fig:si16p_dedx_nocut} shows clearly visible banding +$\Delta$E and E. \cref{fig:si16p_dedx_nocut} shows clearly visible banding structure. No cut on energy deposit or timing with respect to muon hit are applied yet. -With the aid from MC study (Figure~\ref{fig:pid_sim}), the banding on the +With the aid from MC study (\cref{fig:pid_sim}), the banding on the $\Delta$E-E plots can be identified as follows: \begin{itemize} \item the densest spot at the lower left conner belonged to electron hits; @@ -804,13 +799,13 @@ $\Delta$E-E plots can be identified as follows: \end{figure} It is observed that the banding is more clearly visible in a log-log scale -plots like in Figure~\ref{fig:si16p_dedx_cut_explain}, this suggests +plots like in \cref{fig:si16p_dedx_cut_explain}, this suggests a geometrical cut on the logarithmic scale would be able to discriminate protons from other particles. The protons and deuterons bands are nearly parallel to the $\ln(\Delta \textrm{E [keV]}) + \ln(\textrm{E [keV]})$ line, but have a slightly altered slope because $\ln(\textrm{E})$ is always greater than $\ln(\Delta\textrm{E})$. The two parallel lines on -Figure~\ref{fig:si16p_dedx_cut_explain} suggest a check of +\cref{fig:si16p_dedx_cut_explain} suggest a check of $\ln(\textrm{E}) + 0.85\times\ln(\Delta \textrm{E})$ could tell protons from other particles. @@ -829,11 +824,11 @@ $\ln(\textrm{E}) < 9$, which corresponds to $\textrm{E} < 8$~MeV. The cut of $\ln(\textrm{E}) < 9$ is applied first, then $\ln(\textrm{E})+ 0.85\times\ln(\Delta \textrm{E}) $ is plotted as -Figure~\ref{fig:si16p_loge+logde}. The protons make a clear peak in the region +\cref{fig:si16p_loge+logde}. The protons make a clear peak in the region between 14 and 14.8, the next peak at 15 corresponds to deuteron. Imposing the $14<\ln(\textrm{E})+ 0.85\times\ln(\Delta \textrm{E})<14.8$ cut, -the remaining proton band is shown on Figure~\ref{fig:si16p_proton_after_ecut}. +the remaining proton band is shown on \cref{fig:si16p_proton_after_ecut}. \begin{figure}[htb] \centering @@ -854,7 +849,7 @@ the remaining proton band is shown on Figure~\ref{fig:si16p_proton_after_ecut}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Number of muon captures} \label{sub:number_stopped_muons} -The X-ray spectrum from this silicon target on Figure~\ref{fig:si16_xray} is +The X-ray spectrum from this silicon target on \cref{fig:si16_xray} is significantly noisier than the previous data set of SiR2, suffers from both lower statistics and a more relaxed muon definition. The peak of $(2p-1s)$ X-ray at 400.177~keV can still be recognised but on a very high background. The @@ -881,7 +876,7 @@ reducing the background level under the 400.177 keV peak by about one third. Using the same procedure on the region from 396 to 402 keV (without self-absorption correction since this is a thin target), the number of X-rays recorded and the number of captures are shown in -Table~\ref{tab:si16p_ncapture_cal}. +\cref{tab:si16p_ncapture_cal}. \begin{table}[htb] \begin{center} \begin{tabular}{l l c c c} @@ -920,8 +915,8 @@ Table~\ref{tab:si16p_ncapture_cal}. To check the origin of the protons recorded, lifetime measurements were made by cutting on time difference between a hit on one thick silicon and the muon hit. Applying the time cut in 0.5~\si{\micro\second}\ time steps on the proton -events in Figure~\ref{fig:si16p_proton_after_ecut}, the number of surviving -protons on each arm are plotted on Figure~\ref{fig:si16p_proton_lifetime}. The +events in \cref{fig:si16p_proton_after_ecut}, the number of surviving +protons on each arm are plotted on \cref{fig:si16p_proton_lifetime}. The curves show decay constants of $762.9 \pm 13.7$~\si{\nano\second}\ and $754.6 \pm 11.9$, which are consistent with the each other, and with mean life time of muons in @@ -939,7 +934,7 @@ The fits are consistent with lifetime of muons in silicon in from after 500~ns, before that, the time constants are shorter ($655.9\pm 9.9$ and $731.1\pm8.9$) indicates the contamination from muon captured on material with higher $Z$. Therefore a timing cut from 500~ns is used to select good silicon events, the -remaining protons are shown in Figure~\ref{fig:si16p_proton_ecut_500nstcut}. +remaining protons are shown in \cref{fig:si16p_proton_ecut_500nstcut}. The spectra have a low energy cut off at 2.5~MeV because protons with energy lower than that could not pass through the thin silicon to make the cuts as the range of 2.5~MeV protons in silicon is about 68~\si{\micro\meter}. @@ -954,7 +949,7 @@ range of 2.5~MeV protons in silicon is about 68~\si{\micro\meter}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Proton emission rate from the silicon target} \label{sub:proton_emission_rate_from_the_silicon_target} -The number of protons in Figure~\ref{fig:si16p_proton_ecut_500nstcut} is +The number of protons in \cref{fig:si16p_proton_ecut_500nstcut} is counted from 500~ns after the muon event, where the survival rate is $e^{-500/758} = 0.517$. @@ -974,7 +969,7 @@ The emission rate per muon capture is: &= \dfrac{2.625 \times 10^5}{6.256\times10^6} \nonumber\\ &= 4.20\times10^{-2}\nonumber \end{align} -The proton spectra on the Figure~\ref{fig:si16p_proton_ecut_500nstcut} and the +The proton spectra on the \cref{fig:si16p_proton_ecut_500nstcut} and the emission rate are only effective ones, since the energy of protons are modified by energy loss in the target, and low energy protons could not escape the target. Therefore further corrections are needed for both rate and spectrum of @@ -989,11 +984,11 @@ The uncertainty of the emission rate could come from several sources: background under the X-ray peak (5.5\%) and the efficiency calibration \item number of protons: efficiency of the cuts in energy, impacts of the timing resolution on timing cut. The energy cuts' contribution should be - small since it can be seen from Figure~\ref{fig:si16p_loge+logde}, the peak + small since it can be seen from \cref{fig:si16p_loge+logde}, the peak of protons is strong and well separated from others. The uncertainty in timing contribution is significant because all the timing done in this analysis was on the peak of the slow signals. As it is clear from the - Figure~\ref{fig:tme_sir_prompt_rational}, the timing resolution of the + \cref{fig:tme_sir_prompt_rational}, the timing resolution of the silicon detector could not be better than 100~ns. Putting $\pm100$~ns into the timing cut could change the survival rate of proton by about $1-e^{-100/758} \simeq 13\%$. Also, the low statistics contributes a few @@ -1024,7 +1019,7 @@ By using only the lower limit on $\ln(\textrm{E}) + 0.85\times\ln(\Delta \textrm{E})$, the heavy charged particles can be selected. These particles also show a lifetime that is consistent with that of muons in silicon -(Figure~\ref{fig:si16p_allparticle_lifetime}). +(\cref{fig:si16p_allparticle_lifetime}). \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/si16p_allparticle_lifetime} @@ -1041,7 +1036,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\subsection{Rate and spectrum correction} %\label{sub:proton_spectrum_deconvolution} -%The proton spectra on the Figure~\ref{fig:si16p_proton_ecut_500nstcut} and the +%The proton spectra on the \cref{fig:si16p_proton_ecut_500nstcut} and the %emission rate are only effective ones, since the energy of protons are modified %by energy loss in the target, and low energy protons could not escape the %target. Therefore corrections are needed for both rate and spectrum of protons. @@ -1054,7 +1049,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927 %The initial spatial distribution of protons is inferred from the muon beam %momentum using Monte Carlo simulation, and available measured data in momentum %scanning runs. The response function for this thin silicon target is shown in -%Figure~\ref{fig:si16p_toyMC}. +%\cref{fig:si16p_toyMC}. %\begin{figure}[htb] %\centering %\includegraphics[width=0.85\textwidth]{figs/si16p_toyMC} @@ -1069,7 +1064,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927 %The Bayesian method is chosen because it tends to be fast, typical number of %iterations is from 4--8. -%Figure~\ref{fig:si16p_unfold_train} presented results of two tests unfolding with +%\cref{fig:si16p_unfold_train} presented results of two tests unfolding with %two distributions of initial energy, a Gaussian distribution and %a parameterized function in~\eqref{eqn:EH_pdf}. The numbers of protons obtained %from the tests show agreement with the generated numbers. @@ -1084,8 +1079,8 @@ The ratio between the number of protons and other particles at 500~ns is $(1927 %\end{figure} %Finally, the unfolding is applied on the spectra in -%Figure~\ref{si16p_proton_spec}, the results are shown in -%Figure~\ref{si16p_unfold_meas}. +%\cref{si16p_proton_spec}, the results are shown in +%\cref{si16p_unfold_meas}. %\begin{figure}[htb] %\centering %\includegraphics[width=0.85\textwidth]{figs/si16p_unfold_meas} @@ -1127,7 +1122,7 @@ passive silicon runs were applied. \subsection{The number of stopped muons} \label{sub:the_number_of_stopped_muons} The X-ray spectrum on the germanium detector is shown on -Figure~\ref{fig:al100_ge_spec}. +\cref{fig:al100_ge_spec}. \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/al100_ge_spec} @@ -1153,7 +1148,7 @@ target are: \label{sub:particle_identification} Using the same charged particle selection procedure and the cuts on $\ln(\textrm{E})$ and $\ln(\Delta\textrm{E})$, the -proton energy spectrum is shown in Figure~\ref{fig:al100_proton_spec}. +proton energy spectrum is shown in \cref{fig:al100_proton_spec}. \begin{figure}[htb] \centering \includegraphics[width=1\textwidth]{figs/al100_selection} @@ -1163,13 +1158,13 @@ proton energy spectrum is shown in Figure~\ref{fig:al100_proton_spec}. \end{figure} The lifetime of these protons are shown in -Figure~\ref{fig:al100_proton_lifetime}, the fitted decay constant on the right +\cref{fig:al100_proton_lifetime}, the fitted decay constant on the right arm is consistent with the reference value of $864 \pm 2$~\si{\nano\second}~\cite{}. But the left arm gives $918 \pm 16.1$~\si{\nano\second}, significantly larger than the reference value. %The longer lifetime suggested some contributions from %other lighter materials, one possible source is from muons captured on the back -%side of the collimator (Figure~\ref{fig:alcap_setup_detailed}). +%side of the collimator (\cref{fig:alcap_setup_detailed}). %For this reason, the emission rate calculated from the left arm will be taken as upper %limit only. \begin{figure}[htb] @@ -1185,7 +1180,7 @@ and the decay constant on the SiL1-1 alone was nearly about 1000~\si{\micro\seco The reason for this behaviour is not known yet. For this emission rate calculation, this channel is discarded and the rate on the left arm is scaled with a factor of 4/3. The proton spectrum from the aluminium target is plotted -on Figure~\ref{fig:al100_proton_spec_wosil11}. +on \cref{fig:al100_proton_spec_wosil11}. \begin{figure}[htb] \centering diff --git a/thesis/mythesis.sty b/thesis/mythesis.sty index 8cdf67c..c112464 100644 --- a/thesis/mythesis.sty +++ b/thesis/mythesis.sty @@ -52,11 +52,11 @@ bookmarks \RequirePackage{verbatim} \RequirePackage{lipsum} \RequirePackage{datatool} -\RequirePackage[capitalise]{cleveref} \RequirePackage[final]{listings} \RequirePackage{xfrac} %% Units \RequirePackage[]{siunitx} +\RequirePackage{hepnames} %% Various fonts ... %\RequirePackage[T1]{fontenc} %\RequirePackage{charter} @@ -76,6 +76,8 @@ bookmarks %\linespread{1.025} % Palatino leads a little more leading %\usepackage[small]{eulervm} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \RequirePackage{tabularx} \RequirePackage{color} \RequirePackage{pifont} @@ -270,3 +272,6 @@ bookmarks \endgroup% } \renewcommand{\maketitle}[1]{\titlepage{}} + +%% Cleveref should be the last package to not be messed up by others +\RequirePackage[noabbrev]{cleveref} diff --git a/thesis/thesis.tex b/thesis/thesis.tex index 355ddc5..d99899a 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -33,8 +33,8 @@ for the COMET experiment} %\input{chapters/chap2_mu_e_conv} %\input{chapters/chap3_comet} %\input{chapters/chap4_alcap_phys} -%\input{chapters/chap5_alcap_setup} -\input{chapters/chap6_analysis} +\input{chapters/chap5_alcap_setup} +%\input{chapters/chap6_analysis} %\input{chapters/chap7_results} \begin{backmatter} From 36ae84607f55cf06763fec4c122672e9de42b366 Mon Sep 17 00:00:00 2001 From: nam Date: Fri, 12 Sep 2014 19:17:32 +0900 Subject: [PATCH 02/26] prog saved --- thesis/Makefile | 2 +- thesis/chapters/chap5_alcap_setup.tex | 249 +++++++++++++++++ thesis/chapters/chap6_analysis.tex | 373 +++++++------------------- thesis/mythesis.sty | 5 +- thesis/thesis.tex | 6 +- 5 files changed, 357 insertions(+), 278 deletions(-) diff --git a/thesis/Makefile b/thesis/Makefile index ce15a60..9bd3694 100644 --- a/thesis/Makefile +++ b/thesis/Makefile @@ -5,7 +5,7 @@ TARGET= $(DOCNAME).pdf default: $(TARGET) -$(TARGET): $(INPUT) Makefile chapters/*.tex custom_macro.tex mythesis.sty +$(TARGET): $(INPUT) Makefile chapters/*.tex custom_macro.tex mythesis.sty raw/* @rm -f $(DOCNAME).{aux,toc,lof,lot} pdflatex $< && bibtex $(DOCNAME) && pdflatex $< && pdflatex $< diff --git a/thesis/chapters/chap5_alcap_setup.tex b/thesis/chapters/chap5_alcap_setup.tex index 5672daa..481bb34 100644 --- a/thesis/chapters/chap5_alcap_setup.tex +++ b/thesis/chapters/chap5_alcap_setup.tex @@ -289,6 +289,7 @@ carried out. % subsection plastic_scintillators (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Front-end electronics and data acquisition system} The front-end electronics of the AlCap experiment was simple since we employed a trigger-less read out system with waveform digitisers and flash ADCs @@ -413,6 +414,254 @@ automatically starts a new run with the same parameters after about 6 seconds. The short period of each run also allows the detection, and helps to reduce the influence of effects such as electronics drifting, temperature fluctuation. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Detector calibration} +\label{sec:detector_calibration} +The calibration was done mainly for the silicon and germanium detectors +because they would provide energy information. The plastic scintillators were +only checked by oscilloscopes to make sure that the minimum ionisation +particles (MIPs) could be observed. The upstream plastic scintillation +counters and wire chamber, as mentioned, were well-tuned by the MuSun group. + +\subsection{Silicon detector} +\label{sub:silicon_detector} +The energy calibration for the silicon detectors were done routinely during the +run, by: +\begin{itemize} + \item a \SI{79.5}{\becquerel} $^{241}\textrm{Am}$ alpha source. The most + prominent alpha particles have energies of \SI{5.484}{\si{\MeV}} (85.2\%) + and \SI{5.442}{\si{\MeV}} (12.5\%). The alpha particles from the source + would lose about \SI{66}{\kilo\eV} in the \SI{0.5}{\um}-thick dead layer, + and the peak would appear at \SI{5418}{\kilo\eV} (\cref{fig:toyMC_alpha}); + + \item and a tail pulse generator, A tail pulse with amplitude of + \SI{66}{\milli\volt}~was used to simulate the response of the silicon + detectors' preamplifiers to a particle with \SI{1}{\MeV} energy deposition; + + \item During data taking period, electrons in the beam were were also used + for energy calibration of thick silicon detectors where energy deposition + is large enough. The muons at different momenta provided another mean of + calibration in the beam tuning period. +\end{itemize} + +\begin{figure}[htb] + \centering + \includegraphics[width=0.6\textwidth]{figs/toyMC_alpha} + \caption{Energy loss of the alpha particles after a dead layer of + \SI{0.5}{\um}.} + \label{fig:toyMC_alpha} +\end{figure} + +The calibration coefficients for the silicon channels are listed in +\cref{tab:cal_coeff}. + +\begin{table} + \begin{center} + \pgfplotstabletypeset[ + % separator + col sep=comma, + % columns displayed + display columns/0/.style={column name = \textbf{Detector}, string type, + column type=l}, + display columns/1/.style={column name = \textbf{Slope}, column type=c, + dec sep align}, + display columns/2/.style={column name = \textbf{Offset}, column type=r, + dec sep align}, + % format the line breaks + every head row/.style={ + before row={\toprule}, + after row={\midrule}, + columns/Detector/.style={column type=c}, + columns/Slope/.style={column type=c}, + columns/Offset/.style={column type=c} + }, + every last row/.style={after row=\bottomrule}, + ]{raw/si_cal_effs.csv} + \caption{Calibration coefficients of the silicon detector channels} + \label{tab:cal_coeff} + \end{center} +\end{table} +% subsection silicon_detector (end) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Germanium detector} +\label{sub:germanium_detector} +The germanium detector was calibrated using a $^{152}\textrm{Eu}$ +source +\footnote{Energies and intensities of gamma rays are taken from the + X-ray and Gamma-ray Decay Data Standards for Detector Calibration and Other + Applications, which is published by IAEA at \\ + \url{https://www-nds.iaea.org/xgamma_standards/}}, +the recorded pulse height spectrum is shown in \cref{fig:ge_eu152_spec}. The +source was placed at the target position so that the absolute efficiencies can +be calculated. The peak centroids and areas were obtained by fitting a Gaussian +peak on top of a first-order polynomial background. The only exception is the +\SI{1085.84}{\keV} line because of the interference of \SI{1089.74}{\keV}, +the two were fitted with two Gaussian peaks on top of a first-order +polynomial background. + +The relation between pulse height in ADC value and energy is found to be: +\begin{equation} + \textrm{ E [keV]} = 0.1219 \times \textrm{ADC} + 1.1621 +\end{equation} +The energy resolution (full width at half maximum - FWHM) was better than +2.6~\si{\keV}\ for all the $^{152}\textrm{Eu}$ peaks. It was +a little worse at 3.1~\si{\keV}~for the annihilation photons at +511.0~\si{\keV}. + +\begin{figure}[htb] + \centering + \includegraphics[width=0.70\textwidth]{figs/ge_eu152_spec} + \caption{Energy spectrum of the $\rm^{152}\textrm{Eu}$ calibration source + recorded by the germanium detector. The most prominent peaks of + $^{152}\textrm{Eu}$ along with their energies are + annotated in red; the 1460.82 \si{\keV}~line is background from + $^{40}\textrm{K}$; and the annihilation 511.0~\si{\keV}~photons + come both from the source and the surrounding environment.} + \label{fig:ge_eu152_spec} +\end{figure} + +\begin{figure}[htb] + \centering + \includegraphics[width=0.89\textwidth]{figs/ge_ecal_fwhm} + \caption{Germanium energy calibration and resolution.} + \label{fig:ge_fwhm} +\end{figure} + +The absolute efficiencies of the referenced points, and calculated +efficiencies at the X-ray of interest are presented in +\cref{tab:xray_eff}. +%The absolute efficiencies for the $(2p-1s)$ lines of aluminium +%(\SI{346.828}{\keV}) and silicon (\SI{400.177}{\keV}) +%are presented in \cref{tab:xray_eff}. +In the process of efficiency calibration, +corrections for true coincidence summing and self-absorption were not applied. +The true coincidence summing probability is estimated to be very +small, about \num{5.4d-6}, thanks to the far geometry of the calibration. The +absorption in the source cover made of \SI{22}{\mg\per\cm^2} +polyethylene is less than \num{4d-4} for a \SI{100}{\keV} photon. + +A Monte Carlo (MC) study on the acceptance of the germanium detector with two +purposes: +\begin{enumerate} + \item compare between measured and MC efficiencies: a point source made of + $^152$Eu is placed at the target position + \item estimate the uncertainty due to finite-size geometry: the source is + made of silicon with the same dimensions as those of the thick silicon + detector, namely \SI[product-units=power]{1.5 x 50 x 50}{\mm}; then the + primary vertex of $^152$Eu is generated inside the source. +\end{enumerate} + +\begin{table}[htb] + \begin{center} + \pgfplotstabletypeset[ + % separator + col sep=comma, + % columns displayed + % column type={S} means leave formatting to siunitx + display columns/0/.style={column name = \textbf{Photons (\si{\keV})}, + string type, + column type={S[table-format=4.3, table-alignment=center]}}, + display columns/1/.style={column name = \textbf{Efficiency}, + string type, + column type={S[parse-numbers = true, + round-precision=3, + round-mode=figures, + fixed-exponent=-4, + scientific-notation=fixed, + table-format=1.2e-1, + %table-omit-exponent, + ]}}, + display columns/2/.style={column name = \textbf{Uncertainty}, + string type, + column type={S[parse-numbers = true, + round-precision=3, + round-mode=figures, + fixed-exponent=-5, + scientific-notation=fixed, + table-format=1.3e-1, + %table-omit-exponent, + ]}}, + % format the line breaks + every head row/.style={ + before row={\toprule}, + after row={ + %\textbf{\si{\keV}} & \textbf{\num{E-4}} & \textbf{\num{E-4}}\\ + \midrule}, + columns/0/.style={column type=r}, + columns/1/.style={column type=c}, + columns/2/.style={column type=c} + }, + every last row/.style={after row=\bottomrule}, + every nth row={8}{before row={\midrule}}, + ]{raw/ge_eff.csv} + \end{center} + \caption{Absolute efficiencies of the germanium detector in case of + a point-like source placed at the centre of the target (upper half), and + the calculated efficiencies for the X-rays of interest (lower half).} + \label{tab:xray_eff} +\end{table} + +\begin{figure}[htb] + \centering + \includegraphics[width=0.40\textwidth]{figs/ge_eff_cal} + \includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root} + \caption{Absolute efficiency of the germanium detector, the fit was done with + 7 energy points from 244~keV, the shaded area is + 95\% confidence interval of the fit.} + %because it is known that the linearity between + %$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better. + \label{fig:ge_eff_cal} +\end{figure} + +% subsection germanium_detector (end) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\subsection{Beam tuning and muon momentum scanning} +%\label{sub:muon_momentum_scanning} +%Before taking any data, we carried out the muon momentum scanning to understand +%the muon beam, as well as calibrate the detector system. The nominal muon +%momentum used in the Run 2013 had been tuned to 28~MeV\cc\ before the run. By +%changing simultaneously the strength of the key magnet elements in the $\pi$E1 +%beam line with the same factor, the muon beam momentum would be scaled with the +%same factor. + +%The first study was on the range of muons in an active silicon target. The SiL2 +%detector was placed perpendicular to the nominal beam path, after an oval +%collimator. The beam momentum scaling factor was scanned from 1.10 to 1.60, +%muon momenta and energies in the measured points are listed in +%\cref{tab:mu_scales}. +%\begin{table}[htbp] + %\begin{center} + %\begin{tabular}{c c c c} + %\toprule + %\textbf{Scaling} & \textbf{Momentum} & \textbf{Kinetic energy} + %& \textbf{Momentum spread}\\ + %\textbf{factor} & \textbf{(MeV\per\cc)} & \textbf{(MeV)} + %& \textbf{(MeV\per\cc, 3\% FWHM)}\\ + %\midrule + %1.03 & 28.84 & 3.87& 0.87\\ + %1.05 & 29.40 & 4.01& 0.88\\ + %1.06 & 29.68 & 4.09& 0.89\\ + %1.07 & 29.96 & 4.17& 0.90\\ + %1.10 & 30.80 & 4.40& 0.92\\ + %1.15 & 32.20 & 4.80& 0.97\\ + %1.20 & 33.60 & 5.21& 1.01\\ + %1.30 & 36.40 & 6.09& 1.09\\ + %1.40 & 39.20 & 7.04& 1.18\\ + %1.43 & 40.04 & 7.33& 1.20\\ + %1.45 & 40.60 & 7.53& 1.22\\ + %1.47 & 41.16 & 7.73& 1.23\\ + %1.50 & 42.00 & 8.04& 1.26\\ + %\bottomrule + %\end{tabular} + %\end{center} + %\caption{Muon beam scaling factors, energies and momenta.} + %\label{tab:mu_scales} +%\end{table} + +% subsection muon_momentum_scanning (end) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% section detector_calibration (end) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Data sets and statistics} \label{sec:data_sets} diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index cc50dfe..6585976 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -37,9 +37,8 @@ for pulse information calculation is in use. The module looks for the sample that has the maximal deviation from the baseline, takes the deviation as pulse amplitude and the time stamp of the sample as pulse time. The procedure is -illustrated on \cref{fig:tap_maxbin_algo}. This module could not detect -pile up or double pulses in one \tpulseisland{} in -\cref{fig:tap_maxbin_bad}. +illustrated on \cref{fig:tap_maxbin_algo}. This module could not account for +pile-up or double pulses in one \tpulseisland{} in \cref{fig:tap_maxbin_bad}. \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/tap_maxbin_algo} @@ -57,12 +56,12 @@ pile up or double pulses in one \tpulseisland{} in The TSimpleMuonEvent first picks a muon candidate, then loops through all pulses on all detector channels, and picks all pulses occur in -a time window of \SI{\pm 10}{\si{\micro\second}} around each candidate to build +a time window of \SI{\pm 10}{\si{\us}} around each candidate to build a muon event. A muon candidates is a hit on the upstream plastic scintillator -with an amplitude higher than a threshold which was chosen to reject minimum -ionising particles (MIPs). The period of \SI{10}{\si{\micro\second}} is long -enough compares to the mean life time of muons in the target materials -(\SI{0.758}{\si{\micro\second}} for silicon, and \SI{0.864}{\si{\micro\second}} +with an amplitude higher than a threshold which was chosen to reject MIPs. The +period of \SI{10}{\si{\us}} is long enough compares to the mean life time of +muons in the target materials +(\SI{0.758}{\si{\us}} for silicon, and \SI{0.864}{\si{\us}} for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted charged particles would be recorded in this time window. %\begin{figure}[htb] @@ -73,13 +72,13 @@ charged particles would be recorded in this time window. %\end{figure} A pile-up protection mechanism is employed to reject multiple muons events: if -there exists another muon hit in less than \SI{15}{\si{\micro\second}} from the +there exists another muon hit in less than \SI{15}{\si{\us}} from the candidate then both the candidate and the other muon are discarded. This pile-up protection would cut out less than 11\% total number of events because the beam rate was generally less than \SI{8}{\kilo\hertz}. %In runs with active silicon targets, another requirement is applied for the -%candidate: a prompt hit on the target in $\pm 200$ \si{\nano\second}\ around the +%candidate: a prompt hit on the target in $\pm 200$ \si{\ns}\ around the %time of the $\mu$Sc pulse. The number comes from the observation of the %time correlation between hits on the target and the $\mu$Sc %(\cref{fig:tme_sir_prompt_rational}). @@ -112,193 +111,13 @@ shown in \cref{fig:lldq}. \end{figure} % section analysis_modules (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Detector calibration} -\label{sec:detector_calibration} - -\subsection{Silicon detector} -\label{sub:silicon_detector} -The energy calibration for the silicon detectors were done routinely during the -run, mainly by an -$^{241}\textrm{Am}$ alpha source and a tail pulse generator. The source emits -79.5 $\alpha$\si{\per\second} in a \SI{2\pi}{\steradian} solid angle. The most -prominent alpha particles have energies of \SI{5.484}{\si{\mega\electronvolt}} -(85.2\%) and \SI{5.442}{\si{\mega\electronvolt}} (12.5\%). A tail pulse with -amplitude of -\SI{66}{\milli\volt}~was used to simulate the response of the silicon detectors' -preamplifiers to a particle with \SI{1}{\si{\mega\electronvolt}} energy deposition. - -During data taking period, electrons in the beam were were also used for energy -calibration of thick silicon detectors where energy deposition is large enough. -The muons at different momenta provided another mean of calibration in the beam -tuning period. - -The alpha particles from the source would deposit -about 66~keV in the \SI{0.5}{\micro\meter}-thick dead layer, and the peak would -appear at 5418~keV (\cref{fig:toyMC_alpha}). -\begin{figure}[htb] - \centering - \includegraphics[width=0.6\textwidth]{figs/toyMC_alpha} - \caption{Energy loss of the alpha particles after a dead layer of - 0.5~\si{\micro\meter}.} - \label{fig:toyMC_alpha} -\end{figure} - -The calibration coefficients for the silicon channels are listed in -\cref{tab:cal_coeff}. -\begin{table}[htb] - \begin{center} - \begin{tabular}{l c r} - \toprule - \textbf{Detector} & \textbf{Slope} & \textbf{Offset}\\ - \midrule - SiL-2 & 7.86 & 14.14\\ - SiR-2 & 7.96 & 22.98\\ - \midrule - SiL1-1 & 2.61 & 37.34\\ - SiL1-2 & 2.54 & -20.78\\ - SiL1-3 & 2.65 & 67.75\\ - SiL1-4 & 2.54 & -18.45\\ - \midrule - SiR1-1 & 2.53 & 28.69\\ - SiR1-2 & 2.62 & 47.10\\ - SiR1-3 & 2.49 & 6.32\\ - SiR1-4 & 2.53 & 34.81\\ - \bottomrule - \end{tabular} - \end{center} - \caption{Calibration coefficients of the silicon detector channels} - \label{tab:cal_coeff} -\end{table} -% subsection silicon_detector (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Germanium detector} -\label{sub:germanium_detector} -The germanium detector was calibrated using a $^{152}\textrm{Eu}$ -source\footnote{Energies and intensities of gamma rays are taken from the - X-ray and Gamma-ray Decay Data Standards for Detector Calibration and Other - Applications, which is published by IAEA at \\ - \url{https://www-nds.iaea.org/xgamma_standards/}}, the -recorded pulse height spectrum is shown in \cref{fig:ge_eu152_spec}. The -source was placed at the target position so that the absolute efficiencies can -be calibrated. The relation between pulse height in ADC count and energy is -found to be: -\begin{equation} - \textrm{ E [keV]} = 0.1219 \times \textrm{ADC} + 1.1621 -\end{equation} -The energy resolution (full width at half maximum) was better than -2.6~\si{\kilo\electronvolt}\ for all the $^{152}\textrm{Eu}$ peaks. It was a little -worse at 3.1~\si{\kilo\electronvolt}~for the annihilation photons at -511.0~\si{\kilo\electronvolt}. - -The absolute efficiencies for the $(2p-1s)$ lines of aluminium -(346.828~\si{\kilo\electronvolt}) and silicon (400.177~\si{\kilo\electronvolt}) are -presented in \cref{tab:xray_eff}. In the process of efficiency calibration, -corrections for true coincidence summing and self-absorption were not applied. -The true coincidence summing probability is estimated to be very -small, about \sn{5.4}{-6}, thanks to the far geometry of the calibration. The -absorption in the source cover made of 22~\si{\milli\gram\per\si{\centi\meter}^2} -polyethylene is less than \sn{4}{-4} for a 100~\si{\kilo\electronvolt}\ photon. - -\begin{table}[htb] - \begin{center} - \begin{tabular}{c c c} - \toprule - \textbf{X-ray} & \textbf{Efficiency} & \textbf{Uncertainty}\\ - \midrule - 346.828 & $5.12 \times 10^{-4}$ & $0.14\times 10^{-4}$\\ - 400.177 & $4.54 \times 10^{-4}$ & $0.11\times 10^{-4}$\\ - \bottomrule - \end{tabular} - \end{center} - \caption{Calculated efficiencies at X-rays of interest} - \label{tab:xray_eff} -\end{table} - -\begin{figure}[htb] - \centering - \includegraphics[width=0.70\textwidth]{figs/ge_eu152_spec} - \caption{Energy spectrum of the $\rm^{152}\textrm{Eu}$ calibration source - recorded by the germanium detector. The most prominent peaks of - $^{152}\textrm{Eu}$ along with their energies are - annotated in red; the 1460.82 \si{\kilo\electronvolt}~line is background from - $^{40}\textrm{K}$; and the annihilation 511.0~\si{\kilo\electronvolt}~photons - come both from the source and the surrounding environment.} - \label{fig:ge_eu152_spec} -\end{figure} - -\begin{figure}[htb] - \centering - \includegraphics[width=0.89\textwidth]{figs/ge_ecal_fwhm} - \caption{Germanium energy calibration and resolution.} - \label{fig:ge_fwhm} -\end{figure} - -\begin{figure}[htb] - \centering - \includegraphics[width=0.80\textwidth]{figs/ge_ecal_eff} - \caption{Absolute efficiency of the germanium detector, the fit was done with - 7 energy points from 244~keV because it is known that the linearity between - $ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better. The shaded area is - 95\% confidence interval of the fit.} - \label{fig:ge_eff} -\end{figure} - -% subsection germanium_detector (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\subsection{Beam tuning and muon momentum scanning} -%\label{sub:muon_momentum_scanning} -%Before taking any data, we carried out the muon momentum scanning to understand -%the muon beam, as well as calibrate the detector system. The nominal muon -%momentum used in the Run 2013 had been tuned to 28~MeV\cc\ before the run. By -%changing simultaneously the strength of the key magnet elements in the $\pi$E1 -%beam line with the same factor, the muon beam momentum would be scaled with the -%same factor. - -%The first study was on the range of muons in an active silicon target. The SiL2 -%detector was placed perpendicular to the nominal beam path, after an oval -%collimator. The beam momentum scaling factor was scanned from 1.10 to 1.60, -%muon momenta and energies in the measured points are listed in -%\cref{tab:mu_scales}. -%\begin{table}[htbp] - %\begin{center} - %\begin{tabular}{c c c c} - %\toprule - %\textbf{Scaling} & \textbf{Momentum} & \textbf{Kinetic energy} - %& \textbf{Momentum spread}\\ - %\textbf{factor} & \textbf{(MeV\per\cc)} & \textbf{(MeV)} - %& \textbf{(MeV\per\cc, 3\% FWHM)}\\ - %\midrule - %1.03 & 28.84 & 3.87& 0.87\\ - %1.05 & 29.40 & 4.01& 0.88\\ - %1.06 & 29.68 & 4.09& 0.89\\ - %1.07 & 29.96 & 4.17& 0.90\\ - %1.10 & 30.80 & 4.40& 0.92\\ - %1.15 & 32.20 & 4.80& 0.97\\ - %1.20 & 33.60 & 5.21& 1.01\\ - %1.30 & 36.40 & 6.09& 1.09\\ - %1.40 & 39.20 & 7.04& 1.18\\ - %1.43 & 40.04 & 7.33& 1.20\\ - %1.45 & 40.60 & 7.53& 1.22\\ - %1.47 & 41.16 & 7.73& 1.23\\ - %1.50 & 42.00 & 8.04& 1.26\\ - %\bottomrule - %\end{tabular} - %\end{center} - %\caption{Muon beam scaling factors, energies and momenta.} - %\label{tab:mu_scales} -%\end{table} - -% subsection muon_momentum_scanning (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% section detector_calibration (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Charged particles following muon capture on a thick silicon target} \label{sec:charged_particles_from_muon_capture_on_silicon_thick_silicon} -This analysis was done on a subset of the active target runs 2119 -- 2140 -because of the problem of wrong clock frequency found in the data quality -checking shown in \cref{fig:lldq}. The data set contains \sn{6.43}{7} -muon events. -%64293720 +This analysis was done on a subset of the active target runs +\numrange{2119}{2140} because of the problem of wrong clock frequency found in +the data quality checking shown in \cref{fig:lldq}. The data set contains +%\num[fixed-exponent=2, scientific-notation = fixed]{6.4293720E7} muon events. +\num{6.43E7} muon events. Firstly, the number of charged particles emitted after nuclear muon capture on the active target is calculated. This number then is normalised to the number @@ -309,15 +128,15 @@ compared with that from the literature. \label{sub:event_selection} Because of the active target, a stopped muon would cause two coincident hits on the muon counter and the target. The energy of the muon hit on the active -target is also well-defined as a narrow momentum spread beam was used. The +target is also well-defined as the narrow-momentum-spread beam was used. The correlation between the energy and timing of all the hits on the active target is shown in \cref{fig:sir2f_Et_corr}. The most intense spot at zero time and about 5 MeV energy corresponds to stopped muons in the thick target. The band below 1 MeV is due to electrons, either in the beam or from muon decay in orbits, or emitted during the cascading of muon to the muonic 1S state. The valley between time zero and 1200~ns shows the minimum distance in time between -two pulses. It is the limitation of the current pulse parameter extraction -method where no pile up or double pulses is accounted for. +two pulses. It is the mentioned limitation of the current pulse parameter +extraction method where no pile up or double pulses is accounted for. \begin{figure}[htb] \centering @@ -352,12 +171,12 @@ From the energy-timing correlation above, the cuts to select stopped muons are: and the first hit on the silicon active target is in coincidence with that muon counter hit: \begin{equation} - \lvert t_{\textrm{target}} - t_{\mu\textrm{ counter}}\rvert<50\textrm{ ns} + \lvert t_{\textrm{target}} - t_{\mu\textrm{ counter}}\rvert \le \SI{50}{\ns} \label{eqn:sir2_prompt_cut} \end{equation} \item the first hit on the target has energy of that of the muons: \begin{equation} - 3.4 \textrm{ MeV} Date: Fri, 12 Sep 2014 19:17:57 +0900 Subject: [PATCH 03/26] add figs --- .../figs/ge_eff_mc_finitesize_vs_pointlike.png | Bin 0 -> 105017 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 thesis/figs/ge_eff_mc_finitesize_vs_pointlike.png diff --git 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At the beginning of each block, the time counter in each digitiser is reset to ensure time alignment across all modules. The period of 110~ms was chosen to be: -{\em i} long enough compares to the time scale of several \si{\micro\second}\ of the -physics of interest, {\em ii} short enough so that there is no timer rollover -on any digitiser (a FADC runs at its maximum speed of \SI{170}{\mega\hertz} could -handle up to about \SI{1.5}{\second} with its 28-bit time counter). +{\em i} long enough compared to the time scale of several \si{\micro\second}\ +of the physics of interest, {\em ii} short enough so that there is no timer +rollover on any digitiser (a FADC runs at its maximum speed of +\SI{170}{\mega\hertz} could handle up to about \SI{1.5}{\second} with its +28-bit time counter). To ease the task of handling data, the data collecting period was divided into short runs, each run stopped when the logger had recorded 2 GB of data. @@ -495,8 +496,8 @@ the recorded pulse height spectrum is shown in \cref{fig:ge_eu152_spec}. The source was placed at the target position so that the absolute efficiencies can be calculated. The peak centroids and areas were obtained by fitting a Gaussian peak on top of a first-order polynomial background. The only exception is the -\SI{1085.84}{\keV} line because of the interference of \SI{1089.74}{\keV}, -the two were fitted with two Gaussian peaks on top of a first-order +\SI{1085.84}{\keV} line because of the interference of the \SI{1089.74}{\keV} +gamma, the two were fitted with two Gaussian peaks on top of a first-order polynomial background. The relation between pulse height in ADC value and energy is found to be: @@ -527,30 +528,86 @@ a little worse at 3.1~\si{\keV}~for the annihilation photons at \label{fig:ge_fwhm} \end{figure} -The absolute efficiencies of the referenced points, and calculated -efficiencies at the X-ray of interest are presented in -\cref{tab:xray_eff}. -%The absolute efficiencies for the $(2p-1s)$ lines of aluminium -%(\SI{346.828}{\keV}) and silicon (\SI{400.177}{\keV}) -%are presented in \cref{tab:xray_eff}. -In the process of efficiency calibration, -corrections for true coincidence summing and self-absorption were not applied. -The true coincidence summing probability is estimated to be very -small, about \num{5.4d-6}, thanks to the far geometry of the calibration. The -absorption in the source cover made of \SI{22}{\mg\per\cm^2} -polyethylene is less than \num{4d-4} for a \SI{100}{\keV} photon. - -A Monte Carlo (MC) study on the acceptance of the germanium detector with two -purposes: +Following corrections for the peak areas are considered: \begin{enumerate} - \item compare between measured and MC efficiencies: a point source made of - $^152$Eu is placed at the target position - \item estimate the uncertainty due to finite-size geometry: the source is - made of silicon with the same dimensions as those of the thick silicon - detector, namely \SI[product-units=power]{1.5 x 50 x 50}{\mm}; then the - primary vertex of $^152$Eu is generated inside the source. + \item Correction for counting loss due to finite response time of the + detector system, where two gamma rays arrive at the detector within a time + interval short compared to that response time. This correction is + significant in our germanium system because of the current pulse + information extracting method does not count the second pulse. + \item Correction of counting time loss in the reset periods of the transistor + reset preamplifier. A preamplifier of this type would reset itself after + accumulating a predetermined amount of charge. During a reset, the + preamplifier is insensitive so this can be counted as dead time. + \item True coincidence summing correction: two cascade gamma rays hit the + detector at the same time would cause loss of count under the two + respective peaks and gain under the sum energy peak. + \item Correction for self-absorption of a gamma ray by the source itself. \end{enumerate} +The corrections for the first two mechanisms can be estimated by examining +pulse length and intervals between two consecutive pulses in the germanium +detector (\cref{fig:ge_cal_rate_pulselength}). The average pulse +length is \SI{45.7}{\um}, the average count rate obtained from the decay rate +of the interval spectrum is \SI{240}{\per\s}. + +The correction factor for the finite response time of the detector system is +calculated as: +\begin{align} + k_{\textrm{finite response time}} &= e^{2\times \textrm{(pulse length)} + \times \textrm{(count rate)}}\\ + &= e^{2\times 47.5\times10^{-6} \times 241} \nonumber\\ + &= 1.02 \label{eqn:finite_time_response} +\end{align} + +The resets of the preamplifier show up as a peak around \SI{2}{\ms}, +consistent with specification of the manufacturer. Fitting the peak on top of +an exponential background gives the actual reset pulse length of +\SI{1947.34}{\us} and the number of resets during the calibration runs is +2335.0. The total time loss for resetting is hence: +$1947.34\times 10^{-6} \times 2335.0 = 4.55$ \si{\s}. That is a 0.14\% loss +for a measuring time of \SI{3245.5}{\s}. This percentage loss is insignificant +compared with the loss in \eqref{eqn:finite_time_response} and the statistical +uncertainty of peak areas so correction for amplifier resets is not applied. + +\begin{figure}[htb] + \centering + \includegraphics[width=0.95\textwidth]{figs/ge_cal_rate_pulselength} + \caption{Germanium detector pulse length (left) and intervals between pulses + on that detector (right). The peak around \SI{2}{\ms} corresponds to the + resets of the preamplifier. The peak at \SI{250}{\us} is due to triggering + by the timing channel which is on the same digitiser.} + \label{fig:ge_cal_rate_pulselength} +\end{figure} + +The true coincidence summing probability is estimated to be very small, about +\num{5.4d-6}, thanks to the far geometry of the calibration. The absorption in +the source cover made of \SI{22}{\mg\per\cm^2} polyethylene is less than +\num{4d-4} for a \SI{100}{\keV} photon. Therefore these two corrections are +omitted. + +The absolute efficiencies of the reference gamma rays show agreement with those +obtained from a Monte Carlo (MC) study where a point source made of $^{152}$Eu +is placed at the target position (see \cref{fig:ge_eff_cal}). A comparison +between efficiencies in case of the point-like source and a finite-size +source is also done by MC simulation. As shown in \cref{fig:ge_eff_cal}, the +differences are in line with the uncertainties of the measured efficiencies. +%The dimensions of the latter are set to +%resemble the distribution of muons inside the target: Gaussian spreading +%\SI{11}{\mm} vertically, \SI{13}{\mm} horizontally, and \SI{127}{\um} in +\begin{figure}[htb] + \centering + \includegraphics[width=0.40\textwidth]{figs/ge_eff_cal} + \includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root} + \caption{Absolute efficiency of the germanium detector, the fit was done with + 7 energy points from 244~keV, the shaded area is + 95\% confidence interval of the fit.} + %because it is known that the linearity between + %$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better. + \label{fig:ge_eff_cal} +\end{figure} +The absolute efficiencies of the referenced points, and calculated efficiencies +at X-rays of interest are listed in \cref{tab:xray_eff}. \begin{table}[htb] \begin{center} \pgfplotstabletypeset[ @@ -601,18 +658,6 @@ purposes: \label{tab:xray_eff} \end{table} -\begin{figure}[htb] - \centering - \includegraphics[width=0.40\textwidth]{figs/ge_eff_cal} - \includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root} - \caption{Absolute efficiency of the germanium detector, the fit was done with - 7 energy points from 244~keV, the shaded area is - 95\% confidence interval of the fit.} - %because it is known that the linearity between - %$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better. - \label{fig:ge_eff_cal} -\end{figure} - % subsection germanium_detector (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\subsection{Beam tuning and muon momentum scanning} @@ -684,12 +729,12 @@ different targets were carried out for silicon targets: As the emitted protons deposit a significant amount of energy in the target material, thin targets and thus excellent momentum resolution of the low energy -muon beam are critical. Aluminium targets of 50-\si{\micro\meter}\ and -100~\si{\micro\meter}\ thick were used. Although a beam with low momentum spread of -1\% is preferable, it was used for only a small portion of the run due to the -low beam rate (see \cref{fig:Rates}). The beam momentum for each target -was chosen to maximise the number of stopped muons. The collected data sets are -shown in \cref{tb:stat}. +muon beam are critical, aluminium targets of 50-\si{\micro\meter}\ and +100-\si{\micro\meter}\ thick were used. Although a beam with low momentum +spread of 1\% is preferable, it was used for only a small portion of the run +due to the low beam rate (see \cref{fig:Rates}). The beam momentum for each +target was chosen to maximise the number of stopped muons. The collected data +sets are shown in \cref{tb:stat}. \begin{table}[btp!] \begin{center} @@ -865,20 +910,8 @@ update the plots to reflect real-time status of the detector system. Some offline analysis modules has been developed during the beam time and could provide quick feedback in confirming and guiding the decisions at the time. For example, the X-ray spectrum analysis was done to confirm that we could observe -the muon capture process (\cref{fig:muX}), and to help in choosing optimal -momenta which maximised the number of stopped muons. -\begin{figure}[btp] - \centering - \includegraphics[width=0.7\textwidth]{figs/muX.png} - \caption{Germanium - detector spectra in the range of 300 - 450 keV with different setups: no - target, 62-\si{\micro\meter}-thick silicon target, and - 100-\si{\micro\meter}-thick aluminium target. The ($2p-1s$) lines from - aluminium (346.828 keV) and silicon (400.177 keV) are clearly visible, - the double peaks at 431 and 438 keV are from the lead shield, the peak at - 351~keV is a background gamma ray from $^{211}$Bi.} - \label{fig:muX} -\end{figure} +the muon capture process and to help in choosing optimal momenta which +maximised the number of stopped muons. Although the offline analyser is still not fully developed yet, several modules are ready. They are described in detailed in the next chapter. diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index 6585976..3568bd8 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -59,7 +59,7 @@ pulses on all detector channels, and picks all pulses occur in a time window of \SI{\pm 10}{\si{\us}} around each candidate to build a muon event. A muon candidates is a hit on the upstream plastic scintillator with an amplitude higher than a threshold which was chosen to reject MIPs. The -period of \SI{10}{\si{\us}} is long enough compares to the mean life time of +period of \SI{10}{\si{\us}} is long enough compared to the mean life time of muons in the target materials (\SI{0.758}{\si{\us}} for silicon, and \SI{0.864}{\si{\us}} for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted @@ -388,7 +388,7 @@ This number of X-rays needs to be corrected for following effects: &= 1.06 \end{align} The 2-ms-long reset pulses effectively reduce the actual measurement time - compares to other channels, so the correction factor for the effect is: + compared to other channels, so the correction factor for the effect is: \begin{align} k_{\textrm{reset pulse}} &= \frac{\textrm{(measurement time)}} {\textrm{(measurement time)} @@ -830,7 +830,7 @@ The uncertainty of the emission rate could come from several sources: collimator. In the worst case when the muon beam is flatly distributed, that displacement could change the acceptance of the silicon detectors by 12\%. Although no measurement was done to determine the efficiency of the - silicon detectors, it would have small effect compare to other factors. + silicon detectors, it would have small effect compared to other factors. \end{enumerate} The combined uncertainty from known sources above therefore could be as large diff --git a/thesis/thesis.bib b/thesis/thesis.bib index f4f825e..8fb2048 100644 --- a/thesis/thesis.bib +++ b/thesis/thesis.bib @@ -462,6 +462,23 @@ Timestamp = {2014-04-08} } +@Article{Bichsel.2006, + Title = {A method to improve tracking and particle identification in TPCs and silicon detectors}, + Author = {Bichsel, Hans}, + Journal = {Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment}, + Year = {2006}, + Number = {1}, + Pages = {154--197}, + Volume = {562}, + + __markedentry = {[NT:6]}, + Doi = {10.1016/j.nima.2006.03.009}, + File = {Published version:Bichsel.2006.pdf:PDF}, + Owner = {NT}, + Publisher = {Elsevier}, + Timestamp = {2014-09-16} +} + @Article{Bichsel.1988, Title = {{Straggling in Thin Silicon Detectors}}, Author = {Bichsel, H.}, @@ -1048,8 +1065,6 @@ Month = {Aug}, Pages = {741--757}, Volume = {36}, - - __markedentry = {[NT:]}, Doi = {10.1103/PhysRevC.36.741}, File = {Published version:GadioliGadioli.1987.pdf:PDF}, Issue = {2}, @@ -1812,6 +1827,7 @@ Month = {Mar}, Pages = {1106--1110}, Volume = {43}, + Doi = {10.1103/PhysRevC.43.1106}, File = {Published version:MartoffCummings.etal.1991.pdf:PDF}, Issue = {3}, @@ -2283,8 +2299,6 @@ Month = {Jan}, Pages = {135--141}, Volume = {19}, - - __markedentry = {[NT:]}, Doi = {10.1103/PhysRevC.19.135}, File = {Published version:SchlepuetzComiso.etal.1979.pdf:PDF}, Issue = {1}, @@ -2471,7 +2485,7 @@ Pages = {MOLT007}, Volume = {C0303241}, - __markedentry = {[NT:6]}, + __markedentry = {[NT:]}, Archiveprefix = {arXiv}, Eprint = {physics/0306116}, File = {arXiv v1:VerkerkeKirkby.2003-eprintv1.pdf:PDF}, diff --git a/thesis/thesis.tex b/thesis/thesis.tex index ad3439f..9aa2d7b 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -33,8 +33,8 @@ for the COMET experiment} %\input{chapters/chap2_mu_e_conv} %\input{chapters/chap3_comet} %\input{chapters/chap4_alcap_phys} -\input{chapters/chap5_alcap_setup} -%\input{chapters/chap6_analysis} +%\input{chapters/chap5_alcap_setup} +\input{chapters/chap6_analysis} %\input{chapters/chap7_results} \begin{backmatter} From 27ab5737ff45e8d043cd124d57fc96278e8e786c Mon Sep 17 00:00:00 2001 From: nam Date: Thu, 9 Oct 2014 18:13:21 +0900 Subject: [PATCH 05/26] prog saved --- thesis/chapters/chap6_analysis.tex | 149 +++++++++-------------------- thesis/mythesis.sty | 3 +- 2 files changed, 45 insertions(+), 107 deletions(-) diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index 3568bd8..83f20a7 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -91,9 +91,9 @@ the beam rate was generally less than \SI{8}{\kilo\hertz}. To make sure that we will analyse good data, a low level data quality checking was done on the whole data sets. The idea is plotting the variations of basic -parameters, such as noise level, length of \tpulseisland{}, \tpulseisland{} -rate, time correlation to hits on $\mu$Sc, \ldots on each channel during the -data collecting period. Runs with significant difference from the nominal +parameters, such as noise level, length of raw waveforms, pulse rate, time +correlation to hits on the muon counter on each channel during the data +collecting period. Runs with significant difference from the averaging values were further checked for possible causes, and would be discarded if such discrepancy was too large or unaccounted for. Examples of such trend plots are shown in \cref{fig:lldq}. @@ -120,9 +120,10 @@ the data quality checking shown in \cref{fig:lldq}. The data set contains \num{6.43E7} muon events. Firstly, the number of charged particles emitted after nuclear muon capture on -the active target is calculated. This number then is normalised to the number -of nuclear muon capture to obtain an emission rate. Finally, the rate is -compared with that from the literature. +the active target is calculated. The charged particles yield then is normalised +to the number of nuclear muon capture to obtain an emission rate. +%Finally, the +%rate is compared with that from the literature. \subsection{Event selection} \label{sub:event_selection} @@ -196,22 +197,21 @@ starting from at least 1200~ns, therefore another cut is introduced: \end{enumerate} The three cuts~\eqref{eqn:sir2_prompt_cut},~\eqref{eqn:sir2_muE_cut} and -~\eqref{eqn:sir2_2ndhit_cut} reduce the muon events sample to the size of -\num{9.32E+6}. +~\eqref{eqn:sir2_2ndhit_cut} reduce the sample to the size of \num{9.82E+5}. The number of stopped muons can also be calculated from the number of muonic X-rays recorded by the germanium detector. The X-rays are emitted during the cascading of the muon to the muonic 1S state in the time scale of \SI{E-9}{\s}, so the hit caused by the X-rays must be in coincidence with the muon hit on the active target. Therefore an additional timing cut is applied for the germanium -hits: +detector hits: \begin{equation} \lvert t_{\textrm{Ge}} - t_{\mu\textrm{ counter}} \rvert < \SI{500}{\ns} \label{eqn:sir2_ge_cut} \end{equation} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Number of charged particles with energy above \SI{2}{\MeV}} +\subsection{Number of charged particles with energy above \SI{3}{\MeV}} \label{sub:number_of_charged_particles_with_energy_from_8_10_mev} As shown in \cref{fig:sir2_1us_slices} and illustrated by MC simulation in \cref{fig:sir2_mc_pdfs}, there are several components in @@ -235,11 +235,11 @@ the energy spectrum recorded by the active target: \centering \includegraphics[width=0.45\textwidth]{figs/sir2_meas_spec} \includegraphics[width=0.45\textwidth]{figs/sir2_mc_pdfs} - \caption{The observed spectrum in the timing window 1500 -- 9500~ns (left) + \caption{The observed spectrum in the timing window 1300 -- 10000~ns (left) and its components from MC simulation (right). The charged particles spectrum is obtained assuming the spectrum shape and emission rate from - Sobottka and Wills~\cite{SobottkaWills.1968}. The relative scale between - components is arbitrarily chosen for the purpose of illustration.} + Sobottka and Wills~\cite{SobottkaWills.1968}. The relative scales between + components are arbitrarily chosen for the purpose of illustration.} \label{fig:sir2_mc_pdfs} \end{figure} @@ -270,7 +270,8 @@ in~\ref{fig:sir2_mll_fit}, the yields of backgrounds and signal are: \begin{align} n_{\textrm{beam e}} &= 23756 \pm 581\\ n_{\textrm{dio}} &= 111340 \pm 1245\\ - n_{\textrm{sig}} &= 207201 \pm 856 + n_{\textrm{sig}} &= 2.57 \pm 856 + \label{eqn:sir2_n_chargedparticles} \end{align} \begin{figure}[htb] \centering @@ -282,12 +283,6 @@ in~\ref{fig:sir2_mll_fit}, the yields of backgrounds and signal are: \label{fig:sir2_mll_fit} \end{figure} -The total number of charged particles from time zero is then calculated to be: -\begin{equation} - N_{\textrm{charged particles}} =(149.9\pm 0.6)\times 10^4 - \label{eqn:sir2_Nchargedparticle} -\end{equation} - % subsection number_of_charged_particles_with_energy_from_8_10_mev (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Number of nuclear muon captures} @@ -336,92 +331,34 @@ or correction was made. %The area of the $(2p-1s)$ peak is $N_{(2p-1s)} = 2981.5 \pm 65.6$, %obtained by subtracting the background of 101.5 from the spectral integral of %2083 in the region from 396 to 402 keV. -The area of the $(2p-1s)$ peak is $2929.7 \pm 56.4$ obtained by fitting -a Gaussian peak on top of a first-order polynomial background to the spectrum -in \cref{fgi:sir2_xray} in the region from \SIrange{395}{405}{\keV}. +%The area of the $(2p-1s)$ peak is $2929.7 \pm 56.4$ obtained by fitting +%a Gaussian peak on top of a first-order polynomial background to the spectrum +%in \cref{fgi:sir2_xray} in the region from \SIrange{395}{405}{\keV}. +Using the same procedure of fitting and correcting described in +\cref{sub:germanium_detector}, the number of X-rays is calculated to be 370. +Details of the correction factors are given in \cref{tab:sir2_xray_corr}. +\begin{table}[htb] + \begin{center} + \begin{tabular}{l} + \toprule + \textbf{Col1}\\ + \midrule + item1\\ + \bottomrule + \end{tabular} + \end{center} + \caption{Corrections for the number of X-rays from the active target.} + \label{tab:sir2_xray_corr} +\end{table} -This number of X-rays needs to be corrected for following effects: -\begin{itemize} - \item Self-absorption effect: the X-rays emitted could be absorbed by the - target itself, the probability of self-absorption becomes larger in case of - thick sample and low energy photons. - For this silicon target of 1500~\si{\um}\ thick and the photon energy of - 400~keV, and assuming a narrow muon stopping distribution at the centre of - the target, the self-absorption correction is estimated to be: - \begin{align} - k_{\textrm{self absorption}} &= \dfrac{\mu t}{1 - e^{-\mu t}} \nonumber\\ - &= \dfrac {9.614\times 10^{-2} \times 2.33 \times 0.75 \times 10^{-1}} - {1 - e^{-9.614\times 10^{-2} \times 2.33 \times 0.75 \times 10^{-1}}}\nonumber \\ - %&= \dfrac{1}{0.992} \nonumber\\ - &= 1.008 - \end{align} - where $t = \SI{0.075}{\cm}$ is the thickness of the target, and $\mu$ is - the linear attenuation coefficient of silicon for a photon of 400~keV. The - value of $\mu$ is calculated as product of the density of silicon - $\rho = \SI{2.33}{\g\per\cm^3}$ and its mass attenuation coefficient - $\mu/\rho = \SI{9.614E-2}{\cm^2\per\g}$ taken - from the NIST's X-ray Mass Attenuation Coefficients - table~\footnote{\url{http://www.nist.gov/pml/data/xraycoef}}. - \item Dead time of the germanium detector system: there are two causes of - dead time in our germanium detector, (a) the insensitive period due to long - pulse time, and (b) the reset pulses of the transistor reset preamplifier. - The effects of the two dead time could be calculated by examining the - interval between two consecutive pulses on the germanium detector in - \cref{fig:sir2_ge_deadtime}. - \begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/sir2_ges_self_tdiff} - \caption{Interval between to consecutive pulses on the germanium - detector. The peak at 57~\si{\us}\ indicates the pulse length, and - the bump at about 2000~\si{\us}\ shows the width of the reset - pulses. The average count rate of this detector is extracted from the - decay constant of the time spectrum to be - $5.146 \times 10^{-7}\textrm{ ns}^{-1} = 514.6 \textrm{ s}^{-1}$} - \label{fig:sir2_ge_deadtime} - \end{figure} - - The correction factor for the pulse length is calculated by the formula: - \begin{align} - k_{\textrm{pulse length}} &= e^{2\times \textrm{(pulse length)} - \times \textrm{(count rate)}} \nonumber\\ - &= e^{2\times 57\times10^{-6} \times 514.6} \nonumber\\ - &= 1.06 - \end{align} - The 2-ms-long reset pulses effectively reduce the actual measurement time - compared to other channels, so the correction factor for the effect is: - \begin{align} - k_{\textrm{reset pulse}} &= \frac{\textrm{(measurement time)}} - {\textrm{(measurement time)} - - \textrm{(number of reset)}\times - \textrm{(reset pulse length)}}\nonumber\\ - &= 1.033 - \end{align} - - \item The true coincidence summing is negligibly small due to the far - geometry as mentioned in the calibration process, so no correction is made. - %%TODO - \item The geometrical acceptance of the detector: the absolute efficiency - calibration was done with a point-like source, but the actual points of - origin of the X-rays have a finite spatial distribution. The correction - factor is estimated to be \ldots -\end{itemize} -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike} - \caption{Ratio between geometrical acceptance of the germanium detector in - two cases: point-like source and finite-size source.} - \label{fig:ge_eff_mc_finitesize_vs_pointlike} -\end{figure} - -The number of X-rays after applying all above corrections is 3293.5. The X-ray -intensity in \cref{tab:mucap_pars} was normalised to the number of stopped -muons, so the number of stopped muons is: +The X-ray intensity in \cref{tab:mucap_pars} was normalised to the number of +stopped muons, so the number of stopped muons is: \begin{align} N_{\mu\textrm{ stopped}} &= \dfrac{N_{(2p-1s)}}{\epsilon_{2p-1s}\times I_{(2p-1s)}}\nonumber\\ - &= \dfrac{3293.5}{4.54\times10^{-4} \times 0.803} \\ - &= 9.03\times10^6 \nonumber + &= \dfrac{370}{4.38\times10^{-4} \times 0.803} \\ + &= 1.05\times10^6 \nonumber \end{align} where $\epsilon_{(2p-1s)}$ is the calibrated absolute efficiency of the detector for the 400.177~keV line in \cref{tab:xray_eff}, and @@ -431,15 +368,15 @@ $I_{(2p-1s)}$ is the probability of emitting this X-ray per stopped muon Taking the statistical uncertainty of the peak area, and systematic uncertainties from parameters of muon capture, the number of stopped muons calculated from the X-ray measurement is -$(9.03 \pm 0.31)\times 10^6$. This figure is consistent with the number of -stopped muons of $9.32\times10^6$ after the cuts described in the event +$(10.50 \pm 0.65)\times 10^5$. This figure is consistent with the number of +stopped muons of $9.82\times10^5$ after the cuts described in the event selection process. The number of nuclear captured muons is: \begin{equation} N_{\mu\textrm{ nucl.capture}} = N_{\mu\textrm{ stopped}}\times f_{\textrm{cap.Si}} - = 9.03 \times 10^6 \times 0.658 = 7.25 \times 10^6 + = 10.05 \times 10^5 \times 0.658 = 6.91 \times 10^5 \label{eqn:sir2_Ncapture} \end{equation} where the $f_{\textrm{cap.Si}}$ is the probability of nuclear capture per @@ -738,7 +675,7 @@ X-rays recorded and the number of captures are shown in %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Lifetime measurement} -\label{sub:lifetime_measurement} +\label{sub:lifetime_measurement}w To check the origin of the protons recorded, lifetime measurements were made by cutting on time difference between a hit on one thick silicon and the muon hit. Applying the time cut in 0.5~\si{\us}\ time steps on the proton @@ -762,7 +699,7 @@ before that, the time constants are shorter ($655.9\pm 9.9$ and $731.1\pm8.9$) indicates the contamination from muon captured on material with higher $Z$. Therefore a timing cut from 500~ns is used to select good silicon events, the remaining protons are shown in \cref{fig:si16p_proton_ecut_500nstcut}. -The spectra have a low energy cut off at 2.5~MeV because protons with energy +The spectra have a low energy cut off at 2.5~MeV because protons with energy: lower than that could not pass through the thin silicon to make the cuts as the range of 2.5~MeV protons in silicon is about 68~\si{\um}. \begin{figure}[htb] diff --git a/thesis/mythesis.sty b/thesis/mythesis.sty index cce0ca3..9b74655 100644 --- a/thesis/mythesis.sty +++ b/thesis/mythesis.sty @@ -58,7 +58,8 @@ bookmarks \RequirePackage[final]{listings} \RequirePackage{xfrac} %% Units -\RequirePackage[]{siunitx} +%\RequirePackage[]{siunitx} +\RequirePackage[detect-weight=true, detect-family=true]{siunitx} \RequirePackage{hepnames} %% Various fonts ... %\RequirePackage[T1]{fontenc} From 7eabb23a867ee87aca78d5dfe08a3f45321893ea Mon Sep 17 00:00:00 2001 From: nam Date: Sat, 11 Oct 2014 14:31:27 +0900 Subject: [PATCH 06/26] fix chap4 --- thesis/chapters/chap4_alcap_phys.tex | 121 +++++++++++++-------------- thesis/custom_macro.tex | 3 + thesis/thesis.tex | 4 +- 3 files changed, 65 insertions(+), 63 deletions(-) diff --git a/thesis/chapters/chap4_alcap_phys.tex b/thesis/chapters/chap4_alcap_phys.tex index a5bd278..0501d5b 100644 --- a/thesis/chapters/chap4_alcap_phys.tex +++ b/thesis/chapters/chap4_alcap_phys.tex @@ -347,18 +347,18 @@ $n_{avg} = (0.3 \pm 0.02)A^{1/3}$~\cite{Singer.1974}. The neutron emission can be explained by several mechanisms: \begin{enumerate} \item Direct emission follows reaction~\eqref{eq:mucap_proton}: these neutrons - have fairly high energy, from a few \si{\mega\electronvolt}~to as high as 40--50 - \si{\mega\electronvolt}. + have fairly high energy, from a few \si{\si{\MeV}}~to as high as 40--50 + \si{\si{\MeV}}. \item Indirect emission through an intermediate compound nucleus: the energy transferred to the neutron in the process~\eqref{eq:mucap_proton} is 5.2 - \si{\mega\electronvolt} if the initial proton is at rest, in nuclear + \si{\si{\MeV}} if the initial proton is at rest, in nuclear environment, protons have a finite momentum distribution, therefore the mean excitation energy of the daughter nucleus is around 15 to 20 - \si{\mega\electronvolt}~\cite{Mukhopadhyay.1977}. This is above the nucleon + \si{\si{\MeV}}~\cite{Mukhopadhyay.1977}. This is above the nucleon emission threshold in all complex nuclei, thus the daughter nucleus can de-excite by emitting one or more neutrons. In some actinide nuclei, that excitation energy might trigger fission reactions. The energy of indirect - neutrons are mainly in the lower range $E_n \le 10$ \si{\mega\electronvolt} + neutrons are mainly in the lower range $E_n \le 10$ \si{\si{\MeV}} with characteristically exponential shape of evaporation process. On top of that are prominent lines might appear where giant resonances occur. \end{enumerate} @@ -382,7 +382,7 @@ data. There are two reasons for that: neutron emission. The rate is about 15\% for light nuclei and reduces to a few percent for medium and heavy nuclei. \item The charged particles are short ranged: the emitted protons, - deuterons and alphas are typically low energy (2--20~\mega\electronvolt). + deuterons and alphas are typically low energy ( \SIrange{2}{20}{\MeV}). But a relatively thick target is normally needed in order to achieve a reasonable muon stopping rate and charged particle statistics. Therefore, emulsion technique is particularly powerful. @@ -411,9 +411,9 @@ statistics and in fair agreement with Morigana and Fry Protons with higher energy are technically easier to measure, but because of the much lower rate, they can only be studied at meson facilities. Krane and colleagues~\cite{KraneSharma.etal.1979} measured proton emission from -aluminium, copper and lead in the energy range above 40 \mega\electronvolt~and +aluminium, copper and lead in the energy range above \SI{40}{\MeV} and found a consistent exponential shape in all targets. The integrated yields -above 40 \mega\electronvolt~are in the \sn{}{-4}--\sn{}{-3} range (see +above \SI{40}{\MeV} are in the \sn{}{-4}--\sn{}{-3} range (see Table~\ref{tab:krane_proton_rate}), a minor contribution to total proton emission rate. \begin{table}[htb] @@ -462,16 +462,16 @@ The aforementioned difficulties in charged particle measurements could be solved using an active target, just like nuclear emulsion. Sobottka and Wills~\cite{SobottkaWills.1968} took this approach when using a Si(Li) detector to stop muons. They obtained a spectrum of charged particles up to 26 -\mega\electronvolt~in Figure~\ref{fig:sobottka_spec}. The peak below 1.4 -\mega\electronvolt~is due to the recoiling $^{27}$Al. The higher energy events +\si{\MeV}~in Figure~\ref{fig:sobottka_spec}. The peak below 1.4 +\si{\MeV}~is due to the recoiling $^{27}$Al. The higher energy events including protons, deuterons and alphas constitute $(15\pm 2)\%$ of capture events, which is consistent with a rate of $(12.9\pm1.4)\%$ from gelatine observed by Morigana and Fry. This part has an exponential -decay shape with a decay constant of 4.6 \mega\electronvolt. Measday +decay shape with a decay constant of 4.6 \si{\MeV}. Measday noted~\cite{Measday.2001} the fractions of events in -the 26--32 \mega\electronvolt~range being 0.3\%, and above 32 -\mega\electronvolt~range being 0.15\%. This figure is in agreement with the -integrated yield above 40 \mega\electronvolt~from Krane et al. +the 26--32 \si{\MeV}~range being 0.3\%, and above 32 +\si{\MeV}~range being 0.15\%. This figure is in agreement with the +integrated yield above 40 \si{\MeV}~from Krane et al. In principle, the active target technique could be applied to other material such as germanium, sodium iodine, caesium iodine, and other scintillation @@ -480,7 +480,7 @@ identification like in nuclear emulsion, the best one can achieve after all corrections is a sum of all charged particles. It should be noted here deuterons can contribute significantly, Budyashov et al.~\cite{BudyashovZinov.etal.1971} found deuteron components to be -$(34\pm2)\%$ of the charged particle yield above 18 \mega\electronvolt~in +$(34\pm2)\%$ of the charged particle yield above 18 \si{\MeV}~in silicon, and $(17\pm4)\%$ in copper. \begin{figure}[htb] \centering @@ -547,7 +547,7 @@ protons were taken. Wyttenbach et al.\ saw that the cross section of each reaction decreases exponentially with increasing Coulomb barrier. The decay constant for all -$(\mu^-,\nu pxn)$ is about 1.5 per \mega\electronvolt~of Coulomb barrier. They +$(\mu^-,\nu pxn)$ is about 1.5 per \si{\MeV}~of Coulomb barrier. They also commented a ratio for different de-excitation channels: \begin{equation} (\mu^-,\nu p):(\mu^-,\nu pn):(\mu^-,\nu p2n):(\mu^-,\nu p3n) = 1:6:4:4, @@ -572,7 +572,7 @@ nucleus is formed, and then it releases energy by statistical emission of various particles. Three models for momentum distribution of protons in the nucleus were used: (I) the Chew-Goldberger distribution $\rho(p) \sim A/(B^2 + p^2)^2$; (II) Fermi gas at zero temperature; and (III) -Fermi gas at a finite temperature ($kT = 9$ \mega\electronvolt). +Fermi gas at a finite temperature ($kT = 9$ \si{\MeV}). A very good agreement with the experimental result for the alpha emission was obtained with distribution (III), both in the absolute percentage and the energy @@ -598,7 +598,7 @@ the nucleon, the average excitation energy will increase, but the proton emission rate does not significantly improve and still could not explain the large discrepancy. He concluded that the evaporation mechanism can account for only a small fraction of emitted protons. Moreover, the high energy protons -of 25--50 \mega\electronvolt~cannot be explained by the evaporation mechanism. +of 25--50 \si{\MeV}~cannot be explained by the evaporation mechanism. He and Lifshitz~\cite{LifshitzSinger.1978, LifshitzSinger.1980} proposed two major corrections to Ishii's model: \begin{enumerate} @@ -611,14 +611,14 @@ major corrections to Ishii's model: is possibility for particles to escape from the nucleus. \end{enumerate} With these improvements, the calculated proton spectrum agreed reasonably with -data from Morigana and Fry in the energy range $E_p \le 30$ \mega\electronvolt. +data from Morigana and Fry in the energy range $E_p \le 30$ \si{\MeV}. Lifshitz and Singer noted the pre-equilibrium emission is more important for heavy nuclei. Its contribution in light nuclei is about a few percent, increasing to several tens of percent for $100 Date: Sun, 12 Oct 2014 00:37:16 +0900 Subject: [PATCH 07/26] prog saved --- thesis/chapters/chap5_alcap_setup.tex | 164 ++++++++++++++++++++++---- thesis/chapters/chap6_analysis.tex | 120 ++----------------- thesis/thesis.bib | 25 +++- 3 files changed, 169 insertions(+), 140 deletions(-) diff --git a/thesis/chapters/chap5_alcap_setup.tex b/thesis/chapters/chap5_alcap_setup.tex index ba56836..0f8e3d0 100644 --- a/thesis/chapters/chap5_alcap_setup.tex +++ b/thesis/chapters/chap5_alcap_setup.tex @@ -19,7 +19,7 @@ provide veto signals for the silicon and germanium detectors. Two liquid scintillators for neutron measurements were also tested in this run. \begin{figure}[btp] \centering - \includegraphics[width=0.55\textwidth]{figs/alcap_setup_detailed} + \includegraphics[width=0.65\textwidth]{figs/alcap_setup_detailed} \caption{AlCap detectors: two silicon packages inside the vacuum vessel, muon beam detectors including plastic scintillators and a wire chamber, germanium detector and veto plastic scintillators.} @@ -28,22 +28,22 @@ scintillators for neutron measurements were also tested in this run. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Muon beam and vacuum chamber} Muons in the $\pi$E1 beam line are decay products of pions created -as a \SI{590}{\mega\electronvolt} proton beam hits a thick carbon target -(E-target in \cref{fig:psi_exp_hall_all}). The beam line was designed to -deliver muons with momenta ranging from -\SIrange{10}{500}{\mega\electronvolt\per\cc} and -momentum spread from \SIrange{0.26}{8.0}{\percent}. These parameters can be +as a \SI{590}{\mega\electronvolt} proton beam hits a thick carbon target. The +beam line was designed to deliver muons with momenta ranging from +\SIrange{10}{500}{\mega\electronvolt\per\cc} and momentum spread from +\SIrange{0.26}{8.0}{\percent}~\cite{Foroughli.1997}. These parameters can be selected by changing various magnets and slits shown in -\cref{fig:psi_piE1_elements}~\cite{Foroughli.1997}. +\cref{fig:psi_piE1_elements}. -\begin{figure}[p] - \centering - \includegraphics[height=0.85\textheight]{figs/psi_exp_hall_all} - \caption{Layout of the PSI experimental hall, $\pi$E1 experimental area is - marked with the red circle. \\Image taken from - \url{http://www.psi.ch/num/FacilitiesEN/HallenplanPSI.png}} - \label{fig:psi_exp_hall_all} -\end{figure} +%(E-target in \cref{fig:psi_exp_hall_all}). +%\begin{figure}[p] + %\centering + %\includegraphics[height=0.85\textheight]{figs/psi_exp_hall_all} + %\caption{Layout of the PSI experimental hall, $\pi$E1 experimental area is + %marked with the red circle. \\Image taken from + %\url{http://www.psi.ch/num/FacilitiesEN/HallenplanPSI.png}} + %\label{fig:psi_exp_hall_all} +%\end{figure} \begin{figure}[btp] \centering @@ -402,8 +402,8 @@ correlation between detectors would be established in the analysis stage. At the beginning of each block, the time counter in each digitiser is reset to ensure time alignment across all modules. The period of 110~ms was chosen to be: -{\em i} long enough compared to the time scale of several \si{\micro\second}\ -of the physics of interest, {\em ii} short enough so that there is no timer +{\em i}) long enough compared to the time scale of several \si{\micro\second}\ +of the physics of interest, {\em ii}) short enough so that there is no timer rollover on any digitiser (a FADC runs at its maximum speed of \SI{170}{\mega\hertz} could handle up to about \SI{1.5}{\second} with its 28-bit time counter). @@ -430,8 +430,8 @@ The energy calibration for the silicon detectors were done routinely during the run, by: \begin{itemize} \item a \SI{79.5}{\becquerel} $^{241}\textrm{Am}$ alpha source. The most - prominent alpha particles have energies of \SI{5.484}{\si{\MeV}} (85.2\%) - and \SI{5.442}{\si{\MeV}} (12.5\%). The alpha particles from the source + prominent alpha particles have energies of \SI{5.484}{\MeV} (85.2\%) + and \SI{5.442}{\MeV} (12.5\%). The alpha particles from the source would lose about \SI{66}{\kilo\eV} in the \SI{0.5}{\um}-thick dead layer, and the peak would appear at \SI{5418}{\kilo\eV} (\cref{fig:toyMC_alpha}); @@ -753,12 +753,12 @@ sets are shown in \cref{tb:stat}. Al 100 \si{\micro\meter}& 1.09& 14.37&$2.94 \times 10^8$\\ & 1.07& 2.56& $4.99 \times 10^7$\\ \midrule - Al 50 \si{\micro\meter} m & 1.07& 51.94& $8.81 \times 10^8$\\ + Al 50 \si{\micro\meter} & 1.07& 51.94& $8.81 \times 10^8$\\ \bottomrule \end{tabular} \end{center} - \caption{Run statistics. Momentum scaling - normalized to 28 MeV/c.} + \caption{Run statistics. Momentum scaling factors are normalised to + \SI{28}{\MeV\per\cc}.} \label{tb:stat} \end{table} @@ -913,12 +913,126 @@ example, the X-ray spectrum analysis was done to confirm that we could observe the muon capture process and to help in choosing optimal momenta which maximised the number of stopped muons. -Although the offline analyser is still not fully developed yet, several modules -are ready. They are described in detailed in the next chapter. +Although the offline analyser is still not fully available yet, several modules +are ready(\cref{tab:offline_modules}). An initial analysis is possible using +the existing modules thanks to the modularity of the analysis framework. + +\begin{table}[htb] + \begin{center} + \begin{tabular}{l p{8cm}} + \toprule + \textbf{Module name} & \textbf{Functions}\\ + \midrule + MakeAnalysedPulses & make a pulse with parameters extracted from + a waveform\\ + MaxBinAPGenerator & simplest algorithm to get pulse information\\ + TSimpleMuonEvent & sort pulses occur in a fixed time window around the + muon hits\\ + ExportPulse \& PulseViewer & plot waveforms for diagnostics\\ + PlotAmplitude & plot pulse height spectra\\ + PlotAmpVsTdiff & plot pulse correlations in timing and amplitude\\ + EvdE & plot \sdEdx histograms\\ + \bottomrule + \end{tabular} + \end{center} + \caption{Available offline analysis modules.} + \label{tab:offline_modules} +\end{table} + +The MakeAnalysedPulses module takes a raw waveform, calculates the pedestal +from a predefined number of first samples, subtracts this pedestal taking +pulse polarity into account, then calls another module to extract pulse +parameters. At the moment, the simplest module, so-called MaxBinAPGenerator, +for pulse information calculation is in use. The module looks for the +sample that has the maximal deviation from the baseline, takes the deviation as +pulse amplitude and the time stamp of the sample as pulse time. The procedure +is illustrated on \cref{fig:tap_maxbin_algo}. This module could not handle +pile-up or double pulses in one \tpulseisland{} in \cref{fig:tap_maxbin_bad}. +\begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/tap_maxbin_algo} + \caption{Pulse parameters extraction with MaxBinAPGenerator.} + \label{fig:tap_maxbin_algo} +\end{figure} +\begin{figure}[htb] + \centering + \includegraphics[width=0.47\textwidth]{figs/tap_maxbin_bad} + \includegraphics[width=0.47\textwidth]{figs/tap_maxbin_bad2} + \caption{Double pulse and pile up are taken as one single pulse by the + MaxBinAPGenerator} + \label{fig:tap_maxbin_bad} +\end{figure} + +The TSimpleMuonEvent first picks a muon candidate, then loops through all +pulses on all detector channels, and picks all pulses occur in +a time window of \SI{\pm 10}{\si{\us}} around each candidate to build +a muon event. A muon candidates is a hit on the upstream plastic scintillator +with an amplitude higher than a threshold which was chosen to reject MIPs. The +period of \SI{10}{\si{\us}} is long enough compared to the mean life time of +muons in the target materials +(\SI{0.758}{\si{\us}} for silicon, and \SI{0.864}{\si{\us}} +for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted +charged particles would be recorded in this time window. +%\begin{figure}[htb] + %\centering + %\includegraphics[width=0.85\textwidth]{figs/tme_musc_threshold} + %\caption{Pulse height spectrum of the $\mu$Sc scintillator} + %\label{fig:tme_musc_threshold} +%\end{figure} + +A pile-up protection mechanism is employed to reject multiple muons events: if +there exists another muon hit in less than \SI{15}{\us} from the +candidate then both the candidate and the other muon are discarded. This +pile-up protection would cut out less than 11\% total number of events because +the beam rate was generally less than \SI{8}{\kilo\hertz}. + +%In runs with active silicon targets, another requirement is applied for the +%candidate: a prompt hit on the target in $\pm 200$ \si{\ns}\ around the +%time of the $\mu$Sc pulse. The number comes from the observation of the +%time correlation between hits on the target and the $\mu$Sc +%(\cref{fig:tme_sir_prompt_rational}). +%\begin{figure}[htb] + %\centering + %\includegraphics[width=0.85\textwidth]{figs/tme_sir_prompt_rational} + %\caption{Correlation in time between SiR2 hit and muon hit} + %\label{fig:tme_sir_prompt_rational} +%\end{figure} + +To make sure that we will analyse good data, a low level data quality checking +was done on the whole data sets. The idea is plotting the variations of basic +parameters, such as noise level, length of raw waveforms, pulse rate, time +correlation to hits on the muon counter on each channel during the data +collecting period. Runs with significant difference from the averaging +values were further checked for possible causes, and would be discarded if such +discrepancy was too large or unaccounted for. Examples of such trend plots are +shown in \cref{fig:lldq}. +\begin{figure}[htb] + \centering + \includegraphics[width=0.47\textwidth]{figs/lldq_noise} + \includegraphics[width=0.47\textwidth]{figs/lldq_tdiff} + \caption{Example trend plots used in the low level data quality checking: + noise level in FWHM (left) and time correlation with muon hits (right). The + noise level was basically stable in in this data set, except for one + channel. On the right hand side, this sanity check helped find out the + sampling frequency was wrongly applied in the first tranche of the data + set.} + \label{fig:lldq} +\end{figure} % subsection offline_analyser (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% section analysis_strategy (end) +\section{Monte Carlo simulation} +\label{sec:monte_carlo_simulation} +A full Monte Carlo (MC) simulation of the experimental set up has been developed +based on Geant4~\cite{Agostinelli.etal.2003}. The geometrical implementation +was as detailed as possible and could be modified via configuration script at +run time. Descriptions of the muon beam came from the beam line optic +calculation provided by the accelerator experts at PSI. + +The MC model greatly assisted the design of the experiment, such as alignment +of the detectors with respect to the target, and shielding of scattered muons. +It also helps make sense of observed results during the run and data +analysing. % chapter the_alcap_run_2013 (end) diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index 83f20a7..df4e407 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -1,116 +1,14 @@ \chapter{Data analysis} \label{cha:data_analysis} - -\section{Analysis modules} -\label{sec:analysis_modules} -A full analysis has not been completed yet, but initial analysis -based on the existing modules (\cref{tab:offline_modules}) is possible -thanks to the modularity of the analysis framework. - -\begin{table}[htb] - \begin{center} - \begin{tabular}{l p{8cm}} - \toprule - \textbf{Module name} & \textbf{Functions}\\ - \midrule - MakeAnalysedPulses & make a pulse with parameters extracted from - a waveform\\ - MaxBinAPGenerator & simplest algorithm to get pulse information\\ - TSimpleMuonEvent & sort pulses occur in a fixed time window around the - muon hits\\ - ExportPulse \& PulseViewer & plot waveforms for diagnostics\\ - PlotAmplitude & plot pulse height spectra\\ - PlotAmpVsTdiff & plot pulse correlations in timing and amplitude\\ - EvdE & identify charged particles using dE/dx\\ - \bottomrule - \end{tabular} - \end{center} - \caption{Available offline analysis modules.} - \label{tab:offline_modules} -\end{table} - -The MakeAnalysedPulses module takes a raw waveform, calculates the pedestal -from a predefined number of first samples, subtracts this pedestal taking -pulse polarity into account, then calls another module to extract pulse -parameters. At the moment, the simplest module, so-called MaxBinAPGenerator, -for pulse information calculation is in use. The module looks for the -sample that -has the maximal deviation from the baseline, takes the deviation as pulse -amplitude and the time stamp of the sample as pulse time. The procedure is -illustrated on \cref{fig:tap_maxbin_algo}. This module could not account for -pile-up or double pulses in one \tpulseisland{} in \cref{fig:tap_maxbin_bad}. -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/tap_maxbin_algo} - \caption{Pulse parameters extraction with MaxBinAPGenerator.} - \label{fig:tap_maxbin_algo} -\end{figure} -\begin{figure}[htb] - \centering - \includegraphics[width=0.47\textwidth]{figs/tap_maxbin_bad} - \includegraphics[width=0.47\textwidth]{figs/tap_maxbin_bad2} - \caption{Double pulse and pile up are taken as one single pulse by the - MaxBinAPGenerator} - \label{fig:tap_maxbin_bad} -\end{figure} - -The TSimpleMuonEvent first picks a muon candidate, then loops through all -pulses on all detector channels, and picks all pulses occur in -a time window of \SI{\pm 10}{\si{\us}} around each candidate to build -a muon event. A muon candidates is a hit on the upstream plastic scintillator -with an amplitude higher than a threshold which was chosen to reject MIPs. The -period of \SI{10}{\si{\us}} is long enough compared to the mean life time of -muons in the target materials -(\SI{0.758}{\si{\us}} for silicon, and \SI{0.864}{\si{\us}} -for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted -charged particles would be recorded in this time window. -%\begin{figure}[htb] - %\centering - %\includegraphics[width=0.85\textwidth]{figs/tme_musc_threshold} - %\caption{Pulse height spectrum of the $\mu$Sc scintillator} - %\label{fig:tme_musc_threshold} -%\end{figure} - -A pile-up protection mechanism is employed to reject multiple muons events: if -there exists another muon hit in less than \SI{15}{\si{\us}} from the -candidate then both the candidate and the other muon are discarded. This -pile-up protection would cut out less than 11\% total number of events because -the beam rate was generally less than \SI{8}{\kilo\hertz}. - -%In runs with active silicon targets, another requirement is applied for the -%candidate: a prompt hit on the target in $\pm 200$ \si{\ns}\ around the -%time of the $\mu$Sc pulse. The number comes from the observation of the -%time correlation between hits on the target and the $\mu$Sc -%(\cref{fig:tme_sir_prompt_rational}). -%\begin{figure}[htb] - %\centering - %\includegraphics[width=0.85\textwidth]{figs/tme_sir_prompt_rational} - %\caption{Correlation in time between SiR2 hit and muon hit} - %\label{fig:tme_sir_prompt_rational} -%\end{figure} - -To make sure that we will analyse good data, a low level data quality checking -was done on the whole data sets. The idea is plotting the variations of basic -parameters, such as noise level, length of raw waveforms, pulse rate, time -correlation to hits on the muon counter on each channel during the data -collecting period. Runs with significant difference from the averaging -values were further checked for possible causes, and would be discarded if such -discrepancy was too large or unaccounted for. Examples of such trend plots are -shown in \cref{fig:lldq}. -\begin{figure}[htb] - \centering - \includegraphics[width=0.47\textwidth]{figs/lldq_noise} - \includegraphics[width=0.47\textwidth]{figs/lldq_tdiff} - \caption{Example trend plots used in the low level data quality checking: - noise level in FWHM (left) and time correlation with muon hits (right). The - noise level was basically stable in in this data set, except for one - channel. On the right hand side, this sanity check helped find out the - sampling frequency was wrongly applied in the first tranche of the data - set.} - \label{fig:lldq} -\end{figure} -% section analysis_modules (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +This chapter presents initial analysis on subsets of the collected data. +Purposes of the analysis include: +\begin{itemize} + \item testing the analysis chain; + \item verification of the experimental method, specifically the + normalisation of number of stopped muons, and particle identification + using specific energy loss; + \item extracting a preliminary rate of proton emission from aluminium. +\end{itemize} \section{Charged particles following muon capture on a thick silicon target} \label{sec:charged_particles_from_muon_capture_on_silicon_thick_silicon} This analysis was done on a subset of the active target runs diff --git a/thesis/thesis.bib b/thesis/thesis.bib index 8fb2048..91adc65 100644 --- a/thesis/thesis.bib +++ b/thesis/thesis.bib @@ -112,6 +112,23 @@ Timestamp = {2014-04-09} } +@Article{Agostinelli.etal.2003, + Title = {{GEANT4: A Simulation toolkit}}, + Author = {Agostinelli, S. and others}, + Journal = {Nucl.Instrum.Meth.}, + Year = {2003}, + Pages = {250-303}, + Volume = {A506}, + + __markedentry = {[NT:6]}, + Collaboration = {GEANT4}, + Doi = {10.1016/S0168-9002(03)01368-8}, + Owner = {NT}, + Reportnumber = {SLAC-PUB-9350, FERMILAB-PUB-03-339}, + Slaccitation = {%%CITATION = NUIMA,A506,250;%%}, + Timestamp = {2014-10-11} +} + @Article{AhmadAzuelos.etal.1988, Title = {Search for muon-electron and muon-positron conversion}, Author = {Ahmad, S and Azuelos, G and Blecher, M and Bryman, DA and Burnham, RA and Clifford, ETH and Depommier, P and Dixit, MS and Gotow, K and Hargrove, CK and others}, @@ -471,7 +488,7 @@ Pages = {154--197}, Volume = {562}, - __markedentry = {[NT:6]}, + __markedentry = {[NT:]}, Doi = {10.1016/j.nima.2006.03.009}, File = {Published version:Bichsel.2006.pdf:PDF}, Owner = {NT}, @@ -1065,6 +1082,7 @@ Month = {Aug}, Pages = {741--757}, Volume = {36}, + Doi = {10.1103/PhysRevC.36.741}, File = {Published version:GadioliGadioli.1987.pdf:PDF}, Issue = {2}, @@ -1872,7 +1890,7 @@ @Article{MeasdayStocki.etal.2007, Title = {$\gamma$ rays from muon capture in Al 27 and natural Si}, Author = {Measday, David F and Stocki, Trevor J and Moftah, Belal A and Tam, Heywood}, - Journal = {Physical Review C}, + Journal = {Phys. Rev. C}, Year = {2007}, Number = {3}, Pages = {035504}, @@ -2299,6 +2317,7 @@ Month = {Jan}, Pages = {135--141}, Volume = {19}, + Doi = {10.1103/PhysRevC.19.135}, File = {Published version:SchlepuetzComiso.etal.1979.pdf:PDF}, Issue = {1}, @@ -2484,8 +2503,6 @@ Year = {2003}, Pages = {MOLT007}, Volume = {C0303241}, - - __markedentry = {[NT:]}, Archiveprefix = {arXiv}, Eprint = {physics/0306116}, File = {arXiv v1:VerkerkeKirkby.2003-eprintv1.pdf:PDF}, From 2a0f11c72e855eff260bb5b31b959b4aa7f25fce Mon Sep 17 00:00:00 2001 From: nam Date: Tue, 14 Oct 2014 21:10:52 +0900 Subject: [PATCH 08/26] prog saved --- thesis/chapters/chap5_alcap_setup.tex | 1 + thesis/chapters/chap6_analysis.tex | 681 +++++++++++++++++--------- thesis/figs/sir2_ges_self_tdiff.png | Bin 0 -> 243120 bytes thesis/thesis.tex | 4 +- 4 files changed, 458 insertions(+), 228 deletions(-) create mode 100644 thesis/figs/sir2_ges_self_tdiff.png diff --git a/thesis/chapters/chap5_alcap_setup.tex b/thesis/chapters/chap5_alcap_setup.tex index 0f8e3d0..df14625 100644 --- a/thesis/chapters/chap5_alcap_setup.tex +++ b/thesis/chapters/chap5_alcap_setup.tex @@ -765,6 +765,7 @@ sets are shown in \cref{tb:stat}. % section data_sets (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Analysis framework} +\label{sec:analysis_framework} \subsection{Concept} \label{sub:concept} Since the AlCapDAQ is a trigger-less system, it stored all waveforms of the diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index df4e407..b4eb45b 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -9,33 +9,37 @@ Purposes of the analysis include: using specific energy loss; \item extracting a preliminary rate of proton emission from aluminium. \end{itemize} -\section{Charged particles following muon capture on a thick silicon target} -\label{sec:charged_particles_from_muon_capture_on_silicon_thick_silicon} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Number of stopped muons normalisation} +\label{sec:number_of_stopped_muons_normalisation} +The active silicon target runs was used to check for the validity of the +counting of number of stopped muons, where the number can be calculated by two +methods: +\begin{itemize} + \item counting hits on the active target in coincidence with hits on the + upstream scintillator counter; + \item inferred from number of X-rays recorded by the germanium detector. +\end{itemize} This analysis was done on a subset of the active target runs \numrange{2119}{2140} because of the problem of wrong clock frequency found in the data quality checking shown in \cref{fig:lldq}. The data set contains %\num[fixed-exponent=2, scientific-notation = fixed]{6.4293720E7} muon events. \num{6.43E7} muon events. -Firstly, the number of charged particles emitted after nuclear muon capture on -the active target is calculated. The charged particles yield then is normalised -to the number of nuclear muon capture to obtain an emission rate. -%Finally, the -%rate is compared with that from the literature. - -\subsection{Event selection} +\subsection{Number of stopped muons from active target counting} \label{sub:event_selection} Because of the active target, a stopped muon would cause two coincident hits on the muon counter and the target. The energy of the muon hit on the active target is also well-defined as the narrow-momentum-spread beam was used. The correlation between the energy and timing of all the hits on the active target is shown in \cref{fig:sir2f_Et_corr}. The most intense spot at zero time -and about 5 MeV energy corresponds to stopped muons in the thick target. The -band below 1 MeV is due to electrons, either in the beam or from muon decay in -orbits, or emitted during the cascading of muon to the muonic 1S state. The -valley between time zero and 1200~ns shows the minimum distance in time between -two pulses. It is the mentioned limitation of the current pulse parameter -extraction method where no pile up or double pulses is accounted for. +and about \SI{5}{\MeV} energy corresponds to stopped muons in the thick target. +The band below \SI{1}{\MeV} is due to electrons, either in the beam or from +muon decay in orbits, or emitted during the cascading of muon to the muonic 1S +state. The valley between time zero and 1200~ns shows the minimum distance in +time between two pulses. It is the mentioned limitation of the current pulse +parameter extraction method where no pile up or double pulses is accounted for. \begin{figure}[htb] \centering @@ -79,116 +83,19 @@ From the energy-timing correlation above, the cuts to select stopped muons are: \label{eqn:sir2_muE_cut} \end{equation} \end{enumerate} -In order to measure the charged particles after nuclear muon capture, one would -pick events where the emitted particles are well separated from the -muon stop time. The energy timing correlation plot suggests a timing window -starting from at least 1200~ns, therefore another cut is introduced: -\begin{enumerate} - \setcounter{enumi}{2} - \item there are at least two hits on the active target, the time - difference between the second hit on target (decay or capture product) and - the muon counter hit is at least 1300 ns: - \begin{equation} - t_{\textrm{target 2nd hit}} - t_{\mu\textrm{ counter}} \geq \SI{1300}{\ns} - \label{eqn:sir2_2ndhit_cut} - \end{equation} -\end{enumerate} - -The three cuts~\eqref{eqn:sir2_prompt_cut},~\eqref{eqn:sir2_muE_cut} and -~\eqref{eqn:sir2_2ndhit_cut} reduce the sample to the size of \num{9.82E+5}. - -The number of stopped muons can also be calculated from the number of muonic -X-rays recorded by the germanium detector. The X-rays are emitted during the -cascading of the muon to the muonic 1S state in the time scale of \SI{E-9}{\s}, -so the hit caused by the X-rays must be in coincidence with the muon hit on the -active target. Therefore an additional timing cut is applied for the germanium -detector hits: +The two cuts~\eqref{eqn:sir2_prompt_cut} and~\eqref{eqn:sir2_muE_cut} give +a number of stopped muons counted by the active target: \begin{equation} - \lvert t_{\textrm{Ge}} - t_{\mu\textrm{ counter}} \rvert < \SI{500}{\ns} - \label{eqn:sir2_ge_cut} + N_{\mu \textrm{ active Si}} = 9.32 \times 10^6 + \label{eqn:n_stopped_si_count} \end{equation} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Number of charged particles with energy above \SI{3}{\MeV}} -\label{sub:number_of_charged_particles_with_energy_from_8_10_mev} -As shown in \cref{fig:sir2_1us_slices} and illustrated by MC simulation -in \cref{fig:sir2_mc_pdfs}, there are several components in -the energy spectrum recorded by the active target: -\begin{enumerate} - \item charged particles from nuclear muon capture, this is the signal of - interest; - \item beam electrons with a characteristic Landau peak around \SI{800}{\keV}, - dominating at large delay (from \SI{6500}{\ns}), causing background at - energy lower than \SI{1}{\MeV} which drops sharply at energy larger than - \SI{3}{\MeV}; - \item electrons from muon decay-in-orbit (DIO) and recoiled nuclei - from neutron emitting muon captures, peak at - around \SI{300}{\keV}, dominate the region where energy smaller than - \SI{1}{\MeV} and delay less than \SI{3500}{\ns}. This component is - intrinsic background, having the same time structure as that of the signal; - \item stray muons scattered into the target, this component is small compares - to the charged particles yield so it is not considered further. -\end{enumerate} -\begin{figure}[htb] - \centering - \includegraphics[width=0.45\textwidth]{figs/sir2_meas_spec} - \includegraphics[width=0.45\textwidth]{figs/sir2_mc_pdfs} - \caption{The observed spectrum in the timing window 1300 -- 10000~ns (left) - and its components from MC simulation (right). The charged particles - spectrum is obtained assuming the spectrum shape and emission rate from - Sobottka and Wills~\cite{SobottkaWills.1968}. The relative scales between - components are arbitrarily chosen for the purpose of illustration.} - \label{fig:sir2_mc_pdfs} -\end{figure} - -An energy cut at \SI{2}{\MeV} is introduced to avoid the domination of the -beam electrons at low energy. In order to obtain the yields of backgrounds -above \SI{2}{\MeV}, a binned maximum likelihood fit was done. The likelihood of -getting the measured spectrum is defined as: -\begin{equation} - L = \frac{e^{-\mu}\mu^n}{n!}\prod_i \frac{\mu_i^{n_i} e^{-\mu_i}}{n_i!} - \label{eqn:llh_def} -\end{equation} -where $n$ is the total number of events observed, $\mu$ is the expected number -of events according to some linear combination of the signal and the -backgrounds shown in~\ref{fig:sir2_mc_pdfs}, namely: -\begin{align} - n &= n_{\textrm{sig}} + n_{\textrm{beam e}} + n_{\textrm{dio}}\\ - \textrm{(sum pdf)} &= n_{\textrm{sig}}\times\textrm{(sig pdf)} + - n_{\textrm{beam e}}\times\textrm{(beam e pdf)} + - n_{\textrm{dio}}\times\textrm{(dio pdf)}; - \label{eqn:sum_pdf} -\end{align} -and the $i$ index indicates the respective number of events in the $i$-th -bin. - -The fit is done by the RooFit package~\cite{VerkerkeKirkby.2003} where the -negative log likelihood $-2\ln{L}$ is minimised. Fitting results are shown -in~\ref{fig:sir2_mll_fit}, the yields of backgrounds and signal are: -\begin{align} - n_{\textrm{beam e}} &= 23756 \pm 581\\ - n_{\textrm{dio}} &= 111340 \pm 1245\\ - n_{\textrm{sig}} &= 2.57 \pm 856 - \label{eqn:sir2_n_chargedparticles} -\end{align} -\begin{figure}[htb] - \centering - \includegraphics[width=0.42\textwidth]{figs/sir2_mllfit_nbkg} - \includegraphics[width=0.42\textwidth]{figs/sir2_mllfit_nebeam} - \includegraphics[width=0.84\textwidth]{figs/sir2_mllfit} - \caption{Results of the maximum likelihood fit of the energy spectrum on the - active target.} - \label{fig:sir2_mll_fit} -\end{figure} - -% subsection number_of_charged_particles_with_energy_from_8_10_mev (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Number of nuclear muon captures} -\label{sub:number_of_stopped_muons} -The number of nuclear captures can be inferred from the number of recorded -muonic X-rays. The reference values of the parameters needed for the -calculation taken from Suzuki et al.~\cite{SuzukiMeasday.etal.1987} and Measday -et al.~\cite{MeasdayStocki.etal.2007} are listed in \cref{tab:mucap_pars}. +\subsection{Number of stopped muons from the number of X-rays} +\label{sub:number_of_stopped_muons_from_the_number_of_x_rays} +The number of nuclear captures, hence the number of stopped muons in the +active silicon target, can be inferred from the number of emitted +muonic X-rays. The reference energies and intensities of the most prominent +lines of silicon and aluminium are listed in \cref{tab:mucap_pars}. \begin{table}[htb] \begin{center} \begin{tabular}{l l l} @@ -208,130 +115,452 @@ et al.~\cite{MeasdayStocki.etal.2007} are listed in \cref{tab:mucap_pars}. \label{tab:mucap_pars} \end{table} -The muonic X-ray spectrum emitted from the active target is shown in -\cref{fig:sir2_xray}. The $(2p-1s)$ line is seen at -399.5~\si{\keV}, 0.7~\si{\keV}\ off from the reference value of -400.177~\si{\keV}. This discrepancy is within our detector's resolution, -and the calculated efficiency is $(4.549 \pm 0.108)\times 10^{-5}$ -- a 0.15\% -increasing from that of the 400.177~keV line, so no attempt for recalibration -or correction was made. +The muonic X-rays are emitted during the cascading of the muon to the muonic 1S +state in the time scale of \SI{E-9}{\s}, so the hit caused by the X-rays must +be in coincidence with the muon hit on the active target. Therefore an +additional timing cut is applied for the germanium detector hits: +\begin{equation} + \lvert t_{\textrm{Ge}} - t_{\mu\textrm{ counter}} \rvert < \SI{500}{\ns} + \label{eqn:sir2_ge_cut} +\end{equation} + +The germanium spectrum after three +cuts~\eqref{eqn:sir2_prompt_cut},~\eqref{eqn:sir2_muE_cut} +and~\eqref{eqn:sir2_ge_cut} is plotted in \cref{fig:sir2_xray}. The $(2p-1s)$ +line clearly showed up at \SI{400}{\keV} with very low background. A peak at +\SI{476}{\keV} is identified as the $(3p-1s)$ transition. Higher transitions +such as $(4p-1s)$, $(5p-1s)$ and $(6p-1s)$ can also be recognised at +\SI{504}{\keV}, \SI{516}{\keV} and \SI{523}{\keV}, respectively. +%The $(2p-1s)$ +%line is seen at 399.5~\si{\keV}, 0.7~\si{\keV} off from the reference value of +%400.177~\si{\keV}. This discrepancy is within our detector's resolution, +%and the calculated efficiency is $(4.549 \pm 0.108)\times 10^{-5}$ -- a 0.15\% +%increasing from that of the 400.177~keV line, so no attempt for recalibration +%or correction was made. \begin{figure}[htb] \centering - \includegraphics[width=0.85\textwidth]{figs/sir2_xray} - \caption{Prompt muonic X-rays spectrum from the active silicon target, the - two major lines $(2p-1s)$ and $(3p-1s)$ are clearly distinguishable at 400 - and 476 keV, respectively. The $(5p-1s)$ line at 504 keV and $(6p-1s)$ line - at 516 keV can also be seen. + \includegraphics[width=0.85\textwidth]{figs/sir2_xray_22} + \caption{Prompt muonic X-rays spectrum from the active silicon target. } \label{fig:sir2_xray} \end{figure} +The net area of the $(2p-1s)$ is found to be 2929.7 by fitting a Gaussian +peak on top of a first-order polynomial from \SIrange{395}{405}{\keV}. +Using the same procedure of correcting described in +\cref{sub:germanium_detector}, and taking detector acceptance and X-ray +intensity into account (see \cref{tab:sir2_xray_corr}), the number of muon +stopped is: +\begin{equation} + N_{\mu \textrm{ stopped X-ray}} = (9.16 \pm 0.28)\times 10^6, + \label{eqn:n_stopped_xray_count} +\end{equation} +which is consistent with the number of X-rays counted using the active target. +\begin{table}[btp] + \begin{center} + \begin{tabular}{@{}llll@{}} + \toprule + \textbf{Measured X-rays} & \textbf{Value} & \textbf{Absolute error} & \textbf{Relative error} \\ \midrule + Gross integral & 3083 & & \\ + Background & 101.5 & & \\ + Net area $(2p-1s)$ & 2929.7 & 56.4 & 0.02 \\ + \vspace{0.03em}\\ + \toprule + \textbf{Corrections} & \textbf{Value} & \multicolumn{2}{c}{\textbf{Details}}\\ + \midrule + Random summing & 1.06 & \multicolumn{2}{l}{average count rate \SI{491.4}{\Hz},}\\ + & & \multicolumn{2}{l}{pulse length \SI{57}{\us}}\\ + TRP reset & 1.03 & \multicolumn{2}{l}{\SI{298}{\s} loss during \SI{9327}{\s} run period}\\ + Self-absorption & 1.008 & \multicolumn{2}{l}{silicon thickness \SI{750}{\um},}\\ + & & \multicolumn{2}{l}{linear attenuation \SI{0.224}{\per\cm}}\\ + True coincidence & 1 & \multicolumn{2}{l}{omitted} \\ + \vspace{0.03em}\\ + \toprule + \textbf{Efficiency and intensity} & \textbf{Value} & \textbf{Absolute error} & \textbf{Relative error} \\ + \midrule + Detector efficiency & \num{4.40E-4} & \num{0.978E-5} & 0.02 \\ + X-ray intensity & 0.803 & 0.008 & 0.009 \\ + \vspace{0.03em}\\ + \toprule + \textbf{Results} & \textbf{Value} & \textbf{Absolute error} & \textbf{Relative error} \\ + \midrule + Number of X-rays emitted & \num{7.36E6} & \num{0.22E6} & 0.03 \\ + Number of muons stopped & \num{9.16E6} & \num{0.28E6} & 0.03 \\ + \bottomrule + \end{tabular} + \end{center} + \caption{Corrections, efficiency and intensity used in calculating the number + of X-rays from the active target.} + \label{tab:sir2_xray_corr} +\end{table} + +%In order to measure the charged particles after nuclear muon capture, one would +%pick events where the emitted particles are well separated from the +%muon stop time. The energy timing correlation plot suggests a timing window +%starting from at least 1200~ns, therefore another cut is introduced: +%\begin{enumerate} + %\setcounter{enumi}{2} + %\item there are at least two hits on the active target, the time + %difference between the second hit on target (decay or capture product) and + %the muon counter hit is at least 1300 ns: + %\begin{equation} + %t_{\textrm{target 2nd hit}} - t_{\mu\textrm{ counter}} \geq \SI{1300}{\ns} + %\label{eqn:sir2_2ndhit_cut} + %\end{equation} +%\end{enumerate} + +%The three cuts~\eqref{eqn:sir2_prompt_cut},~\eqref{eqn:sir2_muE_cut} and +%~\eqref{eqn:sir2_2ndhit_cut} reduce the sample to the size of \num{9.82E+5}. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Particle identification by specific energy loss} +\label{sec:particle_identification_by_specific_energy_loss} +In this analysis, a subset of runs from \numrange{2808}{2873} with the +100-\si{\um} aluminium target is used because of following advantages: +\begin{itemize} + \item it was easier to stop and adjust the muon stopping distribution in + this thicker target; + \item a thicker target means more stopped muons due to higher muon rate + available at higher momentum and less scattering. +\end{itemize} +Muons momentum of \SI{30.52}{\MeV\per\cc}, 3\%-FWHM spread (scaling factor of +1.09, normalised to \SI{28}{\MeV\per\cc}) were used for this target after +a momentum scanning as described in the next subsection. + +\subsection{Momentum scan for the 100-\si{\um} aluminium target} +\label{sub:momentum_scan_for_the_100_} +Before deciding to use the momentum scaling factor of 1.09, we have scanned +with momentum scales ranging from 1.04 to 1.12 to maximise the +observed X-rays rate(and hence maximising the rate of stopped muons). The X-ray +spectrum at each momentum point was accumulated in more than 30 minutes to +assure a sufficient amount of counts. Details of the scanning runs are listed +in \cref{tab:al100_scan}. +\begin{table}[htb] + \begin{center} + \begin{tabular}{cccc} + \toprule + \textbf{Momentum (\si{\MeV\per\cc})} & \textbf{Scaling factor} & \textbf{Runs} + & \textbf{Length (s)}\\ + \midrule + 29.12 & 1.04 & \numrange{2609}{2613} &2299\\ + 29.68 & 1.06 & \numrange{2602}{2608} &2563\\ + 29.96 & 1.07 & \numrange{2633}{2637} &2030\\ + 30.24 & 1.08 & \numrange{2614}{2621} &3232\\ + 30.52 & 1.09 & \numrange{2808}{2813} &2120\\ + 30.80 & 1.10 & \numrange{2625}{2632} &3234\\ + 31.36 & 1.12 & \numrange{2784}{2792} &2841\\ + \bottomrule + \end{tabular} + \end{center} + \caption{Momentum scanning runs for the 100-\si{\um} aluminium target.} + \label{tab:al100_scan} +\end{table} +The on-site quick analysis suggested the 1.09 scaling factor was the +optimal value so it was chosen for all the runs on this aluminium target. But +the offline analysis later showed that the actual optimal factor was 1.08. +There were two reasons for the mistake: +\begin{enumerate} + \item the X-ray rates were normalised to run length, which is biased + since there are more muons available at higher momentum; + \item the $(2p-1s)$ peaks of aluminium at \SI{346.828}{\keV} were not + fitted properly. The peak is interfered by a background peak at + \SI{351}{\keV} from $^{214}$Pb, but the X-ray peak area was + obtained simply by subtracting an automatically estimated background. +\end{enumerate} +In the offline analysis, the X-ray peak and the background peak are fitted by +two Gaussian peaks on top of a first-order polynomial background. The X-ray peak +area is then normalised to the number of muons hitting the upstream detector +(\cref{fig:al100_xray_fit}). +\begin{figure}[htb] + \centering + \includegraphics[width=0.47\textwidth]{figs/al100_xray_fit} + \includegraphics[width=0.47\textwidth]{figs/al100_xray_musc} + \caption{Fitting of the $(2p-1s)$ muonic X-ray of aluminium and the background + peak at \SI{351}{\keV} (left). The number of muons is integral of the + upstream scintillator spectrum (right) from \numrange{400}{2000} ADC + channels.} + \label{fig:al100_xray_fit} +\end{figure} +The ratio between the number of X-rays and the number of muons as a function +of momentum scaling factor is plotted on \cref{fig:al100_scan_rate}. The trend +showed that muons penetrated deeper as the momentum increased, reaching the +optimal value at the scale of 1.08, then decreased as punch through happened +more often from 1.09. The distributions of stopped muons are illustrated by +MC results on \cref{fig:al100_mu_stop_mc}. With the 1.09 scale beam, the muons +stopped \SI{28}{\um} off-centre to the right silicon arm. +\begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/al100_scan_rate} + \caption{Number of X-rays per incoming muon as a function of momentum + scaling factor.} + \label{fig:al100_scan_rate} +\end{figure} + +\subsection{Event selection for the passive targets} +\label{sub:event_selection_for_the_passive_targets} +As described in the \cref{sec:analysis_framework}, the hits on all detectors +are re-organised into muon events: central muons; and all hits within +\SI{\pm 10}{\us} from the central muons. The dataset from runs +\numrange{2808}{2873} contains \num{1.17E+9} such muon events. + +Selection of proton (and other heavy charged particles) events starts from +searching for muon event that has at least one hit on thick silicon. If there +is a thin silicon hit within a coincidence window of $\pm 0.5$~\si{\us}\ around +the thick silicon hit, the two hits are considered to belong to one particle. +The specific energy loss spectra recorded by the two silicon arms are plotted +on \cref{fig:al100_dedx}. +\begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/al100_dedx} + \caption{Energy loss in thin silicon detectors as a function of total energy + recorded by both thin and thick detectors.} + \label{fig:al100_dedx} +\end{figure} +With the aid from MC study (\cref{fig:pid_sim}), the banding on +\cref{fig:al100_dedx} can be identified as follows: +\begin{itemize} + \item the densest spot at the lower left conner belonged to electron hits; + \item the small blurry cloud just above the electron region was muon hits; + \item the most intense band was due to proton hits; + \item the less intense, upper band caused by deuteron hits; + \item the highest band corresponded to alpha hits; + \item the faint stripe above the deuteron band should be triton + hits, which is consistent with a relatively low probability of emission of + tritons. +\end{itemize} + +The band of protons is then extracted by cut on likelihood probability +calculated as: +\begin{equation} + p_{i} = \dfrac{1}{\sqrt{2\pi}\sigma_{\Delta E}} + e^{\frac{(\Delta E_{meas.} - \Delta E_i)^2} {2\sigma^2_{\Delta E}}} +\end{equation} +where $\Delta E_{\textrm{meas.}}$ is measured energy deposition in the thin +silicon detector by a certain proton at energy $E_i$, $\Delta E_i$ and +$\sigma_{\Delta E}$ are the expected and standard deviation of the energy loss +caused by the proton calculated by MC. A cut value of $3\sigma_{\Delta E}$, or +$p_i \ge 0.011$, was used to extract protons (\cref{fig:al100_protons}). +\begin{figure}[htb] + \centering + \includegraphics[width=0.47\textwidth]{figs/al100_protons} + \includegraphics[width=0.47\textwidth]{figs/al100_protons_px_r} + \caption{Protons (green) selected using the likelihood probability cut + (left). The proton spectrum (right) is obtained by projecting the proton + band onto the total energy axis.} + \label{fig:al100_protons} +\end{figure} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Proton emission rate from aluminium} +\label{sec:proton_emission_rate_from_aluminium} +The analysis is done on the same dataset used in +\cref{sec:particle_identification_by_specific_energy_loss}. Firstly, the +number of protons emitted is extracted using specific energy loss. Then +correction for energy loss inside the target is applied. Finally, the number +of protons is normalised to the number of nuclear muon captures. + +\subsection{Number of protons emitted} +\label{sub:number_of_protons_emitted} +From the particle identification above, number of protons having energy in the +range from \SIrange{2.2}{8.5}{\MeV} hitting the two arms are: +\begin{align} + N_{\textrm{p meas. left}} = 1789 \pm 42.3\\ + N_{\textrm{p meas. right}} = 2285 \pm 47.8 +\end{align} +The right arm received significantly more protons than the left arm did, which +is expected because in \cref{sub:momentum_scan_for_the_100_} it is shown that +muons stopped off centre to the right arm. + +The uncertainties are statistical only. The systematic uncertainties due to +the cut on protons is estimated to be small compared to the statistical ones. + +\subsection{Corrections for the number of protons} +\label{sub:corrections_for_the_number_of_protons} +The protons spectra observed by the silicon detectors have been modified by +the energy loss inside the target so correction (or unfolding) is necessary. +In the unfolding process, a response function that relates proton's true energy +and the measured one is needed. + +The response function is +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\section{Charged particles following muon capture on a thick silicon target} +%\label{sec:charged_particles_from_muon_capture_on_silicon_thick_silicon} + +%Firstly, the number of charged particles emitted after nuclear muon capture on +%the active target is calculated. The charged particles yield then is normalised +%to the number of nuclear muon capture to obtain an emission rate. +%Finally, the +%rate is compared with that from the literature. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\subsection{Number of charged particles with energy above \SI{3}{\MeV}} +%\label{sub:number_of_charged_particles_with_energy_from_8_10_mev} +%As shown in \cref{fig:sir2_1us_slices} and illustrated by MC simulation +%in \cref{fig:sir2_mc_pdfs}, there are several components in +%the energy spectrum recorded by the active target: +%\begin{enumerate} + %\item charged particles from nuclear muon capture, this is the signal of + %interest; + %\item beam electrons with a characteristic Landau peak around \SI{800}{\keV}, + %dominating at large delay (from \SI{6500}{\ns}), causing background at + %energy lower than \SI{1}{\MeV} which drops sharply at energy larger than + %\SI{3}{\MeV}; + %\item electrons from muon decay-in-orbit (DIO) and recoiled nuclei + %from neutron emitting muon captures, peak at + %around \SI{300}{\keV}, dominate the region where energy smaller than + %\SI{1}{\MeV} and delay less than \SI{3500}{\ns}. This component is + %intrinsic background, having the same time structure as that of the signal; + %\item stray muons scattered into the target, this component is small compares + %to the charged particles yield so it is not considered further. +%\end{enumerate} +%\begin{figure}[htb] + %\centering + %\includegraphics[width=0.45\textwidth]{figs/sir2_meas_spec} + %\includegraphics[width=0.45\textwidth]{figs/sir2_mc_pdfs} + %\caption{The observed spectrum in the timing window 1300 -- 10000~ns (left) + %and its components from MC simulation (right). The charged particles + %spectrum is obtained assuming the spectrum shape and emission rate from + %Sobottka and Wills~\cite{SobottkaWills.1968}. The relative scales between + %components are arbitrarily chosen for the purpose of illustration.} + %\label{fig:sir2_mc_pdfs} +%\end{figure} + +%An energy cut at \SI{2}{\MeV} is introduced to avoid the domination of the +%beam electrons at low energy. In order to obtain the yields of backgrounds +%above \SI{2}{\MeV}, a binned maximum likelihood fit was done. The likelihood of +%getting the measured spectrum is defined as: +%\begin{equation} + %L = \frac{e^{-\mu}\mu^n}{n!}\prod_i \frac{\mu_i^{n_i} e^{-\mu_i}}{n_i!} + %\label{eqn:llh_def} +%\end{equation} +%where $n$ is the total number of events observed, $\mu$ is the expected number +%of events according to some linear combination of the signal and the +%backgrounds shown in~\ref{fig:sir2_mc_pdfs}, namely: +%\begin{align} + %n &= n_{\textrm{sig}} + n_{\textrm{beam e}} + n_{\textrm{dio}}\\ + %\textrm{(sum pdf)} &= n_{\textrm{sig}}\times\textrm{(sig pdf)} + + %n_{\textrm{beam e}}\times\textrm{(beam e pdf)} + + %n_{\textrm{dio}}\times\textrm{(dio pdf)}; + %\label{eqn:sum_pdf} +%\end{align} +%and the $i$ index indicates the respective number of events in the $i$-th +%bin. + +%The fit is done by the RooFit package~\cite{VerkerkeKirkby.2003} where the +%negative log likelihood $-2\ln{L}$ is minimised. Fitting results are shown +%in~\ref{fig:sir2_mll_fit}, the yields of backgrounds and signal are: +%\begin{align} + %n_{\textrm{beam e}} &= 23756 \pm 581\\ + %n_{\textrm{dio}} &= 111340 \pm 1245\\ + %n_{\textrm{sig}} &= 2.57 \pm 856 + %\label{eqn:sir2_n_chargedparticles} +%\end{align} +%\begin{figure}[htb] + %\centering + %\includegraphics[width=0.42\textwidth]{figs/sir2_mllfit_nbkg} + %\includegraphics[width=0.42\textwidth]{figs/sir2_mllfit_nebeam} + %\includegraphics[width=0.84\textwidth]{figs/sir2_mllfit} + %\caption{Results of the maximum likelihood fit of the energy spectrum on the + %active target.} + %\label{fig:sir2_mll_fit} +%\end{figure} + +% subsection number_of_charged_particles_with_energy_from_8_10_mev (end) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\subsection{Number of nuclear muon captures} +%\label{sub:number_of_stopped_muons} + %The area of the $(2p-1s)$ peak is $N_{(2p-1s)} = 2981.5 \pm 65.6$, %obtained by subtracting the background of 101.5 from the spectral integral of %2083 in the region from 396 to 402 keV. %The area of the $(2p-1s)$ peak is $2929.7 \pm 56.4$ obtained by fitting %a Gaussian peak on top of a first-order polynomial background to the spectrum %in \cref{fgi:sir2_xray} in the region from \SIrange{395}{405}{\keV}. -Using the same procedure of fitting and correcting described in -\cref{sub:germanium_detector}, the number of X-rays is calculated to be 370. -Details of the correction factors are given in \cref{tab:sir2_xray_corr}. -\begin{table}[htb] - \begin{center} - \begin{tabular}{l} - \toprule - \textbf{Col1}\\ - \midrule - item1\\ - \bottomrule - \end{tabular} - \end{center} - \caption{Corrections for the number of X-rays from the active target.} - \label{tab:sir2_xray_corr} -\end{table} -The X-ray intensity in \cref{tab:mucap_pars} was normalised to the number of -stopped muons, so the number of stopped muons is: +%The X-ray intensity in \cref{tab:mucap_pars} was normalised to the number of +%stopped muons, so the number of stopped muons is: -\begin{align} - N_{\mu\textrm{ stopped}} &= - \dfrac{N_{(2p-1s)}}{\epsilon_{2p-1s}\times I_{(2p-1s)}}\nonumber\\ - &= \dfrac{370}{4.38\times10^{-4} \times 0.803} \\ - &= 1.05\times10^6 \nonumber -\end{align} -where $\epsilon_{(2p-1s)}$ is the calibrated absolute efficiency of the -detector for the 400.177~keV line in \cref{tab:xray_eff}, and -$I_{(2p-1s)}$ is the probability of emitting this X-ray per stopped muon -(80.3\% from \cref{tab:mucap_pars}). +%\begin{align} + %N_{\mu\textrm{ stopped}} &= + %\dfrac{N_{(2p-1s)}}{\epsilon_{2p-1s}\times I_{(2p-1s)}}\nonumber\\ + %&= \dfrac{370}{4.38\times10^{-4} \times 0.803} \\ + %&= 1.05\times10^6 \nonumber +%\end{align} +%where $\epsilon_{(2p-1s)}$ is the calibrated absolute efficiency of the +%detector for the 400.177~keV line in \cref{tab:xray_eff}, and +%$I_{(2p-1s)}$ is the probability of emitting this X-ray per stopped muon +%(80.3\% from \cref{tab:mucap_pars}). -Taking the statistical uncertainty of the peak area, and systematic -uncertainties from parameters of muon capture, the number of stopped muons -calculated from the X-ray measurement is -$(10.50 \pm 0.65)\times 10^5$. This figure is consistent with the number of -stopped muons of $9.82\times10^5$ after the cuts described in the event -selection process. +%Taking the statistical uncertainty of the peak area, and systematic +%uncertainties from parameters of muon capture, the number of stopped muons +%calculated from the X-ray measurement is +%$(10.50 \pm 0.65)\times 10^5$. This figure is consistent with the number of +%stopped muons of $9.82\times10^5$ after the cuts described in the event +%selection process. -The number of nuclear captured muons is: -\begin{equation} - N_{\mu\textrm{ nucl.capture}} = - N_{\mu\textrm{ stopped}}\times f_{\textrm{cap.Si}} - = 10.05 \times 10^5 \times 0.658 = 6.91 \times 10^5 - \label{eqn:sir2_Ncapture} -\end{equation} -where the $f_{\textrm{cap.Si}}$ is the probability of nuclear capture per -stopped muon from \cref{tab:mucap_pars}. +%The number of nuclear captured muons is: +%\begin{equation} + %N_{\mu\textrm{ nucl.capture}} = + %N_{\mu\textrm{ stopped}}\times f_{\textrm{cap.Si}} + %= 10.05 \times 10^5 \times 0.658 = 6.91 \times 10^5 + %\label{eqn:sir2_Ncapture} +%\end{equation} +%where the $f_{\textrm{cap.Si}}$ is the probability of nuclear capture per +%stopped muon from \cref{tab:mucap_pars}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Emission rate of charged particles} -\label{sub:emission_rate_of_charged_particles} -The emission rate of charged particles is calculated by taking the ratio of -number of charged particles in ~\eqref{eqn:sir2_Nchargedparticle} and number of -nuclear muon capture in~\eqref{eqn:sir2_Ncapture}: -\begin{equation} - R_{\textrm{Si}} = \frac{N_{\textrm{charged particle}}}{N_{\mu\textrm{ nucl.capture}}} - = \frac{149.9\times10^4}{7.25\times10^6} = 0.252 -\end{equation} -Uncertainties of this rate calculation are listed in -\cref{tab:sir2_uncertainties}, including: -\begin{itemize} - \item uncertainties from number of charged particles, both statistical and - systematic (from spectrum shape and fitting) ones are absorbed in the - quoted value in~\eqref{sir2_Nchargedparticle}; - \item uncertainties from number of nuclear capture: - \begin{itemize} - \item statistical error of the peak area calculation, - \item systematic errors from the efficiency calibration, and referenced - values of X-ray intensity and capture probability. - \end{itemize} -\end{itemize} -So, the emission rate is: -\begin{equation} - R_{\textrm{Si}} = 0.252 \pm 0.009 - \label{eqn:sir2_rate_cal} -\end{equation} +%\subsection{Emission rate of charged particles} +%\label{sub:emission_rate_of_charged_particles} +%The emission rate of charged particles is calculated by taking the ratio of +%number of charged particles in ~\eqref{eqn:sir2_Nchargedparticle} and number of +%nuclear muon capture in~\eqref{eqn:sir2_Ncapture}: +%\begin{equation} + %R_{\textrm{Si}} = \frac{N_{\textrm{charged particle}}}{N_{\mu\textrm{ nucl.capture}}} + %= \frac{149.9\times10^4}{7.25\times10^6} = 0.252 +%\end{equation} +%Uncertainties of this rate calculation are listed in +%\cref{tab:sir2_uncertainties}, including: +%\begin{itemize} + %\item uncertainties from number of charged particles, both statistical and + %systematic (from spectrum shape and fitting) ones are absorbed in the + %quoted value in~\eqref{sir2_Nchargedparticle}; + %\item uncertainties from number of nuclear capture: + %\begin{itemize} + %\item statistical error of the peak area calculation, + %\item systematic errors from the efficiency calibration, and referenced + %values of X-ray intensity and capture probability. + %\end{itemize} +%\end{itemize} +%So, the emission rate is: +%\begin{equation} + %R_{\textrm{Si}} = 0.252 \pm 0.009 + %\label{eqn:sir2_rate_cal} +%\end{equation} -\begin{table}[htb] - \begin{center} - \begin{tabular}{l l l} - \toprule - %\textbf{Source} & \textbf{Type} & \textbf{Relative error}\\ - Number of charged particles & &\\ - Statistical and systematic & &0.004\\ - \midrule - Number of nuclear capture & &\\ - Statistical & Peak area calculation& 0.022\\ - Systematic & Efficiency calibration & 0.024\\ - & X-ray intensity & 0.009\\ - & Capture probability & 0\\ +%\begin{table}[htb] + %\begin{center} + %\begin{tabular}{l l l} + %\toprule + %Number of charged particles & &\\ + %Statistical and systematic & &0.004\\ + %\midrule + %Number of nuclear capture & &\\ + %Statistical & Peak area calculation& 0.022\\ + %Systematic & Efficiency calibration & 0.024\\ + %& X-ray intensity & 0.009\\ + %& Capture probability & 0\\ - \midrule - Total relative error & & 0.035\\ - Total absolute error & & 0.009\\ + %\midrule + %Total relative error & & 0.035\\ + %Total absolute error & & 0.009\\ - \bottomrule - \end{tabular} - \end{center} - \caption{Uncertainties of the emission rate from the thick silicon target} - \label{tab:sir2_uncertainties} -\end{table} + %\bottomrule + %\end{tabular} + %\end{center} + %\caption{Uncertainties of the emission rate from the thick silicon target} + %\label{tab:sir2_uncertainties} +%\end{table} % subsection partial_emission_rate_of_charged_particle_in_8_10_mev_range (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/thesis/figs/sir2_ges_self_tdiff.png b/thesis/figs/sir2_ges_self_tdiff.png new file mode 100644 index 0000000000000000000000000000000000000000..ff592b8d1cde5ddf61994dce3a9d807ca5109509 GIT binary patch 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a/thesis/thesis.tex b/thesis/thesis.tex index ac73cc3..9aa2d7b 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -32,8 +32,8 @@ for the COMET experiment} %\input{chapters/chap1_intro} %\input{chapters/chap2_mu_e_conv} %\input{chapters/chap3_comet} -\input{chapters/chap4_alcap_phys} -\input{chapters/chap5_alcap_setup} +%\input{chapters/chap4_alcap_phys} +%\input{chapters/chap5_alcap_setup} \input{chapters/chap6_analysis} %\input{chapters/chap7_results} From c7cad3f7925ef35d8432a7e95e26cc518aecef97 Mon Sep 17 00:00:00 2001 From: nam Date: Wed, 15 Oct 2014 10:14:16 +0900 Subject: [PATCH 09/26] prog saved --- thesis/chapters/chap6_analysis.tex | 776 +----------------- thesis/figs/al100_dedx.pdf | Bin 0 -> 57460 bytes thesis/figs/al100_ge_spec.pdf | Bin 0 -> 20322 bytes thesis/figs/al100_mu_stop_mc.pdf | Bin 0 -> 15897 bytes thesis/figs/al100_proton_lifetime.pdf | Bin 0 -> 19059 bytes thesis/figs/al100_proton_lifetime_sil11.pdf | Bin 0 -> 71445 bytes 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100644 thesis/figs/al100_dedx.pdf create mode 100644 thesis/figs/al100_ge_spec.pdf create mode 100644 thesis/figs/al100_mu_stop_mc.pdf create mode 100644 thesis/figs/al100_proton_lifetime.pdf create mode 100644 thesis/figs/al100_proton_lifetime_sil11.pdf create mode 100644 thesis/figs/al100_proton_lifetime_wosil11.pdf create mode 100644 thesis/figs/al100_proton_spec.pdf create mode 100644 thesis/figs/al100_proton_spec_wosil11.pdf create mode 100644 thesis/figs/al100_protons.pdf create mode 100644 thesis/figs/al100_protons_px_r.pdf create mode 100644 thesis/figs/al100_resp.pdf create mode 100644 thesis/figs/al100_scan_rate.pdf create mode 100644 thesis/figs/al100_selection.pdf create mode 100644 thesis/figs/al100_xray_fit.pdf create mode 100644 thesis/figs/al100_xray_musc.pdf create mode 100644 thesis/figs/alcapdaq_pcs.pdf create mode 100644 thesis/figs/alcapdaq_scheme.pdf create mode 100644 thesis/figs/analysis_scheme.pdf create mode 100644 thesis/figs/beam.pdf create mode 100644 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mode 100644 thesis/figs/si16_xray.pdf create mode 100644 thesis/figs/si16p_allparticle_lifetime.pdf create mode 100644 thesis/figs/si16p_dedx.pdf create mode 100644 thesis/figs/si16p_dedx_cut.pdf create mode 100644 thesis/figs/si16p_dedx_log.pdf create mode 100644 thesis/figs/si16p_dedx_loge+logde.pdf create mode 100644 thesis/figs/si16p_dedx_nocut_log.pdf create mode 100644 thesis/figs/si16p_dedx_proton_select.pdf create mode 100644 thesis/figs/si16p_loge+logde.pdf create mode 100644 thesis/figs/si16p_proton_after_ecut.pdf create mode 100644 thesis/figs/si16p_proton_ecut_500nstcut.pdf create mode 100644 thesis/figs/si16p_proton_lifetime copy.pdf create mode 100644 thesis/figs/si16p_proton_lifetime.pdf create mode 100644 thesis/figs/si16p_toyMC.pdf create mode 100644 thesis/figs/si16p_xray.pdf create mode 100644 thesis/figs/sir2_bias_alpha.pdf create mode 100644 thesis/figs/sir2_edep.pdf create mode 100644 thesis/figs/sir2_edep_components.pdf create mode 100644 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b4eb45b..ea806d0 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -287,13 +287,16 @@ of momentum scaling factor is plotted on \cref{fig:al100_scan_rate}. The trend showed that muons penetrated deeper as the momentum increased, reaching the optimal value at the scale of 1.08, then decreased as punch through happened more often from 1.09. The distributions of stopped muons are illustrated by -MC results on \cref{fig:al100_mu_stop_mc}. With the 1.09 scale beam, the muons -stopped \SI{28}{\um} off-centre to the right silicon arm. +MC results on the right hand side of \cref{fig:al100_scan_rate}. With the 1.09 +scale beam, the muons stopped \SI{28}{\um} off-centre to the right silicon arm. \begin{figure}[htb] \centering - \includegraphics[width=0.85\textwidth]{figs/al100_scan_rate} + \includegraphics[width=0.47\textwidth]{figs/al100_scan_rate} + \includegraphics[width=0.47\textwidth]{figs/al100_mu_stop_mc} \caption{Number of X-rays per incoming muon as a function of momentum - scaling factor.} + scaling factor (left); and muon stopping distributions from MC simulation + (right). The depth of muons is measured normal to surface of the target + facing the muon beam.} \label{fig:al100_scan_rate} \end{figure} @@ -365,13 +368,14 @@ of protons is normalised to the number of nuclear muon captures. From the particle identification above, number of protons having energy in the range from \SIrange{2.2}{8.5}{\MeV} hitting the two arms are: \begin{align} - N_{\textrm{p meas. left}} = 1789 \pm 42.3\\ - N_{\textrm{p meas. right}} = 2285 \pm 47.8 + N_{\textrm{p meas. left}} = 1822 \pm 42.7\\ + N_{\textrm{p meas. right}} = 2373 \pm 48.7 \end{align} The right arm received significantly more protons than the left arm did, which -is expected because in \cref{sub:momentum_scan_for_the_100_} it is shown that +is expected as in \cref{sub:momentum_scan_for_the_100_} it is shown that muons stopped off centre to the right arm. +%%TODO The uncertainties are statistical only. The systematic uncertainties due to the cut on protons is estimated to be small compared to the statistical ones. @@ -379,742 +383,34 @@ the cut on protons is estimated to be small compared to the statistical ones. \label{sub:corrections_for_the_number_of_protons} The protons spectra observed by the silicon detectors have been modified by the energy loss inside the target so correction (or unfolding) is necessary. -In the unfolding process, a response function that relates proton's true energy -and the measured one is needed. +The unfolding, essentially, is finding a response function that relates proton's +true energy and measured value. This can be done in MC simulation by generating +protons with a spatial distribution as close as possible to the real +distribution of muons inside the target, then counting the number of protons +reaching the silicon detectors. Such response function conveniently includes +the geometrical acceptance. -The response function is -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\section{Charged particles following muon capture on a thick silicon target} -%\label{sec:charged_particles_from_muon_capture_on_silicon_thick_silicon} - -%Firstly, the number of charged particles emitted after nuclear muon capture on -%the active target is calculated. The charged particles yield then is normalised -%to the number of nuclear muon capture to obtain an emission rate. -%Finally, the -%rate is compared with that from the literature. - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\subsection{Number of charged particles with energy above \SI{3}{\MeV}} -%\label{sub:number_of_charged_particles_with_energy_from_8_10_mev} -%As shown in \cref{fig:sir2_1us_slices} and illustrated by MC simulation -%in \cref{fig:sir2_mc_pdfs}, there are several components in -%the energy spectrum recorded by the active target: -%\begin{enumerate} - %\item charged particles from nuclear muon capture, this is the signal of - %interest; - %\item beam electrons with a characteristic Landau peak around \SI{800}{\keV}, - %dominating at large delay (from \SI{6500}{\ns}), causing background at - %energy lower than \SI{1}{\MeV} which drops sharply at energy larger than - %\SI{3}{\MeV}; - %\item electrons from muon decay-in-orbit (DIO) and recoiled nuclei - %from neutron emitting muon captures, peak at - %around \SI{300}{\keV}, dominate the region where energy smaller than - %\SI{1}{\MeV} and delay less than \SI{3500}{\ns}. This component is - %intrinsic background, having the same time structure as that of the signal; - %\item stray muons scattered into the target, this component is small compares - %to the charged particles yield so it is not considered further. -%\end{enumerate} -%\begin{figure}[htb] - %\centering - %\includegraphics[width=0.45\textwidth]{figs/sir2_meas_spec} - %\includegraphics[width=0.45\textwidth]{figs/sir2_mc_pdfs} - %\caption{The observed spectrum in the timing window 1300 -- 10000~ns (left) - %and its components from MC simulation (right). The charged particles - %spectrum is obtained assuming the spectrum shape and emission rate from - %Sobottka and Wills~\cite{SobottkaWills.1968}. The relative scales between - %components are arbitrarily chosen for the purpose of illustration.} - %\label{fig:sir2_mc_pdfs} -%\end{figure} - -%An energy cut at \SI{2}{\MeV} is introduced to avoid the domination of the -%beam electrons at low energy. In order to obtain the yields of backgrounds -%above \SI{2}{\MeV}, a binned maximum likelihood fit was done. The likelihood of -%getting the measured spectrum is defined as: -%\begin{equation} - %L = \frac{e^{-\mu}\mu^n}{n!}\prod_i \frac{\mu_i^{n_i} e^{-\mu_i}}{n_i!} - %\label{eqn:llh_def} -%\end{equation} -%where $n$ is the total number of events observed, $\mu$ is the expected number -%of events according to some linear combination of the signal and the -%backgrounds shown in~\ref{fig:sir2_mc_pdfs}, namely: -%\begin{align} - %n &= n_{\textrm{sig}} + n_{\textrm{beam e}} + n_{\textrm{dio}}\\ - %\textrm{(sum pdf)} &= n_{\textrm{sig}}\times\textrm{(sig pdf)} + - %n_{\textrm{beam e}}\times\textrm{(beam e pdf)} + - %n_{\textrm{dio}}\times\textrm{(dio pdf)}; - %\label{eqn:sum_pdf} -%\end{align} -%and the $i$ index indicates the respective number of events in the $i$-th -%bin. - -%The fit is done by the RooFit package~\cite{VerkerkeKirkby.2003} where the -%negative log likelihood $-2\ln{L}$ is minimised. Fitting results are shown -%in~\ref{fig:sir2_mll_fit}, the yields of backgrounds and signal are: -%\begin{align} - %n_{\textrm{beam e}} &= 23756 \pm 581\\ - %n_{\textrm{dio}} &= 111340 \pm 1245\\ - %n_{\textrm{sig}} &= 2.57 \pm 856 - %\label{eqn:sir2_n_chargedparticles} -%\end{align} -%\begin{figure}[htb] - %\centering - %\includegraphics[width=0.42\textwidth]{figs/sir2_mllfit_nbkg} - %\includegraphics[width=0.42\textwidth]{figs/sir2_mllfit_nebeam} - %\includegraphics[width=0.84\textwidth]{figs/sir2_mllfit} - %\caption{Results of the maximum likelihood fit of the energy spectrum on the - %active target.} - %\label{fig:sir2_mll_fit} -%\end{figure} - -% subsection number_of_charged_particles_with_energy_from_8_10_mev (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\subsection{Number of nuclear muon captures} -%\label{sub:number_of_stopped_muons} - -%The area of the $(2p-1s)$ peak is $N_{(2p-1s)} = 2981.5 \pm 65.6$, -%obtained by subtracting the background of 101.5 from the spectral integral of -%2083 in the region from 396 to 402 keV. -%The area of the $(2p-1s)$ peak is $2929.7 \pm 56.4$ obtained by fitting -%a Gaussian peak on top of a first-order polynomial background to the spectrum -%in \cref{fgi:sir2_xray} in the region from \SIrange{395}{405}{\keV}. - -%The X-ray intensity in \cref{tab:mucap_pars} was normalised to the number of -%stopped muons, so the number of stopped muons is: - -%\begin{align} - %N_{\mu\textrm{ stopped}} &= - %\dfrac{N_{(2p-1s)}}{\epsilon_{2p-1s}\times I_{(2p-1s)}}\nonumber\\ - %&= \dfrac{370}{4.38\times10^{-4} \times 0.803} \\ - %&= 1.05\times10^6 \nonumber -%\end{align} -%where $\epsilon_{(2p-1s)}$ is the calibrated absolute efficiency of the -%detector for the 400.177~keV line in \cref{tab:xray_eff}, and -%$I_{(2p-1s)}$ is the probability of emitting this X-ray per stopped muon -%(80.3\% from \cref{tab:mucap_pars}). - -%Taking the statistical uncertainty of the peak area, and systematic -%uncertainties from parameters of muon capture, the number of stopped muons -%calculated from the X-ray measurement is -%$(10.50 \pm 0.65)\times 10^5$. This figure is consistent with the number of -%stopped muons of $9.82\times10^5$ after the cuts described in the event -%selection process. - -%The number of nuclear captured muons is: -%\begin{equation} - %N_{\mu\textrm{ nucl.capture}} = - %N_{\mu\textrm{ stopped}}\times f_{\textrm{cap.Si}} - %= 10.05 \times 10^5 \times 0.658 = 6.91 \times 10^5 - %\label{eqn:sir2_Ncapture} -%\end{equation} -%where the $f_{\textrm{cap.Si}}$ is the probability of nuclear capture per -%stopped muon from \cref{tab:mucap_pars}. -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\subsection{Emission rate of charged particles} -%\label{sub:emission_rate_of_charged_particles} -%The emission rate of charged particles is calculated by taking the ratio of -%number of charged particles in ~\eqref{eqn:sir2_Nchargedparticle} and number of -%nuclear muon capture in~\eqref{eqn:sir2_Ncapture}: -%\begin{equation} - %R_{\textrm{Si}} = \frac{N_{\textrm{charged particle}}}{N_{\mu\textrm{ nucl.capture}}} - %= \frac{149.9\times10^4}{7.25\times10^6} = 0.252 -%\end{equation} -%Uncertainties of this rate calculation are listed in -%\cref{tab:sir2_uncertainties}, including: -%\begin{itemize} - %\item uncertainties from number of charged particles, both statistical and - %systematic (from spectrum shape and fitting) ones are absorbed in the - %quoted value in~\eqref{sir2_Nchargedparticle}; - %\item uncertainties from number of nuclear capture: - %\begin{itemize} - %\item statistical error of the peak area calculation, - %\item systematic errors from the efficiency calibration, and referenced - %values of X-ray intensity and capture probability. - %\end{itemize} -%\end{itemize} -%So, the emission rate is: -%\begin{equation} - %R_{\textrm{Si}} = 0.252 \pm 0.009 - %\label{eqn:sir2_rate_cal} -%\end{equation} - -%\begin{table}[htb] - %\begin{center} - %\begin{tabular}{l l l} - %\toprule - %Number of charged particles & &\\ - %Statistical and systematic & &0.004\\ - %\midrule - %Number of nuclear capture & &\\ - %Statistical & Peak area calculation& 0.022\\ - %Systematic & Efficiency calibration & 0.024\\ - %& X-ray intensity & 0.009\\ - %& Capture probability & 0\\ - - %\midrule - %Total relative error & & 0.035\\ - %Total absolute error & & 0.009\\ - - %\bottomrule - %\end{tabular} - %\end{center} - %\caption{Uncertainties of the emission rate from the thick silicon target} - %\label{tab:sir2_uncertainties} -%\end{table} - -% subsection partial_emission_rate_of_charged_particle_in_8_10_mev_range (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%TODO -%\subsection{Partial emission rate of charged particles from the literature} -%\label{sub:partial_emission_rate_of_charged_particles_from_the_literature} -%\begin{figure}[htb] - %\centering - %\includegraphics[width=0.85\textwidth]{figs/sobottka_spec2} - %\caption{Reproduced charged particle spectrum from muon capture on silicon, - %measured by Sobottka and Wills. Integration region is shown in the green - %box.} - %\label{fig:sobottka_spec} -%\end{figure} -%The spectrum measured by Sobottka and Wills~\cite{SobottkaWills.1968} is -%reproduced in \cref{fig:sobottka_spec}, the spectral integral in the -%energy region from 8 to 10~\si{\MeV}\ is $2086.8 \pm 45.7$. -%The authors obtained the spectrum in a 4~\si{\us}\ gate period which began -%1~\si{\us}\ after a muon stopped, which would take 26.59\% of the emitted -%particles into account. The number of stopped muons was not explicitly stated, -%but can be inferred to be $55715/0.06 = 92858.3$. - -%The partial rate of charged particle from 8 to 10~\si{\MeV}\ is then -%calculated to be: -%\begin{equation} - %R_{\textrm{8-10 MeV}}^{lit.} = - %\dfrac{2086.8}{0.2659 \times 92858.3 \times 0.658} - %= 1.28 \times 10^{-2} -%\end{equation} -%The authors did not mentioned how the uncertainties of their measurement was -%derived, but quoted the emission rate below 26~\si{\MeV}\ to be $0.15 -%\pm 0.02$, which translates to a relative uncertainty of 0.133. The statistical -%uncertainty from the spectral integral and the number of stopped muons is: -%\begin{equation*} - %\dfrac{1}{\sqrt{25000}} + \dfrac{1}{\sqrt{92858.3}} = 0.9 \times 10^{-2} -%\end{equation*} -%Then their systematic uncertainty would be: $0.133 - 0.009 = 0.124$. - -%For the partial spectrum from 8 to 10~\si{\MeV}, the statistical -%contribution to the uncertainty is: -%\begin{equation*} - %\dfrac{1}{\sqrt{2086.8}} + \dfrac{1}{\sqrt{92858.3}} = 2.5 \times 10^{-2} -%\end{equation*} -%So, the combined uncertainty of this partial rate calculation is: $0.124 -%+ 0.025 = 0.150$. The partial rate of charged particles from 8 to -%10~\si{\MeV} per muon capture is: -%\begin{equation} - %R_{\textrm{8-10 MeV}}^{lit.} = (1.28 \pm 0.19) \times 10^{-2} -%\end{equation} -% subsection partial_emission_rate_of_charged_particles_from_the_literature -% (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Charged particles following muon capture on a thin silicon target} -\label{sec:charged_particles_following_muon_capture_on_a_thin_silicon_target} -In this measurement, a passive, 62-\si{\um}-thick silicon target was used as the -target. The silicon target is $5\times5$~\si{\centi\meter}$^2$ in area. The muon -momentum was chosen to be 1.06 after a scanning to maximise the stopping ratio. -The charged particles were measured by two arms of silicon detectors. The -plastic scintillators vetoing information were not used. - -This data set consists of 66 runs, from 3474--3489 and 3491--3540. -Although there are a few issues found in the process of data quality -checking such as one very noisy timing channel, and several runs had -abnormally high rates, the whole data set is determined to be good. Without -an active target and veto, the muon signal is from the muon counter only. The -tree contains total $1.452 \times 10^8$ muon events. %145212698 -\begin{figure}[htb] - \centering - \includegraphics[width=0.49\textwidth]{figs/si16_lldq_noise} - \includegraphics[width=0.49\textwidth]{figs/si16_lldq_islandrate} - \caption{Oddities found in checking data quality: noise level on timing - output of the SiL1-2 was much higher than the other detectors, and some - runs show large pulse rate.} - \label{fig:si16_lldq} -\end{figure} - -\subsection{Particle identification by dE/dx and proton selection} -\label{sub:particle_identification_by_de_dx} -%All silicon hits with energy deposition larger than -%200~\si{\keV}\ that happened within $\pm 10$~\si{\us}\ of the -%muon hit are then -%associated to the muon and stored in the muon event tree. The -%200~\si{\keV}\ cut effectively rejects all MIPs hits on thin silicon -%detectors of which the most probable value is about 40~\si{\keV}. - -%In order to use dE/dx for particle identification, $\Delta$E and total E are -%needed. -The charged particle selection starts from searching for muon event -that has at least one hit on thick silicon. If there is a thin silicon hit -within a coincidence window of $\pm 0.5$~\si{\us}\ around the thick -silicon hit, the two hits are considered to belong to one particle with -$\Delta$E being the energy of the thin hit, and total E being the sum energy of -the two hits. Particle identification is done using correlation between -$\Delta$E and E. \cref{fig:si16p_dedx_nocut} shows clearly visible banding -structure. No cut on energy deposit or timing with respect to muon hit are -applied yet. - -With the aid from MC study (\cref{fig:pid_sim}), the banding on the -$\Delta$E-E plots can be identified as follows: +For the 100-\si{\um} aluminium target and muons at the momentum scale of 1.09, +the parameters of the initial protons are: \begin{itemize} - \item the densest spot at the lower left conner belonged to electron hits; - \item the small blurry cloud just above the electron region was muon hits; - \item the most intense band was due to proton hits; - \item the less intense, upper band caused by deuteron hits; - \item the highest band corresponded to alpha hits; - \item the faint stripe above the deuteron band should be triton - hits, which is consistent with a relatively low probability of emission of - tritons. + \item horizontal distribution: Gaussian \SI{26}{\mm} FWHM, centred at the + centre of the target; + \item vertical distribution: Gaussian \SI{15}{\mm} FWHM, centred at the + centre of the target; + \item depth: Gaussian \SI{69.2}{\um} FWHM, centred at \SI{68.8}{\um}-deep from + the upstream face of the target; + \item energy: flatly distributed from \SIrange{1.5}{15}{\MeV}. \end{itemize} - -%The electrons either from Michel decay or from the beam are MIPs particles, -%which would deposit about 466~keV on the 1500-\si{\um}-thick silicon detector, -%and about 20~keV on the 65-\si{\um}-thick silicon detector. Therefore our thin -%silicon counters could not distinguish electrons from electronic -%noise. The brightest spots on the $\Delta$E-E plots are identified as electrons -%due to -%the total E of about 500~keV, and is the accidental coincidence between -%electron hits on the thick silicon and electronics noise on the thin silicon. - +The resulting response matrices for the two arms are presented in +\cref{fig:al100_resp_matrices}. These are then used as MC truth to train and +test the unfolding code. The code uses an existing ROOT package +called RooUnfold~\cite{Adye.2011} where the iterative Bayesian unfolding +method is implemented. \begin{figure}[htb] \centering - \includegraphics[width=0.95\textwidth]{figs/si16p_dedx_nocut} - \caption{$\Delta$E as a function of E of particles from muon capture on the - thin silicon target.} - \label{fig:si16p_dedx_nocut} + \includegraphics[width=0.85\textwidth]{./figs/al100_resp} + \caption{Response functions for the two silicon arms.} + \label{fig:al100_resp_matrices} \end{figure} - -It is observed that the banding is more clearly visible in a log-log scale -plots like in \cref{fig:si16p_dedx_cut_explain}, this suggests -a geometrical cut on the logarithmic scale would be able to discriminate -protons from other particles. The protons and deuterons bands are nearly -parallel to the $\ln(\Delta \textrm{E [keV]}) + \ln(\textrm{E [keV]})$ line, -but have a slightly altered slope because $\ln(\textrm{E})$ is always greater -than $\ln(\Delta\textrm{E})$. The two parallel lines on -\cref{fig:si16p_dedx_cut_explain} suggest a check of -$\ln(\textrm{E}) + 0.85\times\ln(\Delta \textrm{E})$ could tell -protons from other particles. - -Another feature of the $\Delta$E-E plots is their resolution power for protons -decrease as the energy E increases. The reason for this is the limited energy -resolution of the silicon detectors in use. The plots in logarithmic scale -show that this particle identification is good in the region where -$\ln(\textrm{E}) < 9$, which corresponds to $\textrm{E} < 8$~MeV. -\begin{figure}[htb] - \centering - \includegraphics[width=0.95\textwidth]{figs/si16p_dedx_cut} - \caption{$\Delta$E-E plots in the logarithmic scale and the geometrical cuts - for protons.} - \label{fig:si16p_dedx_nocut_log} -\end{figure} - -The cut of $\ln(\textrm{E}) < 9$ is applied first, then -$\ln(\textrm{E})+ 0.85\times\ln(\Delta \textrm{E}) $ is plotted as -\cref{fig:si16p_loge+logde}. The protons make a clear peak in the region -between 14 and 14.8, the next peak at 15 corresponds to deuteron. -Imposing the -$14<\ln(\textrm{E})+ 0.85\times\ln(\Delta \textrm{E})<14.8$ cut, -the remaining proton band is shown on \cref{fig:si16p_proton_after_ecut}. - -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/si16p_dedx_loge+logde} - \caption{Rationale for the cut on $\ln(\textrm{E})$ and $\ln(\Delta - \textrm{E})$} - \label{fig:si16p_loge+logde} -\end{figure} - -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/si16p_proton_after_ecut} - \caption{Proton bands after cuts on energy} - \label{fig:si16p_proton_after_ecut} -\end{figure} - -% subsection particle_identification_by_de_dx (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Number of muon captures} -\label{sub:number_stopped_muons} -The X-ray spectrum from this silicon target on \cref{fig:si16_xray} is -significantly noisier than the previous data set of SiR2, suffers from both -lower statistics and a more relaxed muon definition. The peak of $(2p-1s)$ -X-ray at 400.177~keV can still be recognised but on a very high background. The -same timing requirement for the hit timing on the germanium detector as -in~\eqref{eqn:sir2_ge_cut}. - -The double peaks of muonic X-rays from the lead shield at 431 and 438~keV are -very intense, reflects the fact that the low momentum muon beam of -29.68~MeV\cc\ (scaling factor 1.06) was strongly scattered by the upstream -counters. After a prompt cut that requires the photon -hit occured in $\pm 1$~\si{\us}\ around the muon hit, the peaks from lead -remain prominent which is an expected result because of all the lead shield -inside the chamber was to capture stray muons. The cut shows its effect on -reducing the background level under the 400.177 keV peak by about one third. - -\begin{figure}[htb] - \centering - \includegraphics[width=0.98\textwidth]{figs/si16p_xray} - \caption{X-ray spectrum from the passive 62-\si{\um}-thick silicon target with - and with out timing cut.} - \label{fig:si16_xray} -\end{figure} - -Using the same procedure on the region from 396 to 402 keV (without -self-absorption correction since this is a thin target), the number of -X-rays recorded and the number of captures are shown in -\cref{tab:si16p_ncapture_cal}. -\begin{table}[htb] - \begin{center} - \begin{tabular}{l l c c c} - \toprule - \textbf{Source}& \textbf{Quantity}& \textbf{Value} & \textbf{Absolute} - & \textbf{Relative}\\ - & & & \textbf{error} & \textbf{error}\\ - \midrule - Measured & $(2p-1s)$ peak area & 2613 & 145.5 & 0.056\\ - \midrule - Calibration & X-ray efficiency & \sn{4.54}{-4} & \sn{1.11}{-5} - & 0.024\\ - \midrule - Reference & X-ray intensity & 0.803 & 0.008 & \sn{9.9}{-3}\\ - & Capture probability & 0.658 & 0 & 0 \\ - \midrule - Corrections& Self absorption & 1 & 0 & 0\\ - & True coincidence summing & 1 &0 & 0\\ - & TRP reset time & 1.01 & 0 & 0 \\ - & Dead time & 1.041& 0 & 0\\ - \midrule - Results & Number of X-rays & \sn{6.05}{6} & \sn{0.37}{6} & 0.06\\ - & Number of $\mu$ stopped & \sn{7.54}{6} & \sn{0.46}{6}&0.06\\ - & Number of captures& \sn{4.96}{6} & \sn{0.31}{6} & 0.06\\ - \bottomrule - \end{tabular} - \end{center} - \caption{Number of X-rays and muon captures in the passive silicon runs.} - \label{tab:si16p_ncapture_cal} -\end{table} -% subsection number_stopped_muons (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsection{Lifetime measurement} -\label{sub:lifetime_measurement}w -To check the origin of the protons recorded, lifetime measurements were made by -cutting on time difference between a hit on one thick silicon and the muon -hit. Applying the time cut in 0.5~\si{\us}\ time steps on the proton -events in \cref{fig:si16p_proton_after_ecut}, the number of surviving -protons on each arm are plotted on \cref{fig:si16p_proton_lifetime}. The -curves show decay constants of $762.9 \pm 13.7$~\si{\ns}\ and $754.6 \pm -11.9$, -which are consistent with the each other, and with mean life time of muons in -silicon in the literatures of $758 \pm 2$~\cite{}. This is the confirmation -that the protons seen by the silicon detectors were indeed from the silicon -target. -\begin{figure}[htb] - \centering - \includegraphics[width=0.75\textwidth]{figs/si16p_proton_lifetime} - \caption{Lifetime measurement of protons seen on the silicon detectors.} - \label{fig:si16p_proton_lifetime} -\end{figure} - -The fits are consistent with lifetime of muons in silicon in from after 500~ns, -before that, the time constants are shorter ($655.9\pm 9.9$ and $731.1\pm8.9$) -indicates the contamination from muon captured on material with higher $Z$. -Therefore a timing cut from 500~ns is used to select good silicon events, the -remaining protons are shown in \cref{fig:si16p_proton_ecut_500nstcut}. -The spectra have a low energy cut off at 2.5~MeV because protons with energy: -lower than that could not pass through the thin silicon to make the cuts as the -range of 2.5~MeV protons in silicon is about 68~\si{\um}. -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/si16p_proton_ecut_500nstcut} - \caption{Proton spectrum after energy and timing cuts} - \label{fig:si16p_proton_ecut_500nstcut} -\end{figure} - -% subsection lifetime_measurement (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Proton emission rate from the silicon target} -\label{sub:proton_emission_rate_from_the_silicon_target} -The number of protons in \cref{fig:si16p_proton_ecut_500nstcut} is -counted from 500~ns after the muon event, where the survival rate is -$e^{-500/758} = 0.517$. - -The geometry acceptance of each silicon arm is estimated to be \sn{2.64}{-2} -using a toy MC study where geantinos are generated within the image of the -collimator on the target, and the number of hits on each silicon package was -counted. Taking the geometry acceptance into account, the number of protons -with energy from 2.5 to 8~MeV emitted is: -\begin{equation} - N_{p \textrm{eff.}} = \dfrac{1927 + 1656}{0.517\times2.64\times10^{-2}} - = 2.625 \times 10^5 -\end{equation} -The emission rate per muon capture is: -\begin{align} - R_{2.5-8\textrm{ MeV}}^{\textrm{eff.}} &= \dfrac{N_{p \textrm{eff.}}} - {N_{\mu \textrm{ captured}}^{\textrm{Si16p}}}\nonumber\\ - &= \dfrac{2.625 \times 10^5}{6.256\times10^6} \nonumber\\ - &= 4.20\times10^{-2}\nonumber -\end{align} -The proton spectra on the \cref{fig:si16p_proton_ecut_500nstcut} and the -emission rate are only effective ones, since the energy of protons are modified -by energy loss in the target, and low energy protons could not escape the -target. Therefore further corrections are needed for both rate and spectrum of -protons. - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Proton emission rate uncertainties} -\label{sub:proton_emission_rate_and_uncertainties_estimation} -The uncertainty of the emission rate could come from several sources: -\begin{enumerate} - \item number of captures $\pm0.562\times10^6$, or 9\%, mainly from the - background under the X-ray peak (5.5\%) and the efficiency calibration - \item number of protons: efficiency of the cuts in energy, impacts of the - timing resolution on timing cut. The energy cuts' contribution should be - small since it can be seen from \cref{fig:si16p_loge+logde}, the peak - of protons is strong and well separated from others. The uncertainty in - timing contribution is significant because all the timing done in this - analysis was on the peak of the slow signals. As it is clear from the - \cref{fig:tme_sir_prompt_rational}, the timing resolution of the - silicon detector could not be better than 100~ns. Putting $\pm100$~ns into - the timing cut could change the survival rate of proton by about - $1-e^{-100/758} \simeq 13\%$. Also, the low statistics contributes a few - percent to the uncertainty budget. - \item acceptance of the silicon packages: muon stopping distribution, - imperfect alignment, efficiency of the detectors, different response to - different species. The muon stopping distribution is important in unfolding - the initial proton spectrum and also greatly affects the rate of protons. - By the end of the run, we found that the target was displaced from the - previously aligned position by 10~mm. Whether this misalignment is serious - or not depends on the spatial distribution of the muons after the - collimator. In the worst case when the muon beam is flatly distributed, - that displacement could change the acceptance of the silicon detectors by - 12\%. Although no measurement was done to determine the efficiency of the - silicon detectors, it would have small effect compared to other factors. -\end{enumerate} - -The combined uncertainty from known sources above therefore could be as large -as 35\%, and the effective proton emission rate in the 2.5--8~MeV could be -written as: -\begin{equation} - R_{2.5-8\textrm{ MeV}}^{\textrm{eff.}} = (4.20\pm1.47)\times 10^{-2} -\end{equation} - -\subsection{Ratio of protons to other heavy charged particles} -\label{sub:heavy_charged_particles_emission_rate} -By using only the lower limit on -$\ln(\textrm{E}) + 0.85\times\ln(\Delta \textrm{E})$, the heavy charged -particles can be selected. These particles also show a lifetime that is -consistent with that of muons in silicon -(\cref{fig:si16p_allparticle_lifetime}). -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/si16p_allparticle_lifetime} - \caption{Lifetime of heavy charged particles} - \label{fig:si16p_allparticle_lifetime} -\end{figure} -The ratio between the number of protons and other particles at 500~ns is $(1927 -+ 1656)/(2202 + 1909) \simeq 0.87$. - -% subsection heavy_charged_particles_emission_rate (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%I have started the initial study on the correction () -% subsection proton_emission_rate_from_the_silicon_target (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\subsection{Rate and spectrum correction} -%\label{sub:proton_spectrum_deconvolution} -%The proton spectra on the \cref{fig:si16p_proton_ecut_500nstcut} and the -%emission rate are only effective ones, since the energy of protons are modified -%by energy loss in the target, and low energy protons could not escape the -%target. Therefore corrections are needed for both rate and spectrum of protons. - -%To solve the unfolding problem, one needs to supply a response function that -%relates the observed energy to the initial energy of protons. This response -%function can be obtained from Monte Carlo simulation where protons with an -%assumed initial spatial distribution inside the target, and a uniform energy -%distribution are generated, then their modified energy spectrum is recorded. -%The initial spatial distribution of protons is inferred from the muon beam -%momentum using Monte Carlo simulation, and available measured data in momentum -%scanning runs. The response function for this thin silicon target is shown in -%\cref{fig:si16p_toyMC}. -%\begin{figure}[htb] - %\centering - %\includegraphics[width=0.85\textwidth]{figs/si16p_toyMC} - %\caption{An example of response function between the observed energy and - %initial energy of protons in a 62-\si{\um}-target.} - %\label{fig:si16p_toyMC} -%\end{figure} - -%The response function is then used to train the unfolding program, which is -%based on the RooUnfold package. The package supports several unfolding methods, -%and I adopted the so-called Bayesian unfolding method~\cite{DAgostini.1995a}. -%The Bayesian method is chosen because it tends to be fast, typical number of -%iterations is from 4--8. - -%\cref{fig:si16p_unfold_train} presented results of two tests unfolding with -%two distributions of initial energy, a Gaussian distribution and -%a parameterized function in~\eqref{eqn:EH_pdf}. The numbers of protons obtained -%from the tests show agreement with the generated numbers. - -%\begin{figure}[htb] - %\centering - %\includegraphics[width=0.85\textwidth]{figs/si16p_unfold_train} - %\caption{Bayesian unfolding tests with two different initial proton energy - %distributions: Gaussian (left) and parameterized function of Sobottka and - %Wills's proton spectrum (right).} - %\label{fig:si16p_unfold_train} -%\end{figure} - -%Finally, the unfolding is applied on the spectra in -%\cref{si16p_proton_spec}, the results are shown in -%\cref{si16p_unfold_meas}. -%\begin{figure}[htb] - %\centering - %\includegraphics[width=0.85\textwidth]{figs/si16p_unfold_meas} - %\caption{Unfolded spectrum from a thin silicon target} - %\label{fig:si16p_unfold_meas} -%\end{figure} -% subsection proton_spectrum_deconvolution (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\subsection{Proton emission rate and uncertainties estimation} -%\label{sub:proton_emission_rate_and_uncertainties_estimation} - -%The rate of proton emission from 2.5--10~\si{\MeV} is: -%\begin{equation} - %R = -%\end{equation} -%\begin{equation} - %R = -%\end{equation} -%The uncertainties are: - -% subsection proton_emission_rate_and_uncertainties_estimation (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% section charged_particles_following_muon_capture_on_a_thin_silicon_target (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%The uncertainties are: - -% subsection proton_emission_rate_and_uncertainties_estimation (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% section charged_particles_following_muon_capture_on_a_thin_silicon_target (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\section{Proton emission following muon capture on an aluminium target} -\label{sec:proton_emission_following_muon_capture_on_an_aluminium_target} -The aluminium is the main object of the AlCap experiment, in this preliminary -analysis I chose one target, Al100 the 100-\si{\um}-thick target, on -a sub-range of the data set runs 2808--2873, as a demonstration. -Because this is a passive target, the same procedure and cuts used in the -passive silicon runs were applied. -\subsection{The number of stopped muons} -\label{sub:the_number_of_stopped_muons} -The X-ray spectrum on the germanium detector is shown on -\cref{fig:al100_ge_spec}. -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/al100_ge_spec} - \caption{X-ray spectrum from the aluminium target, the characteristic - $(2p-1s)$ line shows up at 346.67~keV} - \label{fig:al100_ge_spec} -\end{figure} - -The area of the $(2p-1s)$ line of aluminium and the number of captured in this -target are: -\begin{align} - N_{(2p-1s)\textrm{Al}} &= 3800.0 \pm 179.4 \nonumber\\ - N_{\mu \textrm{ captured}}^{\textrm{Al100}} - &= \dfrac{N_{(2p-1s)\textrm{Al}}} - {\epsilon_{(2p-1s)\textrm{Al}} \times I_{(2p-1s)\textrm{Al}}} - \times f_{\textrm{capture-Al}} \nonumber \\ - &= \dfrac{3800.0} {5.12\times 10^{-4} \times 0.798} \times 0.609 \nonumber \\ - &= (5.664 \pm 0.479) \times 10^6 -\end{align} -% subsection the_number_of_stopped_muons (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Particle identification} -\label{sub:particle_identification} -Using the same charged particle selection -procedure and the cuts on $\ln(\textrm{E})$ and $\ln(\Delta\textrm{E})$, the -proton energy spectrum is shown in \cref{fig:al100_proton_spec}. -\begin{figure}[htb] - \centering - \includegraphics[width=1\textwidth]{figs/al100_selection} - \caption{Selection of protons from the Al100 target: coincidence cut (top), - cuts on energy (middle) and the results (bottom).} - \label{fig:al100_selection} -\end{figure} - -The lifetime of these protons are shown in -\cref{fig:al100_proton_lifetime}, the fitted decay constant on the right -arm is consistent with the reference value of $864 \pm 2$~\si{\ns}~\cite{}. -But the left arm gives $918 \pm 16.1$~\si{\ns}, significantly larger than -the reference value. -%The longer lifetime suggested some contributions from -%other lighter materials, one possible source is from muons captured on the back -%side of the collimator (\cref{fig:alcap_setup_detailed}). -%For this reason, the emission rate calculated from the left arm will be taken as upper -%limit only. -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/al100_proton_lifetime} - \caption{Lifetime of protons from the aluminium Al100 target} - \label{fig:al100_proton_lifetime} -\end{figure} -Further investigation of the problem of longer lifetime was made and the first -channel on the thin silicon detector on that channel was the offender. The -lifetime measurement with out that SiL1-1 channel gives a reasonable result, -and the decay constant on the SiL1-1 alone was nearly about 1000~\si{\us}. -The reason for this behaviour is not known yet. For this emission rate -calculation, this channel is discarded and the rate on the left arm is scaled -with a factor of 4/3. The proton spectrum from the aluminium target is plotted -on \cref{fig:al100_proton_spec_wosil11}. - -\begin{figure}[htb] - \centering - \includegraphics[width=0.40\textwidth]{figs/al100_proton_lifetime_wosil11} - \includegraphics[width=0.40\textwidth]{figs/al100_proton_lifetime_sil11} - \caption{Lifetime of protons without channel SiL1-1 (right) and of the - channel SiL1-1 alone (left).} - \label{fig:al100_proton_lifetime_sil11} -\end{figure} -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/al100_proton_spec_wosil11} - \caption{Spectrum of protons from the Al100 target after cuts on energy and - time, without channel SiL1-1} - \label{fig:al100_proton_spec_wosil11} -\end{figure} -% subsection particle_identification (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Proton emission rate} -\label{sub:proton_emission_rate_and_corrections} -The proton rate is calculated as: -\begin{equation} - N_{p \textrm{eff.}} = \dfrac{1132\times \frac{4}{3} + 2034} - {e^{-500/864}\times2.64\times10^{-2}} - = 1.34 \times 10^5 -\end{equation} -\begin{equation} - R_{2.5-8\textrm{ MeV}}^{\textrm{Al eff.}} = \dfrac{N_{p \textrm{eff.}}} - {N_{\mu \textrm{ captured}}^{\textrm{Al100}}} - = \dfrac{1.34 \times 10^5}{5.664\times10^6} - = 2.37\times10^{-2} -\end{equation} - -The uncertainty of the emission rates will be smaller than that of the rate -from silicon because of a longer lifetime of muons in aluminium and a higher -momentum beam made the misalignment of the target, if any, less important. To -be conservative, I take to 35\% above as this calculation uncertainty, and the -rates will be: -\begin{equation} - R_{2.5-8\textrm{ MeV}}^{\textrm{Al eff.}}=(2.37\pm0.83)\times10^{-2} -\end{equation} -% subsection proton_emission_rate_and_corrections (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% section proton_emission_following_muon_capture_on_an_aluminium_target (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% chapter data_analysis (end) +After training the unfolding code is applied on the measured spectra from the +left and right arms. 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zmMuZgl|kWqy5hIoL%>N60z7aaVZ)H(4-EVD8<-jCTlsr#!S_)0w>dFf>|dGHS4u!e z%KY@c`P(2}`ho%Pn@)KC4}kIl80aZkvyesy6T0*wKaH5T+kpw+>g$OUz9I1&r&{en8+TRad4Ur+~! zW5D3kPjy(}rvB$Tbu1A7{iz=gx0o&-zvx>80=#8i_$>knruh6+hXRv5eyT%*i5oxF zVK9sPVbywPkEG)tRi3INr7xV-6NPTfX z44A~SpdTEGTeQD$6aq|FUDywW2D2Z3s>7-;!Wo5Mj2{|U$j{%R(YQtHMdQE(poKIr zKnC%mIy9Kb^HV?E;yuSA!Ni`0{jiwD>%cC7fjSaQ+FAImI%YAZ>bS+2;t*hBo{k@q!9Y3%Dpg#t|XRlo-XlKcbdk_dsusRLQ+ K@&=m>A^!(z@R&~k literal 0 HcmV?d00001 From b042585a1b3179950edf3a24d3b0ea9d6f071a14 Mon Sep 17 00:00:00 2001 From: nam Date: Wed, 15 Oct 2014 11:39:19 +0900 Subject: [PATCH 10/26] prog saved --- thesis/chapters/chap6_analysis.tex | 58 ++++++++++++++++++++++++++++-- thesis/thesis.tex | 4 +-- 2 files changed, 58 insertions(+), 4 deletions(-) diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index ea806d0..3d60cdf 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -382,7 +382,8 @@ the cut on protons is estimated to be small compared to the statistical ones. \subsection{Corrections for the number of protons} \label{sub:corrections_for_the_number_of_protons} The protons spectra observed by the silicon detectors have been modified by -the energy loss inside the target so correction (or unfolding) is necessary. +the energy loss inside the target so correction (also called unfolding, or +reconstruction) is necessary. The unfolding, essentially, is finding a response function that relates proton's true energy and measured value. This can be done in MC simulation by generating protons with a spatial distribution as close as possible to the real @@ -413,4 +414,57 @@ method is implemented. \label{fig:al100_resp_matrices} \end{figure} After training the unfolding code is applied on the measured spectra from the -left and right arms. The unfolded proton spectra +left and right arms. The unfolded proton spectra in \cref{fig:al100_unfold} +reasonably reflect the distribution of initial protons which is off-centred to +the right arm. The path length to the left arm is longer so less protons at +energy lower than \SI{5}{\MeV} could reach the detectors. The sharp low-energy +cut off on the right arm is consistent with the Coulomb barrier for protons, +which is \SI{4.1}{\MeV} for protons emitted from $^{27}$Mg. + +Comparing the reconstructed spectra from \SIrange{5}{8}{\MeV}, the protons +yields are consistent with each other: +\begin{align} + N_{\textrm{p reco. left}} &= (110.9 \pm 2.0)\times 10^3\\ + N_{\textrm{p reco. right}} &= (110.2 \pm 2.3)\times 10^3 +\end{align} +Therefore, the number of emitted protons is taken as average value: +\begin{equation} + N_{\textrm{p reco.}} = (110.6 \pm 2.2) \times 10^3 +\end{equation} + +\begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/al100_unfold} + \caption{Unfolded proton spectra from the 100-\si{\um} aluminium target.} + \label{fig:al100_unfold} +\end{figure} + +\subsection{Number of nuclear captures} +\label{sub:number_of_nuclear_captures} +\begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/al100_ge_spec} + \caption{X-ray spectrum from the aluminium target, the characteristic + $(2p-1s)$ line shows up at 346.67~keV} +\label{fig:al100_ge_spec} +\end{figure} + +The X-ray spectrum on the germanium detector is shown on +\cref{fig:al100_ge_spec}. Fitting the double peaks on top of a first-order +polynomial gives the X-ray peak area of $5903.5 \pm 109.2$. With the same +procedure as in the case of the active target, the number stopped muons and +the number of nuclear captures are: +\begin{align} + N_{\mu \textrm{ stopped}} &= (1.57 \pm 0.05)\times 10^7\\ + N_{\mu \textrm{ nucl. cap.}} &= (9.57\pm 0.31)\times 10^6 +\end{align} +The proton emission rate in the range from \SIrange{5}{8}{\MeV} is therefore: +\begin{equation} + R_{\textrm{p}} = \frac{110.6\times 10^3}{9.57\times 10^6} = 1.16\times + 10^{-2} + \label{eq:proton_rate_al} +\end{equation} + +\subsection{Uncertainties of the emission rate} +\label{sub:uncertainties_of_the_emission_rate} + diff --git a/thesis/thesis.tex b/thesis/thesis.tex index 9aa2d7b..ac73cc3 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -32,8 +32,8 @@ for the COMET experiment} %\input{chapters/chap1_intro} %\input{chapters/chap2_mu_e_conv} %\input{chapters/chap3_comet} -%\input{chapters/chap4_alcap_phys} -%\input{chapters/chap5_alcap_setup} +\input{chapters/chap4_alcap_phys} +\input{chapters/chap5_alcap_setup} \input{chapters/chap6_analysis} %\input{chapters/chap7_results} From 788e96cc5491551e88cc98d632172cd24e812c3f Mon Sep 17 00:00:00 2001 From: nam Date: Thu, 23 Oct 2014 14:54:52 +0900 Subject: [PATCH 11/26] prog saved --- thesis/chapters/chap6_analysis.tex | 20 +++++++- thesis/chapters/chap7_results.tex | 80 ++++-------------------------- thesis/thesis.bib | 72 +++++++++++++++++++++++++-- thesis/thesis.tex | 8 +-- 4 files changed, 100 insertions(+), 80 deletions(-) diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index 3d60cdf..3fa28dd 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -465,6 +465,22 @@ The proton emission rate in the range from \SIrange{5}{8}{\MeV} is therefore: \label{eq:proton_rate_al} \end{equation} -\subsection{Uncertainties of the emission rate} -\label{sub:uncertainties_of_the_emission_rate} +%\subsection{Uncertainties of the emission rate} +%\label{sub:uncertainties_of_the_emission_rate} +%The uncertainties of the emission rate come from: +%\begin{itemize} + %\item uncertainties in the number of protons: + %\begin{itemize} + %\item statistical uncertainty of the measured spectra; + %\item systematic uncertainty due to misidentification; + %\item systematic uncertainty from the unfolding + %\end{itemize} + %\item uncertainties in the number of nuclear captures: + %\begin{itemize} + %\item statistical uncertainty of the number of X-rays; + %\item uncertainty of the detector acceptance; + %\item uncertainty from the corrections: random summing and transistor + %reset amplifier + %\end{itemize} +%\end{itemize} diff --git a/thesis/chapters/chap7_results.tex b/thesis/chapters/chap7_results.tex index 0019bec..0e8d39e 100644 --- a/thesis/chapters/chap7_results.tex +++ b/thesis/chapters/chap7_results.tex @@ -1,74 +1,14 @@ -\chapter{Discussions} -\label{cha:discussions} +\chapter{Results and discussions} +\label{cha:results_and_discussions} +\section{Verification of the experimental method} +\label{sec:verification_of_the_experimental_method} -\section{Thick aluminium target measurement} -\label{sub:active_target_measurement} -With a thick and active silicon target, I have tried to reproduce an existing -result from Sobottka and Wills~\cite{SobottkaWills.1968}. This is important in -giving confidence in our experimental method. The idea is the same as that of -the old measurement, where muons were stopped inside a bulk active target and -the capture products were measured. Due to the limitation of the -currently available analysis tool, a direct comparison with the result of -Sobottka and Wills is not practical at the moment. +\subsection{Number of stopped muons normalisation} +\label{sub:number_of_stopped_muons_normalisation} -But a partial comparison is available for a part of the spectrum from 8 to -10~MeV, where my result of $(1.22 \pm 0.19) \times 10^{-2} $ is consistent with -the derived value $(1.28\pm0.19)\times10^{-2}$ from the paper of Sobottka and -Wills. The agreement was partly because of large error bars in both results. -In my part, the largest error came from the uncertainty on choosing the -integration window. This can be solved with a more sophisticated pulse -finding/calculating algorithm so that the contribution of muons in the energy -spectrum can be eliminated by imposing a cut in pulse timing. The -under-testing pulse template fitting module could do this job soon. - -The range of 8--10~MeV was chosen to be large enough so that the uncertainty of -integration window would not to be too great; and at the same time be small -enough so the protons (and other heavier charged particles) would not escape -the active target. This range is also more convenient for calculating the -partial rate from the old paper of Sobottka and Wills. - -% section protons_following_muon_capture_on_silicon (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\section{Thin silicon target measurement} -\label{sub:thin_and_passive_target_measurement} -The charged particles in the low energy region of 2.5--8~MeV were measured by -dE/dx method. The particle identification was good in lower energy part, but -losing its resolution power as energy increases. The current set up could do -the PID up to about 8~MeV for protons. This energy range is exactly the -relevant range to the COMET experiment (Figure~\ref{fig:proton_impact_CDC}). - -In that useful energy range, the analysis showed a good separation of protons -from other heavy charged particles. The contribution of protons in the total -charged particles is 87\%. This is the high limit only since the heavier -particles at this energy range are most likely to stopped in the thin -detectors. More statistic would be needed to estimate the contributions from -other particles. - -The effective emission rate of protons per muon capture in this measurement is -4.20\%, with a large uncertainty contribution comes from limitation of the -timing determination. The spectral integral in the region 2.5--8~MeV on -Figure~\ref{fig:sobottka_spec} is about 70\% of the spectrum from 1.4 to -26~\MeV, and corresponds to an emission rate of about 10\% per muon capture. -The two figures are not in disagreement. - -In order to have a better comparison, a correction or unfolding for energy -loss and more MC simulation study are needed. I am on progress of these study. - -% subsection thin_and_passive_target_measurement (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Aluminium target measurement} -\label{sec:aluminium_target_measurement} -The proton emission rate was derived as 2.37\%, but the problem on the SiL1-1 -channel was not solved yet. One possible cause is the muons captured on other -lighter material inside the chamber. More investigation will be made on this -matter. - -The rate of 2.37\% on aluminium appears to be smaller on that of silicon but -the two results are both effective rates, modified by energy loss inside the -target. Unfolding and MC study for the correction are ongoing. -% section aluminium_target_measurement (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% chapter discussions (end) +\subsection{Particle identification and unfolding} +\label{sub:particle_identification_and_unfolding} +\section{Emission rate of protons and the COMET Phase I's CDC} +\label{sec:emission_rate_of_protons_and_the_comet_phase_i_s_cdc} diff --git a/thesis/thesis.bib b/thesis/thesis.bib index 91adc65..154be37 100644 --- a/thesis/thesis.bib +++ b/thesis/thesis.bib @@ -119,8 +119,6 @@ Year = {2003}, Pages = {250-303}, Volume = {A506}, - - __markedentry = {[NT:6]}, Collaboration = {GEANT4}, Doi = {10.1016/S0168-9002(03)01368-8}, Owner = {NT}, @@ -487,8 +485,6 @@ Number = {1}, Pages = {154--197}, Volume = {562}, - - __markedentry = {[NT:]}, Doi = {10.1016/j.nima.2006.03.009}, File = {Published version:Bichsel.2006.pdf:PDF}, Owner = {NT}, @@ -1284,6 +1280,25 @@ Timestamp = {2014-04-01} } +@Article{IsaakEngfer.etal.1983, + Title = {{INCLUSIVE NEUTRON AND CHARGED PARTICLE SPECTRA FROM THE + ABSORPTION OF STOPPED NEGATIVE PIONS IN NICKEL ISOTOPES}}, + Author = {Isaak, H.P. and Engfer, R. and Hartmann, R. and Hermes, + E.A. and Pruys, H.S. and others}, + Journal = {Nucl.Phys.}, + Year = {1983}, + Pages = {385}, + Volume = {A392}, + + __markedentry = {[NT:]}, + Doi = {10.1016/0375-9474(83)90134-3}, + File = {Published version:IsaakEngfer.etal.1983.pdf:PDF}, + Owner = {NT}, + Reportnumber = {SIN-PR-81-12}, + Slaccitation = {%%CITATION = NUPHA,A392,385;%%}, + Timestamp = {2014-10-16} +} + @Article{Ishii.1959, Title = {An Analysis of the Charged Particles Emitted Following Negative Muon Absorptions in Photographic Emulsions}, Author = {Ishii, Chikai}, @@ -1511,6 +1526,54 @@ Url = {http://prola.aps.org/abstract/PR/v165/i4/p1190_1} } +@Article{KozlowskiZglinski.1978, + Title = {{The Nuclear Excitations and Particle Emission Following + Muon Capture}}, + Author = {Kozlowski, T. and Zglinski, A.}, + Journal = {Nucl.Phys.}, + Year = {1978}, + Pages = {368-380}, + Volume = {A305}, + + __markedentry = {[NT:]}, + Doi = {10.1016/0375-9474(78)90345-7}, + File = {Published version:KozlowskiZglinski.1978.pdf:PDF}, + Owner = {NT}, + Slaccitation = {%%CITATION = NUPHA,A305,368;%%}, + Timestamp = {2014-10-16} +} + +@Article{KozlowskiZglinski.1974, + Title = {{Nuclear muon capture - a simple model}}, + Author = {Kozlowski, T. and Zglinski, A.}, + Journal = {Phys.Lett.}, + Year = {1974}, + Pages = {222-224}, + Volume = {B50}, + + __markedentry = {[NT:]}, + Doi = {10.1016/0370-2693(74)90543-7}, + File = {Published version:KozlowskiZglinski.1974.pdf:PDF}, + Owner = {NT}, + Slaccitation = {%%CITATION = PHLTA,B50,222;%%}, + Timestamp = {2014-10-16} +} + +@Article{KozlowskiZglinski.1974b, + Title = {{Pre-equilibrium particle emission after the nuclear muon + capture}}, + Author = {Kozlowski, T. and Zglinski, A.}, + Journal = {Nukleonika}, + Year = {1974}, + Pages = {721-725}, + Volume = {19}, + + __markedentry = {[NT:6]}, + Owner = {NT}, + Slaccitation = {%%CITATION = NUKLA,19,721;%%}, + Timestamp = {2014-10-16} +} + @Article{KraneSharma.etal.1979, Title = {Energetic charged-particle spectrum following $\mu$-capture by nuclei}, Author = {Krane, KS and Sharma, TC and Swenson, LW and McDaniels, DK and Varghese, P and Wood, BE and Silbar, RR and Wohlfahrt, HD and Goulding, CA}, @@ -2503,6 +2566,7 @@ Year = {2003}, Pages = {MOLT007}, Volume = {C0303241}, + Archiveprefix = {arXiv}, Eprint = {physics/0306116}, File = {arXiv v1:VerkerkeKirkby.2003-eprintv1.pdf:PDF}, diff --git a/thesis/thesis.tex b/thesis/thesis.tex index ac73cc3..d9df6d7 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -29,13 +29,13 @@ for the COMET experiment} \end{frontmatter} \mainmatter -%\input{chapters/chap1_intro} -%\input{chapters/chap2_mu_e_conv} -%\input{chapters/chap3_comet} +\input{chapters/chap1_intro} +\input{chapters/chap2_mu_e_conv} +\input{chapters/chap3_comet} \input{chapters/chap4_alcap_phys} \input{chapters/chap5_alcap_setup} \input{chapters/chap6_analysis} -%\input{chapters/chap7_results} +\input{chapters/chap7_results} \begin{backmatter} \input{chapters/backmatter} From 078802df953817a5b420b9b81cbe07d86fc4bd19 Mon Sep 17 00:00:00 2001 From: nam Date: Tue, 28 Oct 2014 22:30:26 +0900 Subject: [PATCH 12/26] prog saved --- thesis/chapters/chap6_analysis.tex | 193 +++++++++++++++++++++-------- thesis/figs/al100_resp.pdf | Bin 24204 -> 24277 bytes thesis/thesis.bib | 19 +++ thesis/thesis.tex | 12 +- 4 files changed, 169 insertions(+), 55 deletions(-) diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index 3fa28dd..0bd4bae 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -337,13 +337,15 @@ The band of protons is then extracted by cut on likelihood probability calculated as: \begin{equation} p_{i} = \dfrac{1}{\sqrt{2\pi}\sigma_{\Delta E}} - e^{\frac{(\Delta E_{meas.} - \Delta E_i)^2} {2\sigma^2_{\Delta E}}} + \exp{\left[\dfrac{(\Delta E_{meas.} - \Delta E_i)^2} {2\sigma^2_{\Delta + E}}\right]} \end{equation} -where $\Delta E_{\textrm{meas.}}$ is measured energy deposition in the thin +where $\Delta E_{\textrm{meas.}}$ is energy deposition measured by the thin silicon detector by a certain proton at energy $E_i$, $\Delta E_i$ and $\sigma_{\Delta E}$ are the expected and standard deviation of the energy loss -caused by the proton calculated by MC. A cut value of $3\sigma_{\Delta E}$, or -$p_i \ge 0.011$, was used to extract protons (\cref{fig:al100_protons}). +caused by the proton calculated by MC study. A threshold is set to extract +protons at 0.011 (equivalent to $3\sigma_{\Delta E}$), the band of protons is +shown in (\cref{fig:al100_protons}). \begin{figure}[htb] \centering \includegraphics[width=0.47\textwidth]{figs/al100_protons} @@ -354,6 +356,12 @@ $p_i \ge 0.011$, was used to extract protons (\cref{fig:al100_protons}). \label{fig:al100_protons} \end{figure} +The cut efficiency in the energy range from \SIrange{2}{12}{\MeV} is estimated +by MC study. The fraction of protons that do not satisfy the probability cut +is 0.5\%. The number of other charged particles that are misidentified as +protons depends on the ratios between those species and protons. Assuming +a proton:deuteron:triton:alpha:muon ratio of 5:2:1:2:2, the number of +misidentified hits is 0.1\% of the number of protons. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Proton emission rate from aluminium} \label{sec:proton_emission_rate_from_aluminium} @@ -365,25 +373,20 @@ of protons is normalised to the number of nuclear muon captures. \subsection{Number of protons emitted} \label{sub:number_of_protons_emitted} -From the particle identification above, number of protons having energy in the -range from \SIrange{2.2}{8.5}{\MeV} hitting the two arms are: +The numbers of protons in the energy range from \SIrange{2.2}{8.5}{\MeV} after +applying the probability cut are: \begin{align} - N_{\textrm{p meas. left}} = 1822 \pm 42.7\\ - N_{\textrm{p meas. right}} = 2373 \pm 48.7 + N_{\textrm{p meas. left}} = 1822\\% \pm 42.7\\ + N_{\textrm{p meas. right}} = 2373% \pm 48.7 \end{align} The right arm received significantly more protons than the left arm did, which -is expected as in \cref{sub:momentum_scan_for_the_100_} it is shown that -muons stopped off centre to the right arm. - -%%TODO -The uncertainties are statistical only. The systematic uncertainties due to -the cut on protons is estimated to be small compared to the statistical ones. +is expected as in \cref{sub:momentum_scan_for_the_100_} where it is shown that +muons stopped off-centred to the right arm. \subsection{Corrections for the number of protons} \label{sub:corrections_for_the_number_of_protons} The protons spectra observed by the silicon detectors have been modified by -the energy loss inside the target so correction (also called unfolding, or -reconstruction) is necessary. +the energy loss inside the target so correction (or unfolding) is necessary. The unfolding, essentially, is finding a response function that relates proton's true energy and measured value. This can be done in MC simulation by generating protons with a spatial distribution as close as possible to the real @@ -413,28 +416,65 @@ method is implemented. \caption{Response functions for the two silicon arms.} \label{fig:al100_resp_matrices} \end{figure} -After training the unfolding code is applied on the measured spectra from the -left and right arms. The unfolded proton spectra in \cref{fig:al100_unfold} -reasonably reflect the distribution of initial protons which is off-centred to -the right arm. The path length to the left arm is longer so less protons at -energy lower than \SI{5}{\MeV} could reach the detectors. The sharp low-energy -cut off on the right arm is consistent with the Coulomb barrier for protons, -which is \SI{4.1}{\MeV} for protons emitted from $^{27}$Mg. +%After training, the unfolding code is applied on the measured spectra from the +%left and right arms. The unfolded proton spectra in \cref{fig:al100_unfold} +%reasonably reflect the distribution of initial protons which is off-centred to +%the right arm. The path length to the left arm is longer so less protons at +%energy lower than \SI{5}{\MeV} could reach the detectors. The sharp low-energy +%cut off on the right arm is consistent with the Coulomb barrier for protons, +%which is \SI{4.1}{\MeV} for protons emitted from $^{27}$Mg. +The unfolded spectra using the two observed spectra at the two arms as input +are shown in \cref{fig:al100_unfold}. The two unfolded spectra generally agree +with each other, except for a few first and last bins. The discrepancy and +large uncertainties at the low energy region are because of only a small +number of protons with those energies could reach the detectors. The jump on +the right arm at around \SI{9}{\MeV} can be explained as the punch-through +protons were counted as the proton veto counters were not used in this +analysis. -Comparing the reconstructed spectra from \SIrange{5}{8}{\MeV}, the protons -yields are consistent with each other: +%Several studies were conducted to assess the performance of the unfolding +%code, including: +%\begin{itemize} + %\item stability against cut-off energy; + %\item comparison between the two arms; + %\item and unfolding of a MC-generated spectrum. +%\end{itemize} +The stability of the unfolding code is tested by varying the lower cut-off +energy of the input spectrum. \cref{fig:al100_cutoff_study} show that the +shapes of the unfolded spectra are stable. The lower cut-off energy of the +output increases as that of the input increases, and the shape is generally +unchanged after a few bins. +\begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/al100_cutoff_study} + \caption{Unfolded spectra with different cut-off energies.} + \label{fig:al100_cutoff_study} +\end{figure} +The proton yields calculated from observed spectra in two arms are compared in +\cref{fig:al100_integral_comparison} where the upper limit of the integrals +is fixed at \SI{8}{\MeV}, and the lower limit is varied in \SI{400}{\keV} step. +The difference is large at cut-off energies less than \SI{4}{\MeV} due to +large uncertainties at the first bins. Above \SI{4}{\MeV}, the two arms show +consistent numbers of protons. +\begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/al100_integral_comparison} + \caption{Proton yields calculated from two arms.} + \label{fig:al100_integral_comparison} +\end{figure} +The yields of protons from \SIrange{4}{8}{\MeV} are: \begin{align} - N_{\textrm{p reco. left}} &= (110.9 \pm 2.0)\times 10^3\\ - N_{\textrm{p reco. right}} &= (110.2 \pm 2.3)\times 10^3 + N_{\textrm{p unfold left}} &= (165.4 \pm 2.7)\times 10^3\\ + N_{\textrm{p unfold right}} &= (173.1 \pm 2.9)\times 10^3 \end{align} Therefore, the number of emitted protons is taken as average value: \begin{equation} - N_{\textrm{p reco.}} = (110.6 \pm 2.2) \times 10^3 + N_{\textrm{p unfold}} = (169.3 \pm 2.9) \times 10^3 \end{equation} \begin{figure}[htb] \centering - \includegraphics[width=0.85\textwidth]{figs/al100_unfold} + \includegraphics[width=0.85\textwidth]{figs/al100_unfolded_lr} \caption{Unfolded proton spectra from the 100-\si{\um} aluminium target.} \label{fig:al100_unfold} \end{figure} @@ -458,29 +498,84 @@ the number of nuclear captures are: N_{\mu \textrm{ stopped}} &= (1.57 \pm 0.05)\times 10^7\\ N_{\mu \textrm{ nucl. cap.}} &= (9.57\pm 0.31)\times 10^6 \end{align} -The proton emission rate in the range from \SIrange{5}{8}{\MeV} is therefore: + +\subsection{Proton emission rate} +\label{sub:proton_emission_rate} +The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore: \begin{equation} - R_{\textrm{p}} = \frac{110.6\times 10^3}{9.57\times 10^6} = 1.16\times + R_{\textrm{p}} = \frac{169.3\times 10^3}{9.57\times 10^6} = 1.74\times 10^{-2} \label{eq:proton_rate_al} \end{equation} -%\subsection{Uncertainties of the emission rate} -%\label{sub:uncertainties_of_the_emission_rate} -%The uncertainties of the emission rate come from: -%\begin{itemize} - %\item uncertainties in the number of protons: - %\begin{itemize} - %\item statistical uncertainty of the measured spectra; - %\item systematic uncertainty due to misidentification; - %\item systematic uncertainty from the unfolding - %\end{itemize} - %\item uncertainties in the number of nuclear captures: - %\begin{itemize} - %\item statistical uncertainty of the number of X-rays; - %\item uncertainty of the detector acceptance; - %\item uncertainty from the corrections: random summing and transistor - %reset amplifier - %\end{itemize} -%\end{itemize} +The total proton emission rate can be estimated by assuming a spectrum shape +with the same parameterisation as in \eqref{eqn:EH_pdf}. The fit parameters +are shown in . With such parameterisation, the integration in +range from \SIrange{4}{8}{\MeV} is 51\% of the total number of protons. The +total proton emission rate is therefore $3.5\times 10^{-2}$. +\subsection{Uncertainties of the emission rate} +\label{sub:uncertainties_of_the_emission_rate} +The uncertainties of the emission rate come from: +\begin{itemize} + \item uncertainties in the number of nuclear captures: these were discussed + in \cref{sub:number_of_stopped_muons_from_the_number_of_x_rays}; + \item uncertainties in the number of protons: + \begin{itemize} + \item statistical uncertainties of the measured spectra which are + propagated during the unfolding process; + \item systematic uncertainties due to misidentification: this number is + small compared to other uncertainties as discussed in + \cref{sub:event_selection_for_the_passive_targets}; + \item systematic uncertainty from the unfolding + \end{itemize} +\end{itemize} +The last item is studied by MC method using the parameterisation in +\cref{sub:proton_emission_rate}: +\begin{itemize} + \item protons with energy distribution obeying the parameterisation are + generated inside the target. The spatial distribution is the same as that + of in \cref{sub:corrections_for_the_number_of_protons}. MC truth including + initial energies and positions are recorded; + \item the number of protons reaching the silicon detectors are counted, + the proton yield is set to be the same as the measured yield to make the + statistical uncertainties comparable; + \item the unfolding is applied on the observed proton spectra, and the + results are compared with the MC truth. +\end{itemize} +\begin{figure}[htb] + \centering + \includegraphics[width=0.48\textwidth]{figs/al100_MCvsUnfold} + \includegraphics[width=0.48\textwidth]{figs/al100_unfold_truth_ratio} + \caption{Comparison between an unfolded spectrum and MC truth: spectra + (left), and yields (right). The ratio is defined as $\textrm{(Unfold - MC + truth)/(MC truth)}$} + \label{fig:al100_MCvsUnfold} +\end{figure} +\Cref{fig:al100_MCvsUnfold} shows that the yield obtained after unfolding is +in agreement with that from the MC truth. The difference is less than 5\% if +the integration is taken in the range from \SIrange{4}{8}{\MeV}. Therefore +a systematic uncertainty of 5\% is assigned for the unfolding routine. + +A summary of uncertainties in the measurement of proton emission rate is +presented in \cref{tab:al100_uncertainties_all}. +\begin{table}[htb] + \begin{center} + \begin{tabular}{@{}ll@{}} + \toprule + \textbf{Item}& \textbf{Value} \\ + \midrule + Number of muons & 3.2\% \\ + Statistical from measured spectra & 1.6\% \\ + Systematic from unfolding & 5.0\% \\ + Systematic from PID & \textless0.5\% \\ + \midrule + Total & 6.1\%\\ + \bottomrule + \end{tabular} + \end{center} + \caption{Uncertainties of the proton emission rate.} + \label{tab:al100_uncertainties_all} +\end{table} + +The proton emission rate is then $(3.5 \pm 0.2)$\%. diff --git a/thesis/figs/al100_resp.pdf b/thesis/figs/al100_resp.pdf index d4728d2963b8be8c35e581e9652243e89370ee6f..963ea3a9f81834ae5b05954b6b97613c1d7a7be1 100644 GIT binary patch delta 12129 zcmZviby$;M*!UGeVW8wtkrD(3qmdZh9UC!XgrszLJ<&)#(0p6a-rSV71y!Y9Zl%=^5ywhn?P1WU1I 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b/thesis/chapters/chap1_intro.tex @@ -83,6 +83,6 @@ sensitivities. Details of the study on proton emission are described in Chapters~\ref{cha:alcap_phys},~\ref{cha:the_alcap_run_2013},~\ref{cha:data_analysis}: physics, method, experimental set up, data analysis. The results and impacts of the study on COMET Phase-I design is discussed in -Chapter~\ref{cha:discussions}. +Chapter~\ref{cha:results_and_discussions}. % chapter introduction (end) diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index 0bd4bae..e1d0462 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -343,9 +343,9 @@ calculated as: where $\Delta E_{\textrm{meas.}}$ is energy deposition measured by the thin silicon detector by a certain proton at energy $E_i$, $\Delta E_i$ and $\sigma_{\Delta E}$ are the expected and standard deviation of the energy loss -caused by the proton calculated by MC study. A threshold is set to extract -protons at 0.011 (equivalent to $3\sigma_{\Delta E}$), the band of protons is -shown in (\cref{fig:al100_protons}). +caused by the proton calculated by MC study. A threshold is set at \num{1E-4} to +extract protons, the resulted band of protons is shown in +(\cref{fig:al100_protons}). \begin{figure}[htb] \centering \includegraphics[width=0.47\textwidth]{figs/al100_protons} @@ -510,9 +510,15 @@ The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore: The total proton emission rate can be estimated by assuming a spectrum shape with the same parameterisation as in \eqref{eqn:EH_pdf}. The fit parameters -are shown in . With such parameterisation, the integration in -range from \SIrange{4}{8}{\MeV} is 51\% of the total number of protons. The -total proton emission rate is therefore $3.5\times 10^{-2}$. +are shown in \cref{fig:al100_parameterisation}. With such parameterisation, the +integration in range from \SIrange{4}{8}{\MeV} is 51\% of the total number of +protons. The total proton emission rate is therefore $3.5\times 10^{-2}$. +\begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/al100_parameterisation} + \caption{Fitting of the unfolded spectra.} + \label{fig:al100_parameterisation} +\end{figure} \subsection{Uncertainties of the emission rate} \label{sub:uncertainties_of_the_emission_rate} diff --git a/thesis/chapters/chap7_results.tex b/thesis/chapters/chap7_results.tex index 0e8d39e..39b77bd 100644 --- a/thesis/chapters/chap7_results.tex +++ b/thesis/chapters/chap7_results.tex @@ -2,13 +2,71 @@ \label{cha:results_and_discussions} \section{Verification of the experimental method} \label{sec:verification_of_the_experimental_method} - -\subsection{Number of stopped muons normalisation} +\subsection{Number of stopped muons calculation} \label{sub:number_of_stopped_muons_normalisation} - +The number of stopped muons calculated from the muonic X-ray spectrum is shown +to be consistent with that calculated from the active target spectrum. This +proves the validity of normalisation using muon X-ray measurement. \subsection{Particle identification and unfolding} \label{sub:particle_identification_and_unfolding} +The particle identification using specific energy loss using cut on +likelihood probability is shown in +\cref{sub:event_selection_for_the_passive_targets}. Since the distribution of +$\Delta E$ at a given $E$ is not Gaussian, the fraction of protons that do not +make the cut is 0.5\%, much larger than the threshold at \num{1E-4}. However, +that missing fraction is small compared to the statistical uncertainty of the +measurement (2.3\%) so the threshold is sufficient. + +The observed spectra on the two silicon arms reflect the muon stopping +distribution discussed in \cref{sub:momentum_scan_for_the_100_} where more +muons stopped at the downstream side of the target. The proton yields +calculated from two arms are consistent with each other, and show that the muon +stopping distribution used to generate the response matrices is reasonable. \section{Emission rate of protons and the COMET Phase I's CDC} \label{sec:emission_rate_of_protons_and_the_comet_phase_i_s_cdc} +The proton emission rate from the 100-\si{\um} aluminium target is +$(3.5 \pm 0.2)$\%. This rate is significantly larger than the calculation rate +of 0.97\% by Lifshitz and Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980}. +The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in +\eqref{eqn:wyttenbach_ratio}. +The rate smaller that the proton emission rate from silicon of +5.3\%~\cite{Measday.2001} which is expected since an odd-odd nucleus as +$^{28}$Al is less stable than an even-odd one. +For the COMET Phase I experiment, the emission rate of 3.5\% is about 5 times +smaller than the figure using to design the CDC. The measured spectrum shape +peaks around \SI{4}{\MeV} rather than \SI{2.5}{\MeV} in the silicon +spectrum(\cref{fig:sobottka_spec}). Therefore the proton hit rate on the CDC +should be smaller than the current estimation. + +The CDC proton hit rate is calculated by a toy MC study. The protons with the +energy spectrum as the parameterisation in \cref{sub:proton_emission_rate} are +generated inside the COMET's muon stopping targets which are 17 +200-\si{\um}-thick aluminium discs. A proton absorber made of CFRP is placed +\SI{5}{\cm} far from the inner wall of the CDC. +A muon stopping rate of \SI{1.3E9}{\Hz} is assumed as in the COMET Phase I's +TDR. The number of proton emitted is then $\num{1.3E9} \times 0.609 \times +0.035 = \SI{2.8E7}{\Hz}$. The hit rates on a single cell in the inner most +layer due to these protons with +different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. +\begin{table}[htb] + \begin{center} + \begin{tabular}{l r} + \toprule + \textbf{Absorber thickness} & \textbf{Hit rate}\\ + \midrule + \SI{1}{\mm} & \SI{2}{\Hz}\\ + \SI{0.5}{\mm} & \SI{126}{\Hz}\\ + \SI{0}{\mm} & \SI{1436}{\Hz}\\ + \bottomrule + \end{tabular} + \end{center} + \caption{CDC proton hit rates} + \label{tab:proton_cdc_hitrate} +\end{table} + +The proton hit rate even without the absorber is only \SI{1.4}{\kHz}, much +smaller than the current estimation of \SI{11}{\kHz} (using 1-mm-thick +absorber). Therefore a proton absorber is not needed for the COMET Phase I's +CDC. diff --git a/thesis/thesis.tex b/thesis/thesis.tex index 9aa2d7b..2348c75 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -29,13 +29,14 @@ for the COMET experiment} \end{frontmatter} \mainmatter -%\input{chapters/chap1_intro} -%\input{chapters/chap2_mu_e_conv} -%\input{chapters/chap3_comet} -%\input{chapters/chap4_alcap_phys} -%\input{chapters/chap5_alcap_setup} +\input{chapters/chap1_intro} +\input{chapters/chap2_mu_e_conv} +\input{chapters/chap3_comet} +\input{chapters/chap4_alcap_phys} +\input{chapters/chap5_alcap_setup} \input{chapters/chap6_analysis} -%\input{chapters/chap7_results} +\input{chapters/chap7_results} +%\input{chapters/chap8_conclusions} \begin{backmatter} \input{chapters/backmatter} From 2a73339985bac62b29117b0fdb3a8dc5e8ff19ef Mon Sep 17 00:00:00 2001 From: nam Date: Wed, 29 Oct 2014 13:34:04 +0900 Subject: [PATCH 14/26] prog saved --- thesis/chapters/chap1_intro.tex | 13 ++++++++----- thesis/thesis.tex | 2 +- 2 files changed, 9 insertions(+), 6 deletions(-) diff --git a/thesis/chapters/chap1_intro.tex b/thesis/chapters/chap1_intro.tex index d67d927..95a6425 100644 --- a/thesis/chapters/chap1_intro.tex +++ b/thesis/chapters/chap1_intro.tex @@ -58,15 +58,18 @@ observation of CLFV would be a clear signal of new physics beyond the SM. The COMET (\textbf{CO}herent \textbf{M}uon to \textbf{E}lectron \textbf{T}ransition) Collaboration aims to probe the conversion of a muon to -an electron in a nucleus field at a sensitivity of $6\times10^{-17}$, pushing -for a four orders of magnitude improvement from the current limit set by the +an electron in a nucleus field at a single event sensitivity of \num{6E-17}, +pushing for a four orders of magnitude improvement from the current limit set +by the SINDRUM-II~\cite{Bertl.etal.2006}. A staging approach is adopted at the COMET to achieve an intermediate physics result, as well as to gain operational -experience. The first stage, COMET Phase I, is scheduled to start in 2016 with -the goal sensitivity of $3\times 10^{-15}$ after a three-month-running period. +experience. The first stage, COMET Phase I, is scheduled to start data taking +in 2016 with the goal single event sensitivity of $3\times 10^{-15}$ after +a three-month running period. A cylindrical drift chamber being developed by the Osaka University group -will be the main tracking detector in the COMET Phase I. It is anticipated that +together with the Kyushu University group and the Chinese groups +will be a main tracking detector in the COMET Phase I. It is anticipated that the chamber will be heavily occupied by protons emitted after nuclear muon capture in the stopping target, and thus an absorber will be installed to reduce the proton hit rate to a tolerable level. A study of proton emission diff --git a/thesis/thesis.tex b/thesis/thesis.tex index 2348c75..c960e36 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -36,7 +36,7 @@ for the COMET experiment} \input{chapters/chap5_alcap_setup} \input{chapters/chap6_analysis} \input{chapters/chap7_results} -%\input{chapters/chap8_conclusions} +\input{chapters/chap8_conclusions} \begin{backmatter} \input{chapters/backmatter} From ce95dfbb6b6be284fa8b8e026f5f7f1b4f56501c Mon Sep 17 00:00:00 2001 From: nam Date: Wed, 29 Oct 2014 15:14:01 +0900 Subject: [PATCH 15/26] prog saved --- thesis/chapters/chap2_mu_e_conv.tex | 61 +++++++++++++++++------------ thesis/chapters/frontmatter.tex | 2 +- thesis/thesis.tex | 16 ++++---- 3 files changed, 45 insertions(+), 34 deletions(-) diff --git a/thesis/chapters/chap2_mu_e_conv.tex b/thesis/chapters/chap2_mu_e_conv.tex index 6c6166c..a1a84ed 100644 --- a/thesis/chapters/chap2_mu_e_conv.tex +++ b/thesis/chapters/chap2_mu_e_conv.tex @@ -9,7 +9,7 @@ spin one-half particles, called fermions: six quarks and six leptons. The six leptons form three generations (or flavours), namely: \begin{equation*} \binom{\nu_e}{e^-}, \quad \binom{\nu_\mu}{\mu^-} \quad \textrm{ and } \quad - \binom{\nu_\tau}{\tau^-} + \binom{\nu_\tau}{\tau^-}. \end{equation*} Each lepton is assigned a lepton flavour quantum number, $L_e$, $L_\mu$, @@ -24,7 +24,7 @@ or, the interaction of an electron-type antineutrino with a proton (inverse beta decay): \begin{align*} &\quad \overline{\nu}_e + p \rightarrow e^+ + n \\ - L_e \quad &-1 \quad \textrm{ }0 \quad -1 \textrm{ } \quad 0 +L_e \quad &-1 \quad \textrm{ }0 \quad -1 \textrm{ } \quad 0 \end{align*} The decay of a muon to an electron and a photon, where lepton flavour numbers @@ -40,15 +40,25 @@ are violated by one unit or more, is forbidden: \end{aligned} \label{eq:mueg} \end{equation} + +However, it is observed that neutrinos do change flavour in the so-called +neutrino oscillations where a neutrino of a certain lepton flavour +can be measured to have a different flavour as it travels in space-time. The +phenomenon has been confirmed in many experiments with solar neutrinos, +atmospheric neutrinos, reactor neutrinos and beam neutrinos. The observation +of neutrino oscillations means that the lepton flavour is not strictly +conserved and neutrinos are massive. The massive neutrinos allow lepton +flavour violation in the charged leptons, but at an unmeasurably small level +as described in \cref{sec:lepton_flavour_violation}. %One more decay? %\hl{TODO: Why massless neutrinos help lepton flavour conservation??} %\hl{TODO: copied from KunoOkada} %In the minimal version of the SM, where only one Higgs doublet is included and - %massless neutrinos are assumed, lepton flavor conservation is an automatic + %massless neutrinos are assumed, lepton conservation is an automatic %consequence of gauge invariance and the renormalizability of the SM %Lagrangian. It is the basis of a natural explanation for the smallness of - %lepton flavor violation (LFV) in charged lepton processes. + %lepton violation (LFV) in charged lepton processes. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Muon and its decays in the Standard Model} @@ -111,15 +121,15 @@ or with an associated $e^+ e^-$ pair: \label{eq:mu3e2nu} \end{equation} -The dominant process, \micheldecay is commonly called Michel decay. It can be -described by the V-A interaction which is a special case of a local, +The dominant process, \micheldecay is commonly called the Michel decay. It can +be described by the V-A interaction which is a special case of a local, derivative-free, lepton-number-conserving four-fermion interaction. %using $V-A$ %inteaction, a special case of four-fermion interaction, by Louis %Michel~\cite{Michel.1950}. The model contains independent real parameters that can be determined from measurements of muon life time, muon decay and inverse muon -decay. Experimental results from extensive measurements of Michel parameters +decay. Experimental results from extensive measurements of the Michel parameters are consistent with the predictions of the V-A theory~\cite{Michel.1950,FetscherGerber.etal.1986,BeringerArguin.etal.2012}. @@ -127,9 +137,9 @@ The radiative decay~\eqref{eq:mue2nugamma} is treated as an internal bremsstrahlung process~\cite{EcksteinPratt.1959}. %It occurs at the rate of about 1\% of all muon decays. Since it is not possible to clearly separated this mode -from Michel decay in the soft-photon limit, the radiative mode is regarded as +from the Michel decay in the soft-photon limit, the radiative mode is regarded as a subset of the Michel decay. An additional parameter is included to describe -the electron and photon spectra in this decay channel. Like the case of +the electron and photon spectra in this decay channel. Like the case of the Michel decay, experiments results on the branching ratio and the parameter are in agreement with the SM's predictions~\cite{BeringerArguin.etal.2012}. @@ -221,8 +231,8 @@ CLFV processes with muons are also suppressed to similar practically unmeasurable levels.%\hl{TODO: Feynman diagram} Therefore, any experimental observation of CLFV would be an unambiguous signal of the physics beyond the -SM. Many models for physics beyond the SM, including supersymmetric (SUSY) -models, extra dimensional models, little Higgs models, predict +SM. Many theoretical models for physics beyond the SM, including supersymmetric +(SUSY) models, extra dimensional models, little Higgs models, predict significantly larger CLFV ~\cite{MarcianoMori.etal.2008, MiharaMiller.etal.2013, BernsteinCooper.2013}. %\hl{TODO: DNA of CLFV charts} @@ -257,15 +267,15 @@ significantly larger CLFV %occur at large rates by many new physics models, Among the CLFV processes, the \mueg and the \muec are expected to have large effect by many models. The current -experimental limits on these two decay modes are set by MEG -experiment~\cite{Adam.etal.2013} and SINDRUM-II +experimental limits on these two decay modes are set respectively by the MEG +experiment~\cite{Adam.etal.2013} and the SINDRUM-II experiment~\cite{Bertl.etal.2006}: \begin{equation} - \mathcal{B}(\mu^+ \rightarrow e^+ \gamma) < 5.7 \times 10^{-13} + \mathcal{B}(\mu^+ \rightarrow e^+ \gamma) < 5.7 \times 10^{-13}\, \end{equation} -, and: +and: \begin{equation} - \mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13} + \mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13}\. \end{equation} %\hl{TODO: mueg and muec relations, Lagrangian \ldots} @@ -278,25 +288,26 @@ experiment~\cite{Bertl.etal.2006}: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Phenomenology of \mueconv} \label{sec:phenomenoly_of_muec} -The conversion of a captured muon into an electron in the field of a nucleus -has been one of the most powerful probe to search for CLFV. This section +The conversion of a captured negative muon in a muonic atom into an electron +in the field of a nucleus has been one of the most powerful probe to search for +CLFV. This section highlights phenomenology of the \muec. \subsection{What is \mueconv} \label{sub:what_is_muec} -When a muon is stopped in a material, it is quickly captured by atoms -into a high orbital momentum state, forming a muonic atom, then +When a negatively charged muon is stopped in a material, it is quickly captured +by an atom into a high orbital momentum state, forming a muonic atom, then it rapidly cascades to the lowest state 1S. There, it undergoes either: \begin{itemize} \item normal Michel decay: \micheldecay; or - \item weak capture by the nucleus: $\mu^- p \rightarrow \nu_\mu n$ + \item weak capture by the nucleus: $\mu^- p \rightarrow \nu_\mu n$. \end{itemize} In the context of physics beyond the SM, the exotic process of \mueconv where a muon decays to an electron without neutrinos is also -expected, but it has never been observed. +expected, but has never been observed: \begin{equation} - \mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z) + \mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)\. \end{equation} The emitted electron in this decay mode , the \mueconv electron, is mono-energetic at an energy far above the @@ -322,8 +333,8 @@ The quantity measured in searches for \mueconv is the ratio between the rate of \frac{\Gamma(\mu^-N \rightarrow e^-N)}{\Gamma(\textrm{capture})} \label{eq:muerate_def} \end{equation} -The normalisation to captures has advantages when one does calculation since -many details of the nuclear wavefunction cancel out in the ratio. +%The normalisation to captures has advantages when one does calculation since +%many details of the nuclear wavefunction cancel out in the ratio. %Detailed %calculations have been performed by Kitano et al.~\cite{KitanoKoike.etal.2002a, %KitanoKoike.etal.2007}, and Cirigliano et al.~\cite{Cirig} diff --git a/thesis/chapters/frontmatter.tex b/thesis/chapters/frontmatter.tex index ff7c89b..4fa23f9 100644 --- a/thesis/chapters/frontmatter.tex +++ b/thesis/chapters/frontmatter.tex @@ -10,7 +10,7 @@ Osaka University} \begin{abstract} %[\smaller \thetitle\\ \vspace*{1cm} \smaller {\theauthor}] \thispagestyle{empty} -COMET [1] is an experiment that aims to search for a charged lepton flavor + COMET [1] is an experiment that aims to search for a charged lepton flavour violation (CLFV) process, the muon-to-electron conversion in the presence of a nucleus, \muec. The process is forbidden in the Standard Model (SM), however is diff --git a/thesis/thesis.tex b/thesis/thesis.tex index c960e36..2c4a93b 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -21,7 +21,7 @@ following nuclear muon capture\\ \vspace{2mm} for the COMET experiment} \author{Nam Hoai Tran} -\date{September, 2014} +\date{October, 2014} \begin{document} \begin{frontmatter} @@ -29,14 +29,14 @@ for the COMET experiment} \end{frontmatter} \mainmatter -\input{chapters/chap1_intro} +%\input{chapters/chap1_intro} \input{chapters/chap2_mu_e_conv} -\input{chapters/chap3_comet} -\input{chapters/chap4_alcap_phys} -\input{chapters/chap5_alcap_setup} -\input{chapters/chap6_analysis} -\input{chapters/chap7_results} -\input{chapters/chap8_conclusions} +%\input{chapters/chap3_comet} +%\input{chapters/chap4_alcap_phys} +%\input{chapters/chap5_alcap_setup} +%\input{chapters/chap6_analysis} +%\input{chapters/chap7_results} +%\input{chapters/chap8_conclusions} \begin{backmatter} \input{chapters/backmatter} From b21181a08abdc7a3c86720f6bf7edfde9f96e583 Mon Sep 17 00:00:00 2001 From: nam Date: Wed, 29 Oct 2014 19:51:47 +0900 Subject: [PATCH 16/26] prog saved --- thesis/chapters/chap2_mu_e_conv.tex | 18 +- thesis/chapters/chap3_comet.tex | 288 ++++++++++++++--------- thesis/figs/{sched.png => old_sched.png} | Bin thesis/thesis.bib | 52 +++- thesis/thesis.tex | 4 +- 5 files changed, 230 insertions(+), 132 deletions(-) rename thesis/figs/{sched.png => old_sched.png} (100%) diff --git a/thesis/chapters/chap2_mu_e_conv.tex b/thesis/chapters/chap2_mu_e_conv.tex index a1a84ed..4363e09 100644 --- a/thesis/chapters/chap2_mu_e_conv.tex +++ b/thesis/chapters/chap2_mu_e_conv.tex @@ -271,11 +271,11 @@ experimental limits on these two decay modes are set respectively by the MEG experiment~\cite{Adam.etal.2013} and the SINDRUM-II experiment~\cite{Bertl.etal.2006}: \begin{equation} - \mathcal{B}(\mu^+ \rightarrow e^+ \gamma) < 5.7 \times 10^{-13}\, + \mathcal{B}(\mu^+ \rightarrow e^+ \gamma) < 5.7 \times 10^{-13}\,, \end{equation} and: \begin{equation} - \mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13}\. + \mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13}\,. \end{equation} %\hl{TODO: mueg and muec relations, Lagrangian \ldots} @@ -307,14 +307,13 @@ In the context of physics beyond the SM, the exotic process of \mueconv where a muon decays to an electron without neutrinos is also expected, but has never been observed: \begin{equation} - \mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)\. + \mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)\,. \end{equation} -The emitted electron in this decay -mode , the \mueconv electron, is mono-energetic at an energy far above the -endpoint +The emitted electron in this decay mode, the \mueconv electron, is +mono-energetic at an energy far above the endpoint of the Michel spectrum (52.8 MeV): \begin{equation} - E_{\mu e} = m_\mu - E_b - \frac{E^2_\mu}{2m_N} + E_{\mu e} = m_\mu - E_b - \frac{E^2_\mu}{2m_N}\,. \end{equation} where $m_\mu$ is the muon mas; $E_b \simeq Z^2\alpha^2 m_\mu/2$ is the binding energy of the muonic atom; and the last term is the nuclear recoil energy @@ -351,7 +350,10 @@ The mean lifetime $\tau = 1/\Gamma$, then: \end{equation} The mean lifetimes of free muons and muons in a material are well-known, therefore the number of captures can be inferred from the number of stops. For -aluminium, $\frac{\Gamma_{\textrm{capture}}}{\Gamma_{\textrm{stop}}} = 0.609$ +aluminium, +\begin{equation} + \frac{\Gamma_{\textrm{capture}}}{\Gamma_{\textrm{stop}}} = 0.609 +\end{equation} and the mean lifetime of stopped muons is 864 ns~\cite{SuzukiMeasday.etal.1987}. diff --git a/thesis/chapters/chap3_comet.tex b/thesis/chapters/chap3_comet.tex index da9979b..a451973 100644 --- a/thesis/chapters/chap3_comet.tex +++ b/thesis/chapters/chap3_comet.tex @@ -5,8 +5,8 @@ This chapter describes the new experimental search for \mueconv, namely COMET - (\textbf{CO}herent \textbf{M}uon to \textbf{E}lectron \textbf{T}ransition). The experiment will be carried out at the Japan Proton Accelerator Research Complex -(J-PARC), aims at a sensitivity of \sn{6}{-17} i.e. 10,000 times better than the -current best limit. +(J-PARC), aims at a single event sensitivity of \num{6E-17}, i.e. 10,000 times +better than the current best limit. %At the Japan Proton Accelerator Research Complex (J-PARC), an experiment to %search for \muec~conversion, which is called @@ -48,8 +48,9 @@ current best limit. The searches for \mueconv has been ongoing for more than 50 years, started in 1952 with cosmic rays~\cite{LagarriguePeyrou.1952} and then moved to -accelerators. The list in the Table~\ref{tab:mueconv_history} is reproduced -from a recent review of Bernstein and Cooper~\cite{BernsteinCooper.2013}. +accelerators. The list of upper limits for \mueconv in +\cref{tab:mueconv_history} is reproduced from a recent review of Bernstein +and Cooper~\cite{BernsteinCooper.2013}. \begin{table}[htb] \begin{center} \begin{tabular}{l l l c} @@ -79,40 +80,43 @@ from a recent review of Bernstein and Cooper~\cite{BernsteinCooper.2013}. \label{tab:mueconv_history} \end{table} -The most recent experiments were the SINDRUM and SINDRUM-II at the Paul -Scherrer Institute (PSI), Switzerland. The SINDRUM-II measured the branching +The latest experiments were the SINDRUM and SINDRUM-II at the Paul +Scherrer Institute (PSI), Switzerland. The SINDRUM-II +(\cref{fig:sindrumII_setup}) measured the branching ratio of \mueconv on a series of heavy targets: Ti, Pb and Au. The proton beam -at PSI is a continuous wave beam, with a time structure of 0.3 ns bursts every -19.75 \si{\nano\second}. An 8-\si{\milli\meter}-thick CH$_2$ degrader was used to reduce -the radiative pion capture and other prompt backgrounds. Cosmic backgrounds are +at PSI is a continuous beam, with a time structure of 0.3 ns bursts every +19.75 \si{\nano\second}. An 8-\si{\milli\meter}-thick CH$_2$ degrader was used +to reduce the radiative pion capture and other prompt backgrounds. Cosmic +backgrounds are rejected using a combination of -passive shielding, veto counters and reconstruction cuts. The momenta of muons -were 52 \si{\mega\electronvolt\per\cc} and 53 \si{\mega\electronvolt\per\cc}, and the -momentum spread was 2\%. +passive shielding, veto counters and reconstruction cuts. The momenta of beam +muons used in the experiment were \SI{52}{\MeV\per\cc} and +\SI{53}{\MeV\per\cc}, and the momentum spread was 2\%. \begin{figure}[htbp] \centering \includegraphics[width=0.85\textwidth]{figs/sindrumII_setup} \caption{SINDRUM-II set up} \label{fig:sindrumII_setup} \end{figure} -Electrons emitted from the target were tracked in a 0.33 T solenoid field. -Detector system consisted of a superconducting solenoid, two plastic +Electrons emitted from the target were tracked in a 0.33 T solenoidal magnetic +field. Detector system consisted of a superconducting solenoid, two plastic scintillation hodoscopes, a plexiglass Cerenkov hodoscope, and two drift chambers. In the latest measurement, the SINDRUM-II collaboration have not found any conversion electron from captured muons in a gold target, hence set the upper limit for -the branching ratio of \mueconv in gold with 90 \% C.L. at \sn{7.0}{-13}. +the branching ratio of \mueconv in gold with 90 \% C.L. at \num{7.0E-13}. The reconstructed momenta of electrons around the signal region from SINDRUM-II -is shown in the Figure~\ref{fig:sindrumII_result}. It can be seen that the muon +is shown in \cref{fig:sindrumII_result}. It can be seen that the muon decay in orbit background falls steeply near the endpoint as expected, but, the prompt background induced by pions still remains even after the cut in timing and track angle. This indicates the problem of pion contamination is very -important in probing lower sensitivity. +important in probing better sensitivity. \begin{figure}[htbp] \centering \includegraphics[width=0.55\textwidth]{figs/sindrumII_Au_result} - \caption{SINDRUM-II result} + \caption{SINDRUM-II results} +%TODO: explain top and bottom figure \label{fig:sindrumII_result} \end{figure} % subsection experimental_history (end) @@ -124,28 +128,30 @@ A new generation of \mueconv experiments have been proposed with scenarios to overcome pion induced background in the SINDRUM-II. Lobashev and collaborators first suggested the basic idea for new \mueconv at the Moscow Muon Factory; this idea was used to develop the MECO experiment at Brookhaven National -Laboratory. The MECO experiment was cancelled due to budget constraints. The two -modern experiments, COMET at J-PARC and Mu2e at Fermilab use the initial idea +Laboratory. The MECO experiment was cancelled due to budget constraints. Two +recent experiments, COMET at J-PARC and Mu2e at Fermilab, use the initial idea with more upgrades and modifications. -The basic ideas of the modern experiments are: +The basic ideas of the two experiments are: \begin{enumerate} \item Highly intense muon source: the total number of muons needed is of the order of $10^{18}$ in order to achieve a sensitivity of $10^{-16}$. This can be done by producing more pions using a high power proton beam, and having a high efficiency pion collection system; - \item Pulsed proton beam with an appropriate timing: the proton pulse should + \item Pulsed proton beam: the proton pulse should be short compares to the lifetime of muons in the stopping target material, and the period between pulses should be long enough for prompt backgrounds from pion to decay before beginning the measurement. It is also crucial that there is no proton leaks into the measuring interval; \item Curved solenoids for charge and momentum selection: at first, the curved solenoids remove the line of sight backgrounds. A charged particle travels - through a curved solenoidal field will have the centre of the helical - motion drifted up or down depends on the sign of the charge, and the - magnitude of the drift is proportional to its momentum. By using this - effect and placing suitable collimators, charge and momentum selection can - be made. + through a curved solenoidal magnetic field has the centre of the helical + motion drifted up or down with respect to the bending plane depends on the + sign of the charge, and the magnitude of the drift is proportional to its + momentum. By using this effect and placing suitable collimators, charge and + momentum selection can be made. Details of the magnet system are described + in \cref{sub:pion_production_can_capture_solenoid} and + \cref{sub:pion_and_muon_transportation}. \end{enumerate} % subsection new_generation_of_mueconv_experiments (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -156,13 +162,14 @@ The basic ideas of the modern experiments are: \section{Concepts of the COMET experiment} \label{sec:concepts_of_the_comet_experiment} This section elaborates the design choices of the COMET to realise the basic -ideas mentioned above. Figures and numbers, other than noted, are taken from -the COMET's documentations: +ideas mentioned previously. Figures and numbers, other than noted, are taken +from the COMET's documentations: \begin{itemize} %TODO citations - \item Conceptual design report for the COMET experiment~\cite{COMET.2009} - \item Proposal Phase-I 2012 - \item TDR 2014 + \item Conceptual design report for the COMET experiment~\cite{COMET.2009}, + \item Experimental Proposal for Phase-I of the COMET Experiment at + J-PARC~\cite{COMET.2012}, + \item and COMET Phase-I Technical Design Report~\cite{COMET.2014}. \end{itemize} @@ -172,30 +179,30 @@ A high power pulsed proton beam is of utmost importance to achieve the desired sensitivity of the COMET experiment. A slow-extracted proton beam from the J-PARC main ring (MR), which is designed to deliver \sn{3.6}{15} protons per cycle at a frequency of 0.45 Hz, will be used for the COMET experiment. The -proton beam power of the current design is 8 GeV$\times$7 $\mu$A, or -\sn{4.4}{13} protons/s. The beam energy 8 \si{\giga\electronvolt} helps to minimise -the production of antiprotons. +proton beam power of the current design is $\SI{8}{\GeV}\times \SI{7}{\uA}$, or +\num{4.4E13} protons/s at \SI{8}{\GeV}. The beam energy was chosen to minimise +the production of antiprotons which may introduce background events. The proton pulse width is chosen to be 100 ns, and the pulse period to be -$1 \sim 2 \textrm{ }\mu\textrm{s}$. This time structure is sufficient for the -search for \mueconv in an aluminium target where the lifetime of muons is 864 -ns. A plan of accelerator operation to realise the scheme is shown in -the Figure~\ref{fig:comet_mr_4filled}, where 4 out of 9 MR buckets are filled. +from \SIrange{1}{2}{\us}. This time structure is sufficient for the +search for \mueconv in an aluminium target where the mean lifetime of negative +muons in muonic atoms is \SI{864}{\ns}. One possible plan of accelerator +operation to realise the beam pulsing is shown in \cref{fig:comet_mr_4filled}, +where 4 out of 9 MR buckets are filled. As mentioned, it is very important that there is no stray proton arrives in the measuring period between two proton bunches. An extinction factor is defined as the ratio between number of protons in between two pulses and the number of protons in the main pulse. In order to achieve the goal sensitivity of the -COMET, an extinction factor of \sn{}{-9} is required. +COMET, an extinction factor less than \num{E-9} is required. -Requirements for the proton beam are summarised in the -Table~\ref{tab:comet_proton_beam}. +Requirements for the proton beam are summarised in \cref{tab:comet_proton_beam}. \begin{figure}[htb] \centering \includegraphics[width=0.8\textwidth]{figs/comet_mr_4filled} - \caption{The COMET proton bunch structure in the RCS (rapid cycle - synchrotron) and MR where 4 buckets + \caption{The COMET proton bunch structure in the RCS (Rapid Cycling + Synchrotron) and MR where 4 buckets are filled producing 100 \si{\nano\second} bunches separated by 1.2~\si{\micro\second}.} \label{fig:comet_mr_4filled} @@ -234,7 +241,7 @@ pions, are preferred. It is known from other measurements that backward scattered pions (with respect to proton beam direction) of high energy are suppressed, and the yield of low energy pions in the backward direction is not too low compares to that of the forward direction (see -Figure~\ref{fig:pion_yield}). For these reasons, the COMET +\cref{fig:pion_yield}). For these reasons, the COMET decided to collect backward pions. \begin{figure}[htb] \centering @@ -243,10 +250,9 @@ decided to collect backward pions. target.} \label{fig:pion_yield} \end{figure} - The pion capture system is composed of several superconducting solenoids: capture solenoids and matching solenoids. The magnetic field distribution along -the beam axis of the COMET is shown in the Figure~\ref{fig:comet_Bfield}. The +the beam axis of the COMET is shown in \cref{fig:comet_Bfield}. The peak field of 5 T is created by the capture solenoid, and the matching solenoids provide a smooth transition from that peak field to the 3 T field in the pions/muons transportation region. The superconducting solenoids are @@ -258,6 +264,7 @@ will be installed inside the cryostat to reduce radiation heat load. \caption{Magnetic field distribution along the COMET beam line.} \label{fig:comet_Bfield} \end{figure} +%TODO full comet field % subsection pion_production_can_capture_solenoid (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -266,7 +273,7 @@ will be installed inside the cryostat to reduce radiation heat load. Muons and pions are transported to the muon stopping target through a muon beam line, which includes several curved and straight superconducting solenoid magnets. A schematic layout of the muon beam line, include the capture and -detector sections, is shown in Figure~\ref{fig:comet_beamline_layout}. +detector sections, is shown in \cref{fig:comet_beamline_layout}. \begin{figure}[htb] \centering \includegraphics[width=0.95\textwidth]{figs/comet_beamline_layout} @@ -292,7 +299,7 @@ of the drift is given by: &= \frac{1}{qB} \frac{s}{R} \frac{p}{2} \left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right)\\ &= \frac{1}{qB} \theta_{bend} \frac{p}{2} - \left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right) + \left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right)\,, \end{align} where $q$ is the electric charge of the particle; $B$ is the magnetic field at the axis; $s$ and $R$ are the path length and the radius of the curvature; $p$, @@ -312,7 +319,7 @@ produced by additional coils winded around the solenoid coils. The magnitude of the compensating field is: \begin{equation} B_{\textrm{comp}} = \frac{1}{qR} \frac{p_0}{2} - \left( \textrm{cos}\theta_0 + \frac{1}{\textrm{cos}\theta_0} \right) + \left( \textrm{cos}\theta_0 + \frac{1}{\textrm{cos}\theta_0} \right)\,, \end{equation} where the trajectories of charged particles with momentum $p_0$ and pitch angle $\theta_0$ are corrected to be on-axis. An average dipole field of 0.03 T is @@ -321,23 +328,42 @@ needed to select 40 MeV/$c$ muons as required by the COMET design. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Muon stopping target} \label{sub:muon_stopping_target} -Muon stopping target is place at 180\si{\degree}~bending after the pion production -target (Figure~\ref{fig:comet_beamline_layout}) in its own solenoid. The target +Muon stopping target is place at 180\si{\degree}~bending after the pion +production target (\cref{fig:comet_beamline_layout}) in its own solenoid. The +target is designed to maximise the muon stopping efficiency and minimise the energy loss of signal electrons. %\hl{TODO: Target choice: separation, product, lifetime, energy loss\ldots} It is calculated that the branching ratio of \mueconv increases with atomic -number $Z$, and plateaus above $Z \simeq 30$, then decreases as $Z>60$. The -lifetime of muons inside a material decreases quickly as $Z$ increases. -Tracking wise, lower $Z$ material provides better reconstructed momentum -resolution. Therefore, light material is preferable as muon stopping target. +number $Z$, and plateaus above $Z \simeq 30$, then decreases as $Z>60$ (see +\cref{fig:comet_mueconv_RateVsZ}). Although the sensitivity is better for +higher $Z$ material, the acceptance of the measurement time window decreases +quickly because the average lifetime of negative muons inside a material +decreases as $Z^{-4}$. +%Tracking wise, lower $Z$ material provides better +%reconstructed momentum +%resolution. +Therefore, light material is preferable as muon stopping target. +\begin{figure}[hbp] + \centering + \includegraphics[width=0.60\textwidth]{figs/comet_mueconv_RateVsZ} + \caption{Target dependence of the \mueconv rate in different models + calculated by Cirigliano and colleagues~\cite{CiriglianoKitano.etal.2009}. + The conversion rates are normalised to the rate in aluminium. Four models + were considered and noted with letters: D for dipole-interaction-dominated + model, V for vector and S for scalar interactions. The three vertical lines + from left to right correspond to $Z=13$(Al), $Z=22$(Ti), and $Z=82$(Pb)l + respectively.} + \label{fig:comet_mueconv_RateVsZ} +\end{figure} The first choice for the muon stopping target material in the COMET is -aluminium. A titanium target is also considered. Configuration of the target is -shown in the Table~\ref{tab:comet_al_target}. Monte Carlo studies with this +aluminium. A titanium target is also considered in the future. Configuration of +the target is shown in \cref{tab:comet_al_target}. Monte Carlo studies with +this design showed that net stopping efficiency is 0.29, and average energy loss -of signal electrons is about 400 \si{\kilo\electronvolt}. +of signal electrons is about \SI{400}{\keV}. \begin{table}[htb] \begin{center} \begin{tabular}{l l} @@ -358,7 +384,7 @@ of signal electrons is about 400 \si{\kilo\electronvolt}. \end{table} A graded magnetic field (reduces from 3 T to 1 T) is produced at the -location of the stopping target (see Figure~\ref{fig:comet_target_Bfield}) to +location of the stopping target (see \cref{fig:comet_target_Bfield}) to maximise the acceptance for \mueconv signals, since electrons emitted in the backward direction would be reflected due to magnetic mirroring. The graded field also @@ -375,36 +401,36 @@ transport section. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Electron transportation beam line} \label{sub:electron_transportation_beam_line} -The 180\si{\degree}~bending electron transport solenoids help remove line-of-sight +The \ang{180} bending electron transport solenoids help remove line-of-sight between the target and the detector system. It works similarly to the muon transportation section, but is tuned differently to accept electrons of about -105~\si{\mega\electronvolt\per\cc}. A compensation field of 0.17 T along the -vertical direction will be applied. Electrons with momentum less than 80 -\si{\mega\electronvolt\per\cc} are blocked at the exit of this section by +\SI{105}{\MeV\per\cc}. A compensation field of \SI{0.17}{\tesla} along the +vertical direction will be applied. Electrons with momentum less than +\SI{80}{\MeV\per\cc} are blocked at the exit of this section by a collimator to reduce DIO electrons rate. The net acceptance of signals of \mueconv is about 0.32, and the detector hit rate will be in the order of -1~\si{\kilo\hertz}~for \sn{}{11} stopped muons\si{\per\second}. +\SI{1}{\kHz} for a muon stopping rate of \SI{E11}{\Hz}. % subsection electron_transportation_beam_line (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Electron detectors} \label{sub:electron_detectors} The \mueconv signal electrons is measured by an electron detector system, which consists of straw-tube trackers and an electromagnetic calorimeter - shown in -Figure~\ref{fig:comet_detector_system}. The +\cref{fig:comet_detector_system}. The requirements for the detector system is to distinguish electrons from other particles, and measure their momenta, energy and timings. The whole detector system is in a uniform solenoidal magnetic field under vacuum. Passive and active shielding against cosmic rays is considered. The tracking detector has to provide a momentum resolution less than +%%TODO 350 or 150? 350~\si{\kilo\electronvolt\per\cc} in order to achieve a sensitivity of \sn{3}{-17}. There are five stations of straw-tube gas chambers, each provides -two -dimensional information. Each straw tube is 5~\si{\milli\meter} in diameter and has -a 25~\si{\micro\meter}-thick wall. According to a GEANT4 Monte Carlo simulation, -a position resolution of 250~\si{\micro\meter} can be obtained, which is enough for -350~\si{\kilo\electronvolt\per\cc} momentum resolution. The DIO background of 0.15 -events is estimated. +two dimensional information. Each straw tube is 5~\si{\milli\meter} in diameter +and has a 25-\si{\micro\meter}-thick wall. According to a GEANT4 Monte Carlo +simulation, a position resolution of 250~\si{\micro\meter} can be obtained, +which is enough for 350~\si{\kilo\electronvolt\per\cc} momentum resolution. The +DIO background of 0.15 events is expected. The electromagnetic calorimeter serves three purposes: a) to measure electrons energy with high energy resolution; b) to provide timing information and @@ -427,7 +453,7 @@ The requirements for \mueconv signals are: muons decay in flight; \item timing wise, conversion electrons should arrive in the time window of detection which is about 700~\si{\nano\second}~after each proton pulses - (Figure~\ref{fig:comet_meas_timing}). The acceptance in this detection + (\cref{fig:comet_meas_timing}). The acceptance in this detection window is about 0.39 for aluminium. \end{itemize} @@ -472,7 +498,7 @@ Potential backgrounds for the COMET are: \item Accidental background from cosmic rays \end{enumerate} The expected background rates for the COMET at an SES of -\sn{3}{-17} is summarised in Table~\ref{tab:comet_background_estimation}. +\sn{3}{-17} is summarised in \cref{tab:comet_background_estimation}. \begin{table}[htb] \begin{center} %\begin{tabular}{l l} @@ -516,11 +542,12 @@ are believed to greatly reduce potential backgrounds, by several orders of magnitude, for the \mueconv search. That also means that backgrounds are being extrapolated over four orders of magnitude from existing data. In order to obtain data-driven estimates of backgrounds, and inform the detailed design for -the ultimate COMET experiment, and initial phase is desirable. Also, the 5-year -mid-term plan from 2013 of J-PARC includes the construction of the COMET beam -line. For these reasons, the COMET collaboration considers a staged approach -with the first stage, so called COMET Phase-I, with a shorter muon -transportation solenoid, up to the first 90\si{\degree}. +the ultimate COMET experiment, a staged approach is desirable. Also, the +KEK/J-PARC 5-year mid-term plan from 2013 includes the construction +of the COMET beam line. For these reasons, the COMET collaboration considers +to carry out the experiment in two stages. The first stage, so called COMET +Phase-I, with a shorter muon transportation solenoid, up to the first +90\si{\degree}. %\begin{wrapfigure}{r}{0.5\textwidth} %\centering @@ -531,8 +558,8 @@ transportation solenoid, up to the first 90\si{\degree}. %\end{wrapfigure} \begin{SCfigure} \centering - \caption{Lay out of the COMET Phase-I, the target and detector solenoid are - placed after the first 90\si{\degree}~bend.} + \caption{Layout of the COMET Phase-I, the target and detector solenoid are + placed after the end of the first \ang{90} bend.} \includegraphics[width=0.4\textwidth]{figs/comet_phase1_layout} \label{fig:comet_phase1_layout} \end{SCfigure} @@ -545,11 +572,11 @@ The COMET Phase-I has two major goals: and physics background from muon DIO. Straw tube trackers and crystal calorimeter with the same technology in the full COMET will be used, thus these detectors can be regarded as the final prototype. - \item Search for \mueconv with an intermediate sensitivity of \sn{3.1}{-15}, - a two orders of magnitude improvement from the SINDRUM-II limit. To realise - this goal, two options for detectors are being considered, either a reused - of the detectors for background measurements, or a dedicated detector. - The latter will be described in detail later. + \item Search for \mueconv with an intermediate single event sensitivity of + \num{3.1E-15}, a two orders of magnitude improvement from the SINDRUM-II + limit. Another dedicated detector system (described in + \cref{sub:detectors_for_mueconv_search_in_the_phase_i}) is considered for + this physics measurement. \end{enumerate} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -558,11 +585,11 @@ The COMET Phase-I has two major goals: Proton beam for the Phase-I differs only in beam power compares to that of the full COMET. It is estimated that a beam power of 3.2~\si{\kilo\watt}~$=$~8~\si{\giga\electronvolt}~$\times$~0.4~\si{\micro\ampere}~(or -\sn{2.5}{12} protons\si{\per\second}) will be enough for beam properties +\sn{2.5}{12} protons per second) will be enough for beam properties study and achieving the physics goal of this stage. Starting from a lower intensity is also suitable for performing accelerator -studies that are needed to realise 8~\si{\giga\electronvolt} beam extraction from -the J-PARC main ring. +studies that are needed to realise 8~\si{\giga\electronvolt} beam extraction +from the J-PARC main ring. % subsection proton_beam_for_the_comet_phase_i (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Pion production and transportation solenoids} @@ -579,7 +606,7 @@ A correction dipole filed of 0.05 T is also applied to improve the pion yield. The pion/muon beam line for COMET Phase-I consists of the pion capture solenoid section (CS), muon transport solenoid section (TS) up to the first 90\si{\degree}~bending, and a set of matching solenoids (see -Figure~\ref{fig:comet_phase1_magnets}). At the end of the muon beam line, the +\cref{fig:comet_phase1_magnets}). At the end of the muon beam line, the detectors and the detector solenoid (DS) are installed. To reduce beam backgrounds, a beam collimator is placed upstream of the detector solenoid. \begin{figure}[htb] @@ -599,7 +626,7 @@ backgrounds, a beam collimator is placed upstream of the detector solenoid. As mentioned, two types of detectors are considered for physics measurements in the Phase-I. The dedicated detector system consists of a cylindrical drift chamber (CDC), a trigger hodoscope, a proton absorber and a detector solenoid -(Figure~\ref{fig:comet_phase1_cydet}). +(\cref{fig:comet_phase1_cydet}). The whole system is referred as cylindrical detector system (CyDet) in the COMET's documentation. The CyDet has advantages that low momentum particles for the stopping target will not reach the detector, thus the hit rates are kept @@ -614,26 +641,28 @@ CyDet. \label{fig:comet_phase1_cydet} \end{figure} +\subsubsection{CDC configuration} +\label{ssub:CDC configuration} The CDC is the main tracking detector that provides information for reconstruction of charged particle tracks and measuring their momenta. The key parameters for the CDC are listed in the -Table~\ref{tab:comet_phase1_cdc_params}. +\cref{tab:comet_phase1_cdc_params}. Trigger hodoscopes are placed at both upstream and downstream ends of the CDC. -An absorber is placed concentrically with respect to the CDC axis to +A proton absorber is placed concentrically with respect to the CDC axis to reduce potential high rates caused by protons emitted after nuclear muon capture in the stopping target. The CDC covers the region from \SIrange{500}{831}{\milli\meter}~in the radial direction. The length of the CDC is 1500~\si{\milli\meter}. The inner wall is made of -a 100~\si{\micro\meter}-thick aluminised Mylar. The end-plates will be conical -in shape and about 10~\si{\milli\meter}-thick to support the feedthroughs. The outer -wall is -made of 5~\si{\milli\meter}~carbon fibre reinforced plastic (CFRP). +a 500-\si{um}-thick carbon fibre reinforced plastic (CFRP, density +\SI{1.57}{\gram\per\cubic\m}). The end-plates will +be conical in shape and about 10-\si{\mm}-thick to support the +feedthroughs. The outer wall is made of 5-\si{\mm} CFRP. The CDC is arranged in 20 concentric sense layers with alternating positive and negative stereo angles. The sense wires are made of gold-plated tungsten, -30~\si{\micro\meter} in diameter, tensioned to 50~\si{\gram}. The field wires +\SI{25}{\um} in diameter, tensioned to \SI{50}{\gram}. The field wires are uncoated aluminium wires with a diameter of 80~\si{\micro\meter}, at the same tension of \SI{50}{\gram}. A high voltage of $1700\sim1900$~\si{\volt} will be applied to the sense wires with the field wires at ground potential, giving an @@ -674,37 +703,69 @@ these configurations, an intrinsic momentum resolution of \label{tab:comet_phase1_cdc_params} \end{table} -The maximum usable muon beam intensity will be limited by the detector hit +\subsubsection{Hit rate on the CDC} +\label{ssub:hit_rate_on_the_cdc} +The maximal usable muon beam intensity will be limited by the detector hit occupancy. Charge particles with transversal momentum greater than 70 -\si{\mega\electronvolt\per\cc} are expected to reach the CDC. Those particles are: +\si{\mega\electronvolt\per\cc} are expected to reach the CDC. Those include: protons emitted from nuclear muon capture, and electrons from muon decay in -orbit. It is calculated that the hit rate due to proton emission dominates, -where the highest rate is 11~\si{\kilo\hertz\per}cell compares to -5~\si{\kilo\hertz\per} -cell contributing from DIO electrons. Another potential issue caused by protons -is the ageing effect on the CDC as they leave about a 100 times larger +orbit (DIO). It is calculated that the hit rate due to proton emission dominates, +where the highest rate is \SI{11}{\kHz\per}cell compares to +\SI{5}{\kHz\per}cell contributing from DIO electrons. Another potential issue +%%TODO check the hit rates against TDR +caused by protons is the ageing effect on the CDC as they leave about a 100 +times larger energy deposit than the minimum ionisation particles. +%%TODO integration charge ... -For those reasons, we plan to install an absorber to reduce the rate of protons -reaching the CDC. However, there is no experimental data available for the rate +For those reasons, we plan to install a proton absorber to reduce the rate of +protons reaching the CDC. However, there is no experimental data available for +the rate of protons emitted after muon capture in aluminium. In the design of the COMET Phase-I, we use a conservative estimation of the rate of protons from energy spectrum of charged particles emitted from muon capture in $^{28}$Si~\cite{SobottkaWills.1968}. The baseline design for the proton -absorber is 1.0~\si{\milli\meter}-thick CFRP, which contributes -195~\si{\kilo\electronvolt\per\cc} to the momentum resolution of reconstructed -track. +absorber is 1.0~\si{\milli\meter}-thick CFRP, making the total thickness +of material before the sensitive region is \SI{1.5}{\mm} in CFRP. In this +configuration, the inner wall and the proton absorber deteriorate the momentum +resolution of the reconstructed track to 195~\si{\kilo\electronvolt\per\cc}. +The impact of the proton absorber on the CDC's hit rate and momentum +resolution is summarised in \cref{tab:comet_absorber_impact}. +\begin{table}[htb] + \begin{center} + \begin{tabular}{@{}ccc@{}} + \toprule + \textbf{Absorber }& \textbf{Proton }& \textbf{Momentum }\\ + \textbf{thickness }& \textbf{hit rate }& \textbf{resolution }\\ + (\si{\um}) & (\si{\kHz}) & (\si{\keV\per\cc}) \\ + \midrule + 0 & 130 & 131 \\ + 0.5 & 34 & 167 \\ + 1.0 & 11 & 195 \\ + 1.5 & 6 & 252 \\ + \bottomrule + \end{tabular} + \end{center} + \caption{Hit rates and contributions to momentum resolution of the proton + absorber and inner wall of the CDC. The intrinsic momentum resolution due + to multiple scattering is \SI{197}{\keV\per\cc}.} + \label{tab:comet_absorber_impact} +\end{table} In order to obtain a better understanding of the protons emission, and then further optimisation of the CDC, a dedicated experiment to measure proton emission rate and energy spectrum is being carried out at PSI. This experiment is described in detail in next chapters. + +It should be noted that the proton hit rate is not a problem for the COMET +Phase-II where the additional electron transport solenoid will removed all +protons emitted. % subsection detectors_for_mueconv_search_in_the_phase_i (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Sensitivity of the \mueconv search in the Phase-I} \label{sub:sensitivity_of_the_mueconv_search_in_the_phase_i} The SES for the Phase-I is given by -the Equation~\ref{eq:mue_sensitivity}. Using $N_{\mu} = 1.3\times 10^{16}$, +the \eqref{eq:mue_sensitivity}. Using $N_{\mu} = 1.3\times 10^{16}$, $f_{\textrm{cap}} = 0.61$, and $A_e = 0.043$ from MC study for the Phase-I, the SES becomes: \begin{equation} @@ -715,10 +776,11 @@ SES becomes: \subsection{Time line of the COMET Phase-I and Phase-II} \label{sub:time_line_of_the_phase_i} We are now in the construction stage of the COMET Phase-I, which is planned to -be finished by the end of 2016. We will carry out engineering run in 2016, +be finished in the middle of 2016. We will carry out engineering run in the +second half of 2016, and subsequently, physics run in 2017. A beam time of 90 days is expected to achieve the goal sensitivity of the Phase-I. An anticipated schedule for the -COMET, both Phase-I and Phase-II, is shown in Figure~\ref{fig:sched}. +COMET, both Phase-I and Phase-II, is shown in \cref{fig:sched}. \begin{figure}[tbh] \centering \includegraphics[width=0.8\textwidth]{figs/sched} diff --git a/thesis/figs/sched.png b/thesis/figs/old_sched.png similarity index 100% rename from thesis/figs/sched.png rename to thesis/figs/old_sched.png diff --git a/thesis/thesis.bib b/thesis/thesis.bib index 6b34593..abc2226 100644 --- a/thesis/thesis.bib +++ b/thesis/thesis.bib @@ -161,11 +161,11 @@ } @TechReport{COMET.2012, - Title = {Experimental Proposal for Phase-I of the COMET - Experiment at J-PARC}, + Title = {Experimental Proposal for Phase-I of the COMET Experiment at J-PARC}, Author = {R. Akhmetshin and A. Bondar and L. Epshteyn and G. Fedotovich and D. Grigoriev and V. Kazanin and A. Ryzhenenkov and D. Shemyakin and Yu. Yudin and others}, + Institution = {KEK}, Year = {2012}, Month = {7}, Number = {KEK/J-PARC-PAC 2012-10}, @@ -334,6 +334,7 @@ Volume = {729}, Doi = {http://dx.doi.org/10.1016/j.nuclphysa.2003.11.003}, + File = {Published version:AudiWapstra.etal.2003.pdf:PDF}, ISSN = {0375-9474}, Owner = {NT}, Timestamp = {2014-10-26}, @@ -657,16 +658,49 @@ Timestamp = {2014-04-03} } -@Article{COMET.2009, - Title = {Conceptual design report for experimental search for lepton flavor violating $\mu$-- e- conversion at sensitivity of 10^{-16} with a slow-extracted bunched proton beam}, - Author = {COMET}, - Journal = {KEK Report}, +@Article{CiriglianoKitano.etal.2009, + Title = {Model discriminating power of $\mu\rightarrow e$ conversion in nuclei}, + Author = {Cirigliano, Vincenzo and Kitano, Ryuichiro and Okada, Yasuhiro and Tuzon, Paula}, + Journal = {Phys. Rev. D}, Year = {2009}, - Pages = {2009}, - Volume = {10}, + + Month = {Jul}, + Pages = {013002}, + Volume = {80}, + + Doi = {10.1103/PhysRevD.80.013002}, + File = {Published version:CiriglianoKitano.etal.2009.pdf:PDF}, + Issue = {1}, + Numpages = {13}, + Owner = {NT}, + Publisher = {American Physical Society}, + Timestamp = {2014-10-29}, + Url = {http://link.aps.org/doi/10.1103/PhysRevD.80.013002} +} + +@TechReport{COMET.2014, + Title = {COMET Phase-I Technical Design Report}, + Author = {COMET}, + Institution = {KEK}, + Year = {2014}, + Month = {9}, + Type = {Report}, Owner = {NT}, - Timestamp = {2014-07-13} + Timestamp = {2014-10-29} +} + +@TechReport{COMET.2009, + Title = {Conceptual Design Report for experimental search for lepton flavor violating $\mu^- - e^-$ conversion at sensitivity of $10^{-16}$ with a slow-extracted bunched proton beam}, + Author = {COMET}, + Institution = {KEK}, + Year = {2009}, + Type = {Report}, + + Owner = {NT}, + Pages = {2009}, + Timestamp = {2014-07-13}, + Volume = {10} } @Article{ConfortoConversi.etal.1962, diff --git a/thesis/thesis.tex b/thesis/thesis.tex index 2c4a93b..6ae020a 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -30,8 +30,8 @@ for the COMET experiment} \mainmatter %\input{chapters/chap1_intro} -\input{chapters/chap2_mu_e_conv} -%\input{chapters/chap3_comet} +%\input{chapters/chap2_mu_e_conv} +\input{chapters/chap3_comet} %\input{chapters/chap4_alcap_phys} %\input{chapters/chap5_alcap_setup} %\input{chapters/chap6_analysis} From 582b15839eb8626c120b2094bec6d0a896001ae1 Mon Sep 17 00:00:00 2001 From: nam Date: Thu, 30 Oct 2014 01:27:55 +0900 Subject: [PATCH 17/26] prog saved --- thesis/chapters/chap4_alcap_phys.tex | 337 +++++++++++++++------------ thesis/thesis.tex | 4 +- 2 files changed, 196 insertions(+), 145 deletions(-) diff --git a/thesis/chapters/chap4_alcap_phys.tex b/thesis/chapters/chap4_alcap_phys.tex index 0501d5b..a95e682 100644 --- a/thesis/chapters/chap4_alcap_phys.tex +++ b/thesis/chapters/chap4_alcap_phys.tex @@ -5,19 +5,19 @@ \thispagestyle{empty} As mentioned earlier, the emission rate of protons following nuclear muon capture on aluminium is of interest to the COMET Phase-I -since protons can cause a very high hit rate on the proposed cylindrical drift +since protons could cause a very high hit rate on the proposed cylindrical drift chamber. Another \mueconv experiment, namely Mu2e at Fermilab, which aims at a similar goal sensitivity as that of the COMET, also shares the same interest on proton emission. Therefore, a joint COMET-Mu2e project was formed to carry out the measurement of proton, and other charged particles, emission. The experiment, so-called AlCap, has been proposed and approved to be carried out -at PSI in 2013~\cite{AlCap.2013}. In addition to proton, the AlCap +at PSI in 2013~\cite{AlCap.2013}. In addition to proton emission, the AlCap experiment will also measure: \begin{itemize} - \item neutrons, because they can cause backgrounds on other detectors and - damage the front-end electronics; and - \item photons, since they provide ways to normalise number of stopped muons - in the stopping target. + \item neutron emission, because neutrons could cause backgrounds on the other + detectors and damage the front-end electronics; and + \item photon emission to validate the normalisation number of stopped + muons in the stopping target. \end{itemize} The emission of particles following muon capture in nuclei @@ -27,7 +27,7 @@ energy nuclear physics'' where it is postulated that the weak interaction is well understood and muons are used as an additional probe to investigate the nuclear structure~\cite{Singer.1974, Measday.2001}. Unfortunately, the proton emission rate for aluminium in the energy range of -interest is not available. This chapter reviews the current knowledge on +interest has not been measured. This chapter reviews the current knowledge on emission of particles with emphasis on proton. %theoretically and experimentally, hence serves as the motivation for the AlCap %experiment. @@ -66,21 +66,20 @@ emission of particles with emphasis on proton. Theoretically, the capturing process can be described in the following stages~\cite{FermiTeller.1947, WuWilets.1969}: \begin{enumerate} - \item High to low (a few \si{\kilo\electronvolt}) energy: the muon velocity are - greater than the velocity of the valence electrons of the atom. Slowing + \item High to low (a few \si{\kilo\electronvolt}) energy: the muon velocity + are greater than the velocity of the valence electrons of the atom. Slowing down process is similar to that of fast heavy charged particles. It takes - about \sn{}{-9} to \sn{}{-10} \si{\second}~to slow down from a relativistic - \sn{}{8}~\si{\electronvolt}~energy to 2000~\si{\electronvolt}~in condensed matter, + about \SIrange{E-10}{E-9}{\s} to slow down from a relativistic + \SI{E8}{\eV} energy to \SI{2000}{\eV} in condensed matter, and about 1000 times as long in air. \item Low energy to rest: in this phase, the muon velocity is less than that of the valence electrons, the muon is considered to be moving inside a degenerate electron gas. The muon rapidly comes to a stop either in - condensed matters ($\sim$\sn{}{-13}~\si{\second}) or in gases ($\sim$\sn{}{-9} - \si{\second}). - \item Atomic capture: the muon has no kinetic energy, it is captured by the - host atom into one of high orbital states, forming a muonic atom. The + condensed matters ($\simeq\SI{E-13}{\s}$) or in gases ($\simeq\SI{E-9}{\s}$). + \item Atomic capture: when the muon has no kinetic energy, it is captured by + a host atom into one of high orbital states, forming a muonic atom. The distribution of initial states is not well known. The details depend on - whether the material is a solid or gas, insulator or material + whether the material is a solid or gas, insulator or metal. \item Electromagnetic cascade: since all muonic states are unoccupied, the muon cascades down to states of low energy. The transition is accompanied by the emission of Auger electrons or characteristic X-rays, or excitation @@ -88,10 +87,12 @@ stages~\cite{FermiTeller.1947, WuWilets.1969}: state, 1S, from the instant of its atomic capture is $\sim$\sn{}{-14}\si{\second}. \item Muon disappearance: after reaching the 1S state, the muons either - decays with a half-life of \sn{2.2}{-6}~\si{\second}~or gets captured by the - nucleus. In hydrogen, the capture to decay probability ratio is about - \sn{4}{-4}. Around $Z=11$, the capture probability is roughly equal to the - decay probability. In heavy nuclei ($Z\sim50$), the ratio of capture to + decays or gets captured by the nucleus. The possibility to be captured + effectively shortens the mean lifetime of negative muons stopped in + a material. In hydrogen, the capture to decay + probability ratio is about \sn{4}{-4}. Around $Z=11$, the capture + probability is roughly equal to the + decay probability. In heavy nuclei ($Z\geq$), the ratio of capture to decay probabilities is about 25. The K-shell muon will be $m_\mu/m_e \simeq 207$ times nearer the nucleus @@ -108,24 +109,25 @@ stages~\cite{FermiTeller.1947, WuWilets.1969}: \label{sec:nuclear_muon_capture} The nuclear capture process is written as: \begin{equation} - \mu^- + A(N, Z) \rightarrow A(N, Z-1) + \nu_\mu + \mu^- + A(N, Z) \rightarrow A(N, Z-1) + \nu_\mu \,. \label{eq:mucap_general} \end{equation} The resulting nucleus can be either in its ground state or in an excited state. The reaction is manifestation of the elementary ordinary muon capture on the proton: \begin{equation} - \mu^- + p \rightarrow n + \nu_\mu + \mu^- + p \rightarrow n + \nu_\mu \,. \label{eq:mucap_proton} \end{equation} -If the resulting nucleus at is in an excited state, it could cascade to lower -states by emitting light particles and leaving a residual heavy nucleus. The -light particles are mostly neutrons and (or) photons. Neutrons can also be +If the resulting nucleus at is in an excited state, it could cascade down to +lower states by emitting light particles and gamma rays, leaving a residual +heavy nucleus. The light particles are mostly neutrons and (or) photons. +Neutrons can also be directly knocked out of the nucleus via the reaction~\eqref{eq:mucap_proton}. Charged particles are emitted with probabilities of a few percent, and are mainly protons, deuterons and alphas have been observed in still smaller -probabilities. Because of the central interest on proton emission, it is covered -in a separated section. +probabilities. Because of the central interest on proton emission, it is +discussed in a separated section. \subsection{Muon capture on the proton} \label{sub:muon_capture_on_proton} @@ -138,10 +140,10 @@ in a separated section. %$\mu p$ atom is quite active, so it is likely to form muonic molecules like %$p\mu p$, $p\mu d$ and $p\mu t$, which complicate the study of weak %interaction. -The underlying interaction in proton capture in Equation~\eqref{eq:mucap_proton} +The underlying interaction in proton capture in~\eqref{eq:mucap_proton} at nucleon level and quark level -are depicted in the Figure~\ref{fig:feyn_protoncap}. The flow of time is from -the left to the right hand side, as an incoming muon and an up quark +are depicted in \cref{fig:feyn_protoncap}. The direction of time is +from the left to the right hand side, as an incoming muon and an up quark exchange a virtual $W$ boson to produce a muon neutrino and a down quark, hence a proton transforms to a neutron. @@ -156,7 +158,10 @@ a proton transforms to a neutron. \end{figure} The four-momentum transfer in the interaction is fixed at -$q^2 = (q_n - q_p)^2 = -0.88m_\mu^2 \ll m_W^2$. The smallness of the momentum +\begin{equation} + q^2 = (q_n - q_p)^2 = -0.88m_\mu^2 \ll m_W^2\,. +\end{equation} +The smallness of the momentum transfer in comparison to the $W$ boson's mass makes it possible to treat the interaction as a four-fermion interaction with Lorentz-invariant transition amplitude: @@ -181,14 +186,14 @@ is factored out in Eq.~\eqref{eq:4fermion_trans_amp}): \label{eq:weakcurrent_ud} \end{equation} If the nucleon were point-like, the nucleon current would have the same form as -in Eq.~\eqref{eq:weakcurrent_ud} with suitable wavefunctions of the proton and +in \eqref{eq:weakcurrent_ud} with suitable wavefunctions of the proton and neutron. But that is not the case, in order to account for the complication of the nucleon, the current must be modified by six real form factors $g_i(q^2), i = V, M, S, A, T, P$: \begin{align} - J_\alpha &= i\bar{\psi}_n(V^\alpha - A^\alpha)\psi_p,\\ + J_\alpha &= i\bar{\psi}_n(V^\alpha - A^\alpha)\psi_p\,,\\ V^\alpha &= g_V (q^2) \gamma^\alpha + i \frac{g_M(q^2)}{2m_N} - \sigma^{\alpha\beta} q_\beta + g_S(q^2)q^\alpha,\\ + \sigma^{\alpha\beta} q_\beta + g_S(q^2)q^\alpha\,, \textrm{ and}\\ A^\alpha &= g_A(q^2)\gamma^\alpha \gamma_5 + ig_T(q^2) \sigma^{\alpha\beta} q_\beta\gamma_5 + \frac{g_P(q^2)}{m_\mu}\gamma_5 q^\alpha, @@ -223,7 +228,7 @@ muonic molecules $p\mu p$, $d\mu p$ and $t\mu p$, $g_P$ is the least well-defined form factor. Only recently, it is measured with a reasonable precision~\cite{AndreevBanks.etal.2013a}. The values of the six form factors at $q^2 = -0.88m^2_\mu$ are listed in -Table~\ref{tab:formfactors}. +\cref{tab:formfactors}. \begin{table}[htb] \begin{center} \begin{tabular}{l l l} @@ -259,35 +264,8 @@ $\Lambda_t$ is given by: where $\Lambda_c$ and $\Lambda_d$ are partial capture rate and decay rate, respectively, and $Q$ is the Huff factor, which is corrects for the fact that muon decay rate in a bound state is reduced because of the binding energy -reduces the available energy. -%The total capture rates for several selected -%elements are compiled by Measday~\cite{Measday.2001}, -%and reproduced in -%Table~\ref{tab:total_capture_rate}. -%\begin{table}[htb] - %\begin{center} - %\begin{tabular}{l l r@{.}l r@{.}l@{$\pm$}l l} - %\toprule - %\textbf{$Z$ ($Z_{\textrm{eff}}$)} & - %\textbf{Element} & - %\multicolumn{2}{l}{\textbf{Mean lifetime}} & - %\multicolumn{3}{l}{\textbf{Capture rate}} & - %\textbf{Huff factor}\\ - %& & - %\multicolumn{2}{c}{\textbf{(\nano\second)}} & - %\multicolumn{3}{l}{\textbf{$\times 10^3$ (\reciprocal\second)}} &\\ - %\midrule - %1 (1.00) & $^1$H & 2194&90 $\pm$0.07 & 0&450 &0.020 & 1.00\\ - %& $^2$H & 2194&53 $\pm$0.11 & 0&470 &0.029 & \\ - %2 (1.98) & $^3$He & 2186&70 $\pm$0.10 & 2&15 &0.020 & 1.00\\ - %& $^4$He & 2195&31 $\pm$0.05 & 0&470&0.029 & \\ - %\bottomrule - %\end{tabular} - %\end{center} - %\caption{Total capture rate of the muon in nuclei for several selected - %elements, compiled by Measday~\cite{Measday.2001}} - %\label{tab:total_capture_rate} -%\end{table} +reduces the available energy. The correction begins to be significant for +$Z\geq 40$ as shown in \cref{tab:total_capture_rate}. Theoretically, it is assumed that the muon capture rate on a proton of the nucleus depends only on the overlap of the muon with the nucleus. For light @@ -312,13 +290,56 @@ reduced because a smaller phase-space in the nuclear muon capture compares to that of a nucleon; and $X_2 = 3.125$ takes into account the fact that it is harder for protons to transforms into neutrons due to the Pauli exclusion principle in heavy nuclei where there are more neutrons than protons. + +The total capture rates for several selected elements are compiled by +Measday~\cite{Measday.2001}, and reproduced in \cref{tab:total_capture_rate}. +\begin{table}[htb] + \begin{center} + \begin{tabular}{r c S S S} + \toprule + $Z (Z_{eff})$ & \textbf{Element} & \textbf{Mean lifetime (\si{\ns})} + & \textbf{Capture rate ($\times 10^{-3}$ \si{\ns})} & \textbf{Huff factor}\\ + + %& & \textbf{(\si{\ns})} & \textbf{($\times 10^{-3} \si{\Hz}$)} &\\ + \midrule + 1 (1.00)& $^{1}$H & 2194.90 (7)& 0.450 (20)& 1.00 \\ + & $^{2}$H & 2194.53 (11)& 0.470 (29)& \\ + 2 (1.98)& $^{3}$He & 2186.70 (10)& 2.15 (2)& 1.00\\ + & $^{4}$He & 2195.31 (5)& 0.356 (26)&\\ + 3 (2.94)& $^{6}$Li & 2175.3 (4)& 4.68 (12)& 1.00 \\ + & $^{7}$Li & 2186.8 (4)& 2.26 (12)& \\ + 4 (3.89)& $^{9}$Be & 2168 (3)& 6.1 (6)& 1.00 \\ + 5 (4.81)& $^{10}$B & 2072 (3)& 27.5 (7)& 1.00 \\ + & $^{11}$B & 2089 (3)& 23.5 (7)& 1.00 \\ + 6 (5.72)& $^{12}$C & 2028 (2)& 37.9 (5)& 1.00 \\ + & $^{13}$C & 2037 (8)& 35.0 (20)& \\ + 7 (6.61)& $^{14}$N & 1919 (15)& 66 (4)& 1.00 \\ + 8 (7.49)& $^{16}$O & 1796 (3)& 102.5 (10)& 0.998 \\ + & $^{18}$O & 1844 (5)& 88.0 (14)& \\ + 9 (8.32)& $^{19}$F & 1463 (5)& 229 (1)& 0.998 \\ + 13 (11.48)& $^{27}$Al& 864 (2)& 705 (3)& 0.993 \\ + 14 (12.22)& $^{28}$Si& 758 (2)& 868 (3)& 0.992 \\ + 20 (16.15)& Ca & 334 (2)& 2546 (20)& 0.985 \\ + 40 (25.61)& Zr & 110.4 (10)& 8630 (80)& 0.940 \\ + 82 (34.18)& Pb & 74.8 (4)& 12985 (70)& 0.844 \\ + 83 (34.00)& Bi & 73.4 (4)& 13240 (70)& 0.840 \\ + 90 (34.73)& Th & 77.3 (3)& 12560 (50)& 0.824 \\ + 92 (34.94)& U & 77.0 (4)& 12610 (70)& 0.820 \\ + \bottomrule + \end{tabular} + \end{center} + \caption{Total nuclear capture rate for negative muon in several elements, + compiled by Measday~\cite{Measday.2001}} + \label{tab:total_capture_rate} +\end{table} + % subsection total_capture_rate (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Neutron emission} \label{sub:neutron_emission} The average number of neutrons emitted per muon capture generally increases with $Z$, but there are large deviations from the trend due to particular -nuclear structure effects. The trend is shown in Table~\ref{tab:avg_neutron} +nuclear structure effects. The trend is shown in \cref{tab:avg_neutron} and can be expressed by a simple empirical function $n_{avg} = (0.3 \pm 0.02)A^{1/3}$~\cite{Singer.1974}. \begin{table}[htb] @@ -398,7 +419,7 @@ For light elements, the emission rate for proton and alpha are respectively $(9.5 \pm 1.1)\%$ and $(3.4 \pm 0.7)\%$. Subsequently, Kotelchuk and Tyler~\cite{KotelchuckTyler.1968} had a result which was about 3 times more statistics and in fair agreement with Morigana and Fry -(Figure~\ref{fig:kotelchuk_proton_spectrum}) +(\cref{fig:kotelchuk_proton_spectrum}) \begin{figure}[htb] \centering \includegraphics[width=0.65\textwidth]{figs/kotelchuk_proton_spectrum} @@ -414,7 +435,7 @@ colleagues~\cite{KraneSharma.etal.1979} measured proton emission from aluminium, copper and lead in the energy range above \SI{40}{\MeV} and found a consistent exponential shape in all targets. The integrated yields above \SI{40}{\MeV} are in the \sn{}{-4}--\sn{}{-3} range (see -Table~\ref{tab:krane_proton_rate}), a minor contribution to total proton +\cref{tab:krane_proton_rate}), a minor contribution to total proton emission rate. \begin{table}[htb] \begin{center} @@ -438,7 +459,7 @@ emission rate. \end{table} Their result on aluminium, the only experimental data existing for this target, -is shown in Figure~\ref{fig:krane_proton_spec} in comparison with spectra from +is shown in \cref{fig:krane_proton_spec} in comparison with spectra from neighbouring elements, namely silicon measured by Budyashov et al.~\cite{BudyashovZinov.etal.1971} and magnesium measured Balandin et al.~\cite{BalandinGrebenyuk.etal.1978}. The authors noted aluminium data and @@ -462,7 +483,7 @@ The aforementioned difficulties in charged particle measurements could be solved using an active target, just like nuclear emulsion. Sobottka and Wills~\cite{SobottkaWills.1968} took this approach when using a Si(Li) detector to stop muons. They obtained a spectrum of charged particles up to 26 -\si{\MeV}~in Figure~\ref{fig:sobottka_spec}. The peak below 1.4 +\si{\MeV}~in \cref{fig:sobottka_spec}. The peak below 1.4 \si{\MeV}~is due to the recoiling $^{27}$Al. The higher energy events including protons, deuterons and alphas constitute $(15\pm 2)\%$ of capture events, which is consistent with a rate of $(12.9\pm1.4)\%$ from gelatine @@ -513,37 +534,38 @@ active target measurement and found that the reaction $^{28}\textrm{Si}(\mu^-,\nu pn)^{26}\textrm{Mg}$ could occur at a similar rate to that of the $^{28}\textrm{Si}(\mu^-,\nu p)^{27}\textrm{Mg}$. That also indicates that the deuterons and alphas might constitute a fair amount in the -spectrum in Figure~\ref{fig:sobottka_spec}. +spectrum in \cref{fig:sobottka_spec}. Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978} studied $(\mu^-,\nu p)$, $(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$, $(\mu^-,\nu p3n)$ and $(\mu^-,\nu\alpha)$ in a wide range of 18 elements from sodium to bismuth.Their results plotted against the Coulomb barrier for the outgoing protons are given in -Figure~\ref{fig:wyttenbach_rate_1p}, ~\ref{fig:wyttenbach_rate_23p}. The +\cref{fig:wyttenbach_rate_1p} and \cref{fig:wyttenbach_rate_23p}. The classical Coulomb barrier $V$ they used are given by: \begin{equation} V = \frac{zZe^2}{r_0A^{\frac{1}{3}} + \rho}, \label{eqn:classical_coulomb_barrier} \end{equation} where $z$ and $Z$ are the charges of the outgoing particle and of the residual -nucleus, values $r_0 = 1.35 \textrm{ fm}$, and $\rho = 0 \textrm{ fm}$ for +nucleus respectively, $r_0 = 1.35 \textrm{ fm}$, and $\rho = 0 \textrm{ fm}$ for protons were taken. \begin{figure}[htb] \centering - \includegraphics[width=0.85\textwidth]{figs/wyttenbach_rate_1p} + \includegraphics[width=0.48\textwidth]{figs/wyttenbach_rate_1p} + \includegraphics[width=0.505\textwidth]{figs/wyttenbach_rate_23p} \caption{Activation results from Wyttenbach et - al.~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p)$ and - $(\mu^-,\nu pn)$ reactions.} + al.~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p)$, + $(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$ and $(\mu^-,\nu p3n)$ reactions.} \label{fig:wyttenbach_rate_1p} \end{figure} -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/wyttenbach_rate_23p} - \caption{Activation results from Wyttenbach et - al.~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p2n)$ and - $(\mu^-,\nu p3n)$ reactions.} - \label{fig:wyttenbach_rate_23p} -\end{figure} +%\begin{figure}[htb] + %\centering + %\includegraphics[width=0.85\textwidth]{figs/wyttenbach_rate_23p} + %\caption{Activation results from Wyttenbach et + %al.~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p2n)$ and + %$(\mu^-,\nu p3n)$ reactions.} + %\label{fig:wyttenbach_rate_23p} +%\end{figure} Wyttenbach et al.\ saw that the cross section of each reaction decreases exponentially with increasing Coulomb barrier. The decay constant for all @@ -577,7 +599,7 @@ Fermi gas at a finite temperature ($kT = 9$ \si{\MeV}). A very good agreement with the experimental result for the alpha emission was obtained with distribution (III), both in the absolute percentage and the energy distribution (curve (III) in the left hand side of -Figure~\ref{fig:ishii_cal_result}). However, the calculated emission of protons +\cref{fig:ishii_cal_result}). However, the calculated emission of protons at the same temperature falls short by about 10 times compares to the data. The author also found that the distribution (I) is unlikely to be suitable for proton emission, and using that distribution @@ -594,8 +616,8 @@ for alpha emission resulted in a rate 15 times larger than observed. \label{fig:ishii_cal_result} \end{figure} Singer~\cite{Singer.1974} noted that by assuming a reduced effective mass for -the nucleon, the average excitation energy will increase, but the proton -emission rate does not significantly improve and still could not explain the +the nucleon, the average excitation energy increases, but the proton +emission rate is not significantly improved and still could not explain the large discrepancy. He concluded that the evaporation mechanism can account for only a small fraction of emitted protons. Moreover, the high energy protons of 25--50 \si{\MeV}~cannot be explained by the evaporation mechanism. @@ -620,7 +642,7 @@ reactions at similar excitation energies. The pre-equilibrium emission also dominates the higher-energy part, although it falls short at energies higher than 30 \si{\MeV}. The comparison between the calculated proton spectrum and experimental data is shown in -Fig.~\ref{fig:lifshitzsinger_cal_proton}. +\cref{fig:lifshitzsinger_cal_proton}. \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/lifshitzsinger_cal_proton} @@ -641,33 +663,59 @@ proton emission rate $(\mu^-, \nu p)$ and the inclusive emission rate: The deuteron emission channels are included to comparisons with activation data where there is no distinguish between $(\mu^-, \nu pn)$ and $(\mu^-,d)$, \ldots Their calculated emission rates together with available experimental -data is reproduced in Table~\ref{tab:lifshitzsinger_cal_proton_rate}. +data is reproduced in \cref{tab:lifshitzsinger_cal_proton_rate} where +a generally good agreement between calculation and experiment can be seen from. +The rate of $(\mu^-,\nu p)$ reactions for $^{28}\textrm{Al}$ and +$^{39}\textrm{K}$ are found to be indeed +higher than average, though not as high as Vil'gel'mora et +al.~\cite{VilgelmovaEvseev.etal.1971} observed. + \begin{table}[htb] \begin{center} - \begin{tabular}{c c c c c} + \begin{tabular}{l S S[separate-uncertainty=true] + S S[separate-uncertainty=true] c} \toprule - Target nucleus & Calculation & Experiment & Estimate & Comments \\ + {Capturing} & {$(\mu,\nu p)$} & {$(\mu,\nu p)$}& + {$\Sigma(\mu,\nu p(xn))$}& + {$\Sigma(\mu,\nu p(xn))$} & {Est.}\\ + {nucleus} & {calculation} & {experiment} & {calculation} & {experiment} + &{}\\ + %nucleus & calculation & experiment & calculation & experiment \\ %\textbf{Col1}\\ \midrule - $^{27}_{13}$Al & 40 & $>28 \pm 4$ & (70) & 7.5 for $T>40$ MeV \\ - $^{28}_{14}$Si & 144 & $150\pm30$ & & 3.1 and 0.34 $d$ for $T>18$ MeV \\ - $^{31}_{15}$P & 35 & $>61\pm6$ & (91) & \\ - $^{46}_{22}$Ti & & & & \\ - $^{51}_{23}$V & 25 & $>20\pm1.8$ & (32) & \\ - %item1\\ + $^{27}_{13}$Al & 9.7 & {(4.7)} & 40 & {$> 28 \pm 4$} &(70)\\ + $^{28}_{14}$Si & 32 & 53 \pm 10 & 144 & 150 \pm 30 & \\ + $^{31}_{15}$P & 6.7 & {(6.3)} & 35 & {$> 61 \pm 6$}&(91) \\ + $^{39}_{19}$K & 19 & 32 \pm 6 & 67 & {} \\ + $^{41}_{19}$K & 5.1 & {(4.7)} & 30 & {$> 28 \pm 4$} &(70)\\ + $^{51 }_{23}$V &3.7 &2.9 \pm 0.4 &25 &{$>20 \pm 1.8$}& (32)\\ + $^{55 }_{25}$Mn &2.4 &2.8 \pm 0.4 &16 &{$>26 \pm 2.5$}& (35)\\ + $^{59 }_{27}$Co &3.3 &1.9 \pm 0.2 &21 &{$>37 \pm 3.4$}& (50)\\ + $^{60 }_{28}$Ni &8.9 &21.4 \pm 2.3 &49 &40 \pm 5&\\ + $^{63 }_{29}$Cu &4.0 &2.9 \pm 0.6 &25 &{$>17 \pm 3 $}& (36)\\ + $^{65 }_{29}$Cu &1.2 &{(2.3)} &11 &{$>35 \pm 4.5$}& (36)\\ + $^{75 }_{33}$As &1.5 &1.4 \pm 0.2 &14 &{$>14 \pm 1.3$}& (19)\\ + $^{79 }_{35}$Br &2.7 &{} &22 & &\\ + $^{107}_{47}$Ag &2.3 &{} &18 & &\\ + $^{115}_{49}$In &0.63 &{(0.77)} &7.2 &{$>11 \pm 1$} &(12)\\ + $^{133}_{55}$Cs &0.75 &0.48 \pm 0.07 &8.7 &{$>4.9 \pm 0.5$} &(6.7)\\ + $^{165}_{67}$Ho &0.26 &0.30 \pm 0.04 &4.1 &{$>3.4 \pm 0.3$} &(4.6)\\ + $^{181}_{73}$Ta &0.15 &0.26 \pm 0.04 &2.8 &{$>0.7 \pm 0.1$} &(3.0)\\ + $^{208}_{82}$Pb &0.14 &0.13 \pm 0.02 &1.1 &{$>3.0 \pm 0.8$} &(4.1)\\ \bottomrule \end{tabular} \end{center} - \caption{Calculated of the single proton emission rate and the inclusive - proton emission rate. The experimental data are mostly from Wyttenbach et -al.\cite{WyttenbachBaertschi.etal.1978}} + \caption{Probabilities in units of \num{E-3} per muon capture for the + reaction $^A_Z X (\mu,\nu p) ^{A-1}_{Z-2}Y$ and for inclusive proton + emission compiled by Measday~\cite{Measday.2001}. The calculated values + are from Lifshitz and Singer. The experimental data are mostly from + Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978}. For inclusive emission + the experimental figures are lower limits, determined from the + actually measured channels. The figures in crescent parentheses are + estimates for the total inclusive rate derived from the measured exclusive + channels by the use of ratio in \eqref{eqn:wyttenbach_ratio}.} \label{tab:lifshitzsinger_cal_proton_rate} \end{table} -A generally good agreement between calculation and experiment can be seen from -Table~\ref{tab:lifshitzsinger_cal_proton_rate}. The rate of $(\mu^-,\nu p)$ -reactions for $^{28}\textrm{Al}$ and $^{39}\textrm{K}$ are found to be indeed -higher than average, though not as high as Vil'gel'mora et -al.~\cite{VilgelmovaEvseev.etal.1971} observed. For protons with higher energies in the range of 40--90 \si{\MeV}~observed in the emulsion data as well as in later @@ -682,8 +730,8 @@ and it had been shown that the meson exchange current increases the total capture rate in deuterons by 6\%. The result of this model was a mix, it accounted well for Si, Mg and Pb data, but predicted rates about 4 times smaller in cases of Al and Cu, and about 10 times higher in case of AgBr -(Table~\ref{tab:lifshitzsinger_cal_proton_rate_1988}). -\begin{table}[htb] +(\cref{tab:lifshitzsinger_cal_proton_rate_1988}). +\begin{table}[!ht] \begin{center} \begin{tabular}{l l c} \toprule @@ -708,17 +756,18 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Summary on proton emission from aluminium} \label{sub:summary_on_proton_emission_from_aluminium} +%%TODO equations, products as in Sobottkas' There is no direct measurement of proton emission following muon capture in the relevant energy for the COMET Phase-I of 2.5--10 \si{\MeV}: \begin{enumerate} - \item Spectrum wise, only one energy spectrum (Figure~\ref{fig:krane_proton_spec}) + \item Spectrum wise, only one energy spectrum (\cref{fig:krane_proton_spec}) for energies above 40 \si{\MeV}~is available from Krane et al.~\cite{KraneSharma.etal.1979}, where an exponential decay shape with a decay constant of $7.5 \pm 0.4$~\si{\MeV}. At low energy range, the best one can get is the charged particle spectrum, which includes protons, deuterons and alphas, - from the neighbouring element silicon (Figure~\ref{fig:sobottka_spec}). + from the neighbouring element silicon (\cref{fig:sobottka_spec}). This charged particle spectrum peaks around 2.5 \si{\MeV}~and reduces exponentially with a decay constant of 4.6 \si{\MeV}. \item The activation data from Wyttenbach et @@ -748,25 +797,26 @@ A spectrum shape at this energy range is not available. \label{sub:motivation_of_the_alcap_experiment} As mentioned, protons from muon capture on aluminium might cause a very high rate in the COMET Phase-I CDC. The detector is designed to accept particles -with momenta in the range of 75--120 \si{\MeV\per\cc}. -Figure~\ref{fig:proton_impact_CDC} shows that protons with kinetic energies of -2.5--8 \si{\MeV}~will hit the CDC. Such events are troublesome due to -their large energy deposition. Deuterons and alphas at that momentum range is -not of concern because they have lower kinetic energy and higher stopping -power, thus are harder to escape the muon stopping target. +with momenta in the range of \SIrange{75}{120}{\MeV\per\cc}. +\cref{fig:proton_impact_CDC} shows that protons with kinetic energies larger +than \SI{2.5}{\MeV} could hit the CDC. Such events are troublesome due to +their large energy deposition. Deuterons and alphas at the same momentum are +not of concern because they have lower kinetic energy compared with protons and +higher stopping power, thus are harder to escape the muon stopping target. \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/proton_impact_CDC} - \caption{Momentum-kinetic energy relation of protons, deuterons and alphas + \caption{Momentum kinetic energy relation of protons, deuterons and alphas below 10\si{\MeV}. Shaded area is the acceptance of the COMET -Phase-I's CDC. Protons with energies in the range of 2.5--8 -\si{\MeV}~are in the acceptance of the CDC. Deuterons and alphas at -low energies should be stopped inside the muon stopping target.} + Phase-I's CDC. Protons with energies in higher than \SI{2.5}{\MeV} are in the + acceptance of the CDC. Deuterons and alphas at low energies should be stopped + inside the muon stopping target.} \label{fig:proton_impact_CDC} \end{figure} +%%TODO replace a figure without upper limit The COMET plans to introduce a thin, low-$Z$ proton absorber in between the -target and the CDC to produce proton hit rate. The absorber will be effective +target and the CDC to reduce proton hit rate. The absorber will be effective in removing low energy protons. The high energy protons that are moderated by the absorber will fall into the acceptance range of the CDC, but because of the exponential decay shape of the proton spectrum, the hit rate caused by these @@ -774,12 +824,11 @@ protons should be affordable. The proton absorber solves the problem of hit rate, but it degrades the reconstructed momentum resolution. Therefore its thickness and geometry should -be carefully designed. The limited information available makes it difficult to -arrive at a conclusive detector design. The proton emission rate could be 4\% +be carefully optimised. The limited information available makes it difficult to +arrive at a conclusive detector design. The proton emission rate could be 0.97\% as calculated by Lifshitz and Singer~\cite{LifshitzSinger.1980}; or 7\% as -estimated from the $(\mu^-,\nu pn)$ activation data and the ratio -\eqref{eqn:wyttenbach_ratio}~\cite{WyttenbachBaertschi.etal.1978}; or as high -as 15-20\% from silicon and neon. +estimated from the $(\mu^-,\nu pn)$ activation data and the ratio in +\eqref{eqn:wyttenbach_ratio}; or as high as 15-20\% from silicon and neon. For the moment, design decisions in the COMET Phase-I are made based on conservative assumptions: emission rate of 15\% and an exponential decay shape @@ -787,19 +836,21 @@ are adopted follow the silicon data from Sobottka and Will ~\cite{SobottkaWills.1968}. The spectrum shape is fitted with an empirical function given by: \begin{equation} - p(T) = A\left(1-\frac{T_{th}}{T}\right)^\alpha e^{-(T/T_0)}, + p(T) = A\left(1-\frac{T_{th}}{T}\right)^\alpha \exp{-\frac{T}{T_0})}, \label{eqn:EH_pdf} \end{equation} -where $T$ is the kinetic energy of the proton, and the fitted parameters are -$A=0.105\textrm{ MeV}^{-1}$, $T_{th} = 1.4\textrm{ MeV}$, $\alpha = 1.328$ and -$T_0 = 3.1\textrm{ MeV}$. The baseline -design of the absorber is 1.0 \si{\mm}~thick -carbon-fibre-reinforced-polymer (CFRP) which contributes -195~\si{\keV\per\cc}~to the momentum resolution. The absorber also -down shifts the conversion peak by 0.7 \si{\MeV}. This is an issue as -it pushes the signal closer to the DIO background region. For those reasons, -a measurement of the rate and spectrum of proton emission after muon capture is -required in order to optimise the CDC design. +where $T$ is the kinetic energy of the proton in \si{\MeV}, and the fitted +parameters are $A=0.105\textrm{ MeV}^{-1}$, $T_{th} = 1.4\textrm{ MeV}$, +$\alpha = 1.328$ and $T_0 = 3.1\textrm{ MeV}$. The function rises from the +cut-off value of $T_{th}$, its rising edge is governed by the parameter +$\alpha$. The exponential decay component dominates at higher energy. + +The baseline design of the proton absorber for the COMET Phase-I based on +above assumptions is a 1-\si{\mm}-thick CFRP layer as has been described in +\cref{ssub:hit_rate_on_the_cdc}. The hit rate estimation is +conservative and the contribution of the absorber to the momentum resolution +is not negligible, further optimisation is desirable. Therefore a measurement +of the rate and spectrum of proton emission after muon capture is required. % subsection motivation_of_the_alcap_experiment (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Experimental method for proton measurement} @@ -810,16 +861,16 @@ is tunable from \SIrange{28}{45}{\MeV} so that targets at different thickness from \SIrange{25}{100}{\um} can be studied. The $\pi$E1 beam line could deliver \sn{}{3} muons/\si{\s} at 1\% momentum spread, and \sn{}{4} muons/\si{\s} at 3\% momentum spread. The muon stopping distribution -of the muons could be well-identified using this excellent beam. +of the muons could be well-tuned using this excellent beam. Emitting charged particles from nuclear muon capture will be identified by the -specific energy loss. The specific energy loss is calculated as energy loss -per unit path length \sdEdx at a certain energy $E$. The quantity is uniquely -defined for each particle species. - -The specific energy loss is measured in the AlCap using a pair of silicon -detectors: a \SI{65}{\um}-thick detector, and a \SI{1500}{\um}-thick detector. -Each detector is $5\times5$ \si{\cm^2} in area. +specific energy loss. +%The specific energy loss is calculated as energy loss +%per unit path length \sdEdx at a certain energy $E$. The quantity is uniquely +%defined for each particle species. +Experimentally, the specific energy loss is measured in the AlCap using a pair +of silicon detectors: a \SI{65}{\um}-thick detector, and a \SI{1500}{\um}-thick +detector. Each detector is $5\times5$ \si{\cm^2} in area. The thinner one provides $\mathop{dE}$ information, while the sum energy deposition in the two gives $E$, if the particle is fully stopped. The silicon detectors pair could help distinguish protons from other charged particles from diff --git a/thesis/thesis.tex b/thesis/thesis.tex index 6ae020a..b980c80 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -31,9 +31,9 @@ for the COMET experiment} \mainmatter %\input{chapters/chap1_intro} %\input{chapters/chap2_mu_e_conv} -\input{chapters/chap3_comet} +%\input{chapters/chap3_comet} %\input{chapters/chap4_alcap_phys} -%\input{chapters/chap5_alcap_setup} +\input{chapters/chap5_alcap_setup} %\input{chapters/chap6_analysis} %\input{chapters/chap7_results} %\input{chapters/chap8_conclusions} From 95744773fe71e0e902fea6d00f6971e1dcd7891c Mon Sep 17 00:00:00 2001 From: nam Date: Thu, 30 Oct 2014 02:29:28 +0900 Subject: [PATCH 18/26] prog saved --- thesis/chapters/chap5_alcap_setup.tex | 82 ++++++++++++++++----------- thesis/mythesis.sty | 1 + 2 files changed, 51 insertions(+), 32 deletions(-) diff --git a/thesis/chapters/chap5_alcap_setup.tex b/thesis/chapters/chap5_alcap_setup.tex index df14625..52e34bd 100644 --- a/thesis/chapters/chap5_alcap_setup.tex +++ b/thesis/chapters/chap5_alcap_setup.tex @@ -2,9 +2,8 @@ \label{cha:the_alcap_run_2013} \thispagestyle{empty} The first run of the AlCap experiment was performed at the $\pi$E1 beam line -area, PSI from November 26 to December 23, -2013. The goal of the run was to measure protons rate and spectrum following -muon capture on aluminium. +area, PSI from November 26 to December 23, 2013. The goal of the run was to +measure protons rate and their spectrum following muon capture on aluminium. \section{Experimental set up} \label{sec:experimental_set_up} @@ -56,7 +55,7 @@ One of the main requirements of the AlCap experiment was a low energy muon beam with narrow momentum bite in order to achieve a high fraction of stopping muons in the very thin targets. In this Run 2013, muons from \SIrange{28}{45}{\mega\electronvolt\per\cc} and momentum spread of 1\% and -3\%were used. +3\%, respectively, were used. For part of the experiment the target was replaced with one of the silicon detector packages allowed an accurate momentum and range calibration @@ -84,8 +83,9 @@ as a function of momentum for two different momentum bites. The targets and charged particle detectors are installed inside the vacuum chamber as shown in \cref{fig:alcap_setup_detailed}. The muon beam enters -from the right of the image and hits the target, which is placed at the -centre of the vacuum chamber and orientated at 45 degrees to the beam axis. +from the right of \cref{fig:alcap_setup_detailed} and hits the target, which is +placed at the centre of the vacuum chamber and orientated at 45 degrees to the +beam axis. The side walls and bottom flange of the vessel provide several vacuum-feedthroughs for the high voltage and signal cables for the silicon and scintillator detectors inside the chamber. @@ -207,7 +207,7 @@ proportional chamber (\Pmu{}PC) that uses 24 X wires and 24 Y wires at 2~\si{\milli\meter}~intervals. The upstream detectors provide signal of an incoming muon as coincident hits on -the muon trigger and the wire chamber in anti-coincident with the muon +the muon trigger and the wire chamber in anti-coincidence with the muon anti-coincidence counter. This set of detectors along with their read-out system belong to the MuSun experiment, which operated at the same beam line just @@ -326,7 +326,7 @@ lead to the use of several sampling frequencies from 17~\si{\mega\hertz}\ to 250~\si{\mega\hertz}, and three types of digitisers were employed: \begin{itemize} \item custom-built 12-bit 170-MHz FADCs which was designed for the - MuCap experiment. Each FADC board has dimensions the same as those of + MuCap experiment. Each FADC board has the same dimensions as those of a single-width 6U VME module, but is hosted in a custom built crate due to its different power supply mechanical structure. The FADC communicates with a host computer through a 100-Mb/s Ethernet interface using a simple @@ -367,7 +367,7 @@ model V767 which was kindly provided by the MuSun experiment. The Data Acquisition System (DAQ) of the AlCap experiment, so-called AlCapDAQ, provided the readout of front-end electronics, event assembling, data logging, hardware monitoring and control, and the run database of the experiment -(\cref{fig:alcapdaq_pcs}). It was based on MIDAS framework~\footnote{ +(\cref{fig:alcapdaq_pcs}). It was based on the MIDAS framework~\footnote{ MIDAS is a general purpose DAQ software system developed at PSI and TRIUMF:\\ \url{http://midas.triumf.ca}} and consisted of two circuits, {\em i}) a detector circuit for synchronous data readout from the front-end electronics @@ -411,7 +411,7 @@ rollover on any digitiser (a FADC runs at its maximum speed of To ease the task of handling data, the data collecting period was divided into short runs, each run stopped when the logger had recorded 2 GB of data. The data size effectively made each run last for about 5 minutes. The DAQ -automatically starts a new run with the same parameters after about 6 seconds. +automatically started a new run with the same parameters after about 6 seconds. The short period of each run also allows the detection, and helps to reduce the influence of effects such as electronics drifting, temperature fluctuation. @@ -435,11 +435,12 @@ run, by: would lose about \SI{66}{\kilo\eV} in the \SI{0.5}{\um}-thick dead layer, and the peak would appear at \SI{5418}{\kilo\eV} (\cref{fig:toyMC_alpha}); - \item and a tail pulse generator, A tail pulse with amplitude of + \item a tail pulse generator, A tail pulse with amplitude of \SI{66}{\milli\volt}~was used to simulate the response of the silicon - detectors' preamplifiers to a particle with \SI{1}{\MeV} energy deposition; + detectors' preamplifiers to a particle with \SI{1}{\MeV} energy + deposition; and - \item During data taking period, electrons in the beam were were also used + \item during data taking period, electrons in the beam were were also used for energy calibration of thick silicon detectors where energy deposition is large enough. The muons at different momenta provided another mean of calibration in the beam tuning period. @@ -453,6 +454,10 @@ run, by: \label{fig:toyMC_alpha} \end{figure} +The conversion from ADC value to energy is done with a first-order polynomial: +\begin{equation} + \textrm{E [keV]} = \textrm{Slope} \times \textrm{ADC} + \textrm{Offset}. +\end{equation} The calibration coefficients for the silicon channels are listed in \cref{tab:cal_coeff}. @@ -472,6 +477,11 @@ The calibration coefficients for the silicon channels are listed in every head row/.style={ before row={\toprule}, after row={\midrule}, + %%TODO unit of coeffcients + %after row={ \arraybackslash + %{ }& { keV/channel } & { keV }\\ + %\midrule}, + %{}& {(keV/channel)} & {(keV)}\\ \midrule}, columns/Detector/.style={column type=c}, columns/Slope/.style={column type=c}, columns/Offset/.style={column type=c} @@ -534,13 +544,14 @@ Following corrections for the peak areas are considered: detector system, where two gamma rays arrive at the detector within a time interval short compared to that response time. This correction is significant in our germanium system because of the current pulse - information extracting method does not count the second pulse. + information extracting method does not count the second pulse (see + \cref{sub:offline_analyser}). \item Correction of counting time loss in the reset periods of the transistor reset preamplifier. A preamplifier of this type would reset itself after accumulating a predetermined amount of charge. During a reset, the - preamplifier is insensitive so this can be counted as dead time. + preamplifier is insensitive so this can be counted as a dead time. \item True coincidence summing correction: two cascade gamma rays hit the - detector at the same time would cause loss of count under the two + detector at the same time would cause loss of counts under the two respective peaks and gain under the sum energy peak. \item Correction for self-absorption of a gamma ray by the source itself. \end{enumerate} @@ -568,7 +579,7 @@ an exponential background gives the actual reset pulse length of $1947.34\times 10^{-6} \times 2335.0 = 4.55$ \si{\s}. That is a 0.14\% loss for a measuring time of \SI{3245.5}{\s}. This percentage loss is insignificant compared with the loss in \eqref{eqn:finite_time_response} and the statistical -uncertainty of peak areas so correction for amplifier resets is not applied. +uncertainty of peak areas. \begin{figure}[htb] \centering @@ -590,8 +601,12 @@ The absolute efficiencies of the reference gamma rays show agreement with those obtained from a Monte Carlo (MC) study where a point source made of $^{152}$Eu is placed at the target position (see \cref{fig:ge_eff_cal}). A comparison between efficiencies in case of the point-like source and a finite-size -source is also done by MC simulation. As shown in \cref{fig:ge_eff_cal}, the -differences are in line with the uncertainties of the measured efficiencies. +source is also done by MC simulation. The differences between the two sources +are generally smaller than 3\%, which are comparable with the uncertainties of +the efficiency calibration. That means the point-like efficiencies can be used +for a finite-sized source without correction. +%As shown in \cref{fig:ge_eff_cal}, the +%differences are in line with the uncertainties of the measured efficiencies. %The dimensions of the latter are set to %resemble the distribution of muons inside the target: Gaussian spreading %\SI{11}{\mm} vertically, \SI{13}{\mm} horizontally, and \SI{127}{\um} in @@ -599,9 +614,12 @@ differences are in line with the uncertainties of the measured efficiencies. \centering \includegraphics[width=0.40\textwidth]{figs/ge_eff_cal} \includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root} - \caption{Absolute efficiency of the germanium detector, the fit was done with - 7 energy points from 244~keV, the shaded area is - 95\% confidence interval of the fit.} + \caption{Absolute efficiency of the germanium detector (right) and + MC comparison of efficiencies in case of point-like and finite-sized + sources (left). The efficiencies curve is fitted on + 7 measured energy points from \SIrange{244}{1408}{\keV}, the shaded area is + 95\% confidence interval of the fit. The ratios on the left plot are + normalised to the efficiencies of the point-like case at each energy point.} %because it is known that the linearity between %$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better. \label{fig:ge_eff_cal} @@ -770,8 +788,8 @@ sets are shown in \cref{tb:stat}. \label{sub:concept} Since the AlCapDAQ is a trigger-less system, it stored all waveforms of the hits occured in 100-ms-long blocks without considering their physics -significance The analysis code therefore must be able to extract parameters of -the waveforms, then organises the pulses into physics events correlated to +significance. The analysis code therefore must be able to extract parameters of +the waveforms, then organises the pulses into the physics events correlated to stopped muons (\cref{fig:muon_event}). In addition, the analyser is intended to be usable as a real-time component of a MIDAS DAQ, where simple analysis could be done online for monitoring and diagnostic during the run. @@ -786,9 +804,9 @@ analysis could be done online for monitoring and diagnostic during the run. The analysis framework of the AlCap consists of two separate programs. A MIDAS-based analyser framework, \alcapana{}, processes the raw data and -passes its ROOT data output to a second +passes its ROOT data output to the second stage, \rootana{}, where most of the physics analysis is performed. -Both programs were designed to be modularised, which allowed us to develop +Both of the programs were designed to be modularised, which allowed us to develop lightweight analysis modules that were used online to generate plots quickly, while more sophisticated modules can be applied in offline analysis. @@ -908,14 +926,14 @@ update the plots to reflect real-time status of the detector system. %\hl{Screen shots} \subsection{Offline analyser} \label{sub:offline_analyser} -Some offline analysis modules has been developed during the beam time and could +Some offline analysis modules have been developed during the beam time and could provide quick feedback in confirming and guiding the decisions at the time. For example, the X-ray spectrum analysis was done to confirm that we could observe the muon capture process and to help in choosing optimal momenta which maximised the number of stopped muons. Although the offline analyser is still not fully available yet, several modules -are ready(\cref{tab:offline_modules}). An initial analysis is possible using +are ready (\cref{tab:offline_modules}). An initial analysis is possible using the existing modules thanks to the modularity of the analysis framework. \begin{table}[htb] @@ -1000,7 +1018,7 @@ the beam rate was generally less than \SI{8}{\kilo\hertz}. %\end{figure} To make sure that we will analyse good data, a low level data quality checking -was done on the whole data sets. The idea is plotting the variations of basic +was done on the whole data sets. The idea is to plot the variations of basic parameters, such as noise level, length of raw waveforms, pulse rate, time correlation to hits on the muon counter on each channel during the data collecting period. Runs with significant difference from the averaging @@ -1026,13 +1044,13 @@ shown in \cref{fig:lldq}. A full Monte Carlo (MC) simulation of the experimental set up has been developed based on Geant4~\cite{Agostinelli.etal.2003}. The geometrical implementation -was as detailed as possible and could be modified via configuration script at -run time. Descriptions of the muon beam came from the beam line optic +was detailed as much as possible and could be modified via configuration +scripts at run time. Descriptions of the muon beam came from the beam line optic calculation provided by the accelerator experts at PSI. The MC model greatly assisted the design of the experiment, such as alignment of the detectors with respect to the target, and shielding of scattered muons. -It also helps make sense of observed results during the run and data +It also helped make a sense of the observed results during the run and data analysing. % chapter the_alcap_run_2013 (end) diff --git a/thesis/mythesis.sty b/thesis/mythesis.sty index 9b74655..9bdb285 100644 --- a/thesis/mythesis.sty +++ b/thesis/mythesis.sty @@ -61,6 +61,7 @@ bookmarks %\RequirePackage[]{siunitx} \RequirePackage[detect-weight=true, detect-family=true]{siunitx} \RequirePackage{hepnames} +\RequirePackage{array} %% Various fonts ... %\RequirePackage[T1]{fontenc} %\RequirePackage{charter} From 567b61715bd7bfb406b0e03fe110fd55fd4187e3 Mon Sep 17 00:00:00 2001 From: nam Date: Thu, 30 Oct 2014 18:56:57 +0900 Subject: [PATCH 19/26] prog saved --- thesis/chapters/chap1_intro.tex | 4 +- thesis/chapters/chap2_mu_e_conv.tex | 44 ++++++++- thesis/chapters/chap3_comet.tex | 37 +++---- thesis/chapters/chap4_alcap_phys.tex | 24 ++--- thesis/chapters/chap5_alcap_setup.tex | 2 +- thesis/chapters/chap6_analysis.tex | 137 +++++++++++++++++++++++--- thesis/chapters/chap7_results.tex | 120 ++++++++++++---------- thesis/chapters/frontmatter.tex | 22 +++-- thesis/thesis.tex | 14 +-- 9 files changed, 290 insertions(+), 114 deletions(-) diff --git a/thesis/chapters/chap1_intro.tex b/thesis/chapters/chap1_intro.tex index 95a6425..ddae2b1 100644 --- a/thesis/chapters/chap1_intro.tex +++ b/thesis/chapters/chap1_intro.tex @@ -64,7 +64,7 @@ by the SINDRUM-II~\cite{Bertl.etal.2006}. A staging approach is adopted at the COMET to achieve an intermediate physics result, as well as to gain operational experience. The first stage, COMET Phase I, is scheduled to start data taking -in 2016 with the goal single event sensitivity of $3\times 10^{-15}$ after +in 2016 with the goal single event sensitivity of $3.1\times 10^{-15}$ after a three-month running period. A cylindrical drift chamber being developed by the Osaka University group @@ -86,6 +86,6 @@ sensitivities. Details of the study on proton emission are described in Chapters~\ref{cha:alcap_phys},~\ref{cha:the_alcap_run_2013},~\ref{cha:data_analysis}: physics, method, experimental set up, data analysis. The results and impacts of the study on COMET Phase-I design is discussed in -Chapter~\ref{cha:results_and_discussions}. +Chapter~\ref{cha:discussions_on_the_impact_to_the_comet_phase_i}. % chapter introduction (end) diff --git a/thesis/chapters/chap2_mu_e_conv.tex b/thesis/chapters/chap2_mu_e_conv.tex index 4363e09..4fed239 100644 --- a/thesis/chapters/chap2_mu_e_conv.tex +++ b/thesis/chapters/chap2_mu_e_conv.tex @@ -1,7 +1,49 @@ -\chapter{Lepton flavour and $\mu-e$ conversion} +\chapter{Overview} \thispagestyle{empty} \label{cha:clfv} +\section{Introduction} +\label{sec:introduction} +The COMET experiment~\cite{COMET.2007}, proposed at the Japan Proton +Accelerator Research Complex (J-PARC), is a next-generation-experiment that +searches for evidence of charged lepton flavour violation (CLFV) with muons. +The branching ratio of CLFV in the Standard Model, even with massive neutrinos, +is prohibitively small, at the order of $10^{-54}$. Therefore, any experimental +observation of CLFV would be a clear signal of new physics beyond the SM. + +The COMET (\textbf{CO}herent \textbf{M}uon to \textbf{E}lectron +\textbf{T}ransition) Collaboration aims to probe the conversion of a muon to +an electron in a nucleus field at a single event sensitivity of \num{6E-17}, +pushing for a four orders of magnitude improvement from the current limit set +by the +SINDRUM-II~\cite{Bertl.etal.2006}. A staging approach is adopted at the COMET +to achieve an intermediate physics result, as well as to gain operational +experience. The first stage, COMET Phase I, is scheduled to start data taking +in 2016 with the goal single event sensitivity of $3\times 10^{-15}$ after +a three-month running period. + +A cylindrical drift chamber being developed by the Osaka University group +together with the Kyushu University group and the Chinese groups +will be a main tracking detector in the COMET Phase I. It is anticipated that +the chamber will be heavily occupied by protons emitted after nuclear muon +capture in the stopping target, and thus an absorber will be installed to +reduce the proton hit rate to a tolerable level. A study of proton emission +following nuclear muon capture for optimisation of the proton absorber is +presented in this thesis. + +The thesis is structured as follows: +firstly, +the physics motivation of the COMET experiment, with muon's normal decays and +CLFV decays, is described in this later part of this chapter. +Chapter~\ref{cha:comet_overview} gives an overview of the +COMET experiment: beam lines, detectors and their requirements, and expected +sensitivities. Details of the study on proton emission are described in +Chapters~\ref{cha:alcap_phys},~\ref{cha:the_alcap_run_2013},~\ref{cha:data_analysis}: +physics, method, experimental set up, data analysis. The results and impacts of +the study on COMET Phase-I design is discussed in +Chapter~\ref{cha:discussions_on_the_impact_to_the_comet_phase_i}. + + \section{Lepton flavour} \label{sec:lepton_flavour} According to the SM, all matter is built from a small set of fundamental diff --git a/thesis/chapters/chap3_comet.tex b/thesis/chapters/chap3_comet.tex index a451973..ae3abc1 100644 --- a/thesis/chapters/chap3_comet.tex +++ b/thesis/chapters/chap3_comet.tex @@ -642,7 +642,7 @@ CyDet. \end{figure} \subsubsection{CDC configuration} -\label{ssub:CDC configuration} +\label{ssub:CDC_configuration} The CDC is the main tracking detector that provides information for reconstruction of charged particle tracks and measuring their momenta. The key parameters for the CDC are listed in the @@ -725,30 +725,33 @@ of protons emitted after muon capture in aluminium. In the design of the COMET Phase-I, we use a conservative estimation of the rate of protons from energy spectrum of charged particles emitted from muon capture in $^{28}$Si~\cite{SobottkaWills.1968}. The baseline design for the proton -absorber is 1.0~\si{\milli\meter}-thick CFRP, making the total thickness -of material before the sensitive region is \SI{1.5}{\mm} in CFRP. In this -configuration, the inner wall and the proton absorber deteriorate the momentum -resolution of the reconstructed track to 195~\si{\kilo\electronvolt\per\cc}. +absorber is 0.5~\si{\milli\meter}-thick CFRP, making the total thickness +of material before the sensitive region is \SI{1.0}{\mm} in CFRP. In this +configuration, the inner wall and the proton absorber contribute a spread of +\SI{167}{\keV\per\cc} to the momentum of a \mueconv signal electron. This +figure is a little below the spread cause by multiple scatterings on the +chamber gas at \SI{197}{\keV\per\cc}. The impact of the proton absorber on the CDC's hit rate and momentum resolution is summarised in \cref{tab:comet_absorber_impact}. \begin{table}[htb] \begin{center} - \begin{tabular}{@{}ccc@{}} + \begin{tabular}{@{}cccc@{}} \toprule - \textbf{Absorber }& \textbf{Proton }& \textbf{Momentum }\\ - \textbf{thickness }& \textbf{hit rate }& \textbf{resolution }\\ - (\si{\um}) & (\si{\kHz}) & (\si{\keV\per\cc}) \\ + \textbf{Absorber }& \textbf{Total CFRP }&\textbf{Proton }& + \textbf{$\Delta p$}\\ + \textbf{thickness }& \textbf{thickness }&\textbf{hit rate }& \\ + (\si{\mm}) &(\si{\mm}) & (\si{\kHz}) & (\si{\keV\per\cc}) \\ \midrule - 0 & 130 & 131 \\ - 0.5 & 34 & 167 \\ - 1.0 & 11 & 195 \\ - 1.5 & 6 & 252 \\ + 0 & 0.5 & 130 & 131 \\ + 0.5 & 1.0 & 34 & 167 \\ + 1.0 & 1.5 & 11 & 195 \\ + 1.5 & 2.0 & 6 & 252 \\ \bottomrule \end{tabular} \end{center} - \caption{Hit rates and contributions to momentum resolution of the proton - absorber and inner wall of the CDC. The intrinsic momentum resolution due - to multiple scattering is \SI{197}{\keV\per\cc}.} + \caption{Hit rates and contributions to momentum spread of the proton + absorber and inner wall of the CDC. The resolutions are calculated for + mono-energetic electrons of \SI{104.96}{\MeV\per\cc}.} \label{tab:comet_absorber_impact} \end{table} @@ -758,7 +761,7 @@ emission rate and energy spectrum is being carried out at PSI. This experiment is described in detail in next chapters. It should be noted that the proton hit rate is not a problem for the COMET -Phase-II where the additional electron transport solenoid will removed all +Phase-II where the additional electron transport solenoid would removed all protons emitted. % subsection detectors_for_mueconv_search_in_the_phase_i (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/thesis/chapters/chap4_alcap_phys.tex b/thesis/chapters/chap4_alcap_phys.tex index a95e682..cb4a9c3 100644 --- a/thesis/chapters/chap4_alcap_phys.tex +++ b/thesis/chapters/chap4_alcap_phys.tex @@ -540,15 +540,16 @@ Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978} studied $(\mu^-,\nu p)$, $(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$, $(\mu^-,\nu p3n)$ and $(\mu^-,\nu\alpha)$ in a wide range of 18 elements from sodium to bismuth.Their results plotted against the Coulomb barrier for the outgoing protons are given in -\cref{fig:wyttenbach_rate_1p} and \cref{fig:wyttenbach_rate_23p}. The -classical Coulomb barrier $V$ they used are given by: +\cref{fig:wyttenbach_rate_1p}. +%and \cref{fig:wyttenbach_rate_23p}. +The classical Coulomb barrier $V$ they used are given by: \begin{equation} V = \frac{zZe^2}{r_0A^{\frac{1}{3}} + \rho}, \label{eqn:classical_coulomb_barrier} \end{equation} where $z$ and $Z$ are the charges of the outgoing particle and of the residual -nucleus respectively, $r_0 = 1.35 \textrm{ fm}$, and $\rho = 0 \textrm{ fm}$ for -protons were taken. +nucleus respectively, $e^2 = 1.44 \si{\MeV}$, $r_0 = 1.35 \textrm{ fm}$, and +$\rho = 0 \textrm{ fm}$ for protons were taken. \begin{figure}[htb] \centering \includegraphics[width=0.48\textwidth]{figs/wyttenbach_rate_1p} @@ -805,15 +806,14 @@ not of concern because they have lower kinetic energy compared with protons and higher stopping power, thus are harder to escape the muon stopping target. \begin{figure}[htb] \centering - \includegraphics[width=0.85\textwidth]{figs/proton_impact_CDC} - \caption{Momentum kinetic energy relation of protons, deuterons and alphas - below 10\si{\MeV}. Shaded area is the acceptance of the COMET - Phase-I's CDC. Protons with energies in higher than \SI{2.5}{\MeV} are in the - acceptance of the CDC. Deuterons and alphas at low energies should be stopped - inside the muon stopping target.} + \includegraphics[width=0.85\textwidth]{figs/alcap_proton_vs_acceptance} + \caption{Momentum - kinetic energy relation of protons, deuterons and alphas + at low energy region below 20\si{\MeV}. Charged particles in the shaded + area could reach the COMET Phase-I's CDC, for protons that corresponds + kinetic energies higher than \SI{2.5}{\MeV}. Deuterons and alphas at low + energies should be stopped inside the muon stopping target.} \label{fig:proton_impact_CDC} \end{figure} -%%TODO replace a figure without upper limit The COMET plans to introduce a thin, low-$Z$ proton absorber in between the target and the CDC to reduce proton hit rate. The absorber will be effective @@ -846,7 +846,7 @@ cut-off value of $T_{th}$, its rising edge is governed by the parameter $\alpha$. The exponential decay component dominates at higher energy. The baseline design of the proton absorber for the COMET Phase-I based on -above assumptions is a 1-\si{\mm}-thick CFRP layer as has been described in +above assumptions is a 0.5-\si{\mm}-thick CFRP layer as has been described in \cref{ssub:hit_rate_on_the_cdc}. The hit rate estimation is conservative and the contribution of the absorber to the momentum resolution is not negligible, further optimisation is desirable. Therefore a measurement diff --git a/thesis/chapters/chap5_alcap_setup.tex b/thesis/chapters/chap5_alcap_setup.tex index 52e34bd..a5a17ae 100644 --- a/thesis/chapters/chap5_alcap_setup.tex +++ b/thesis/chapters/chap5_alcap_setup.tex @@ -985,7 +985,7 @@ pile-up or double pulses in one \tpulseisland{} in \cref{fig:tap_maxbin_bad}. The TSimpleMuonEvent first picks a muon candidate, then loops through all pulses on all detector channels, and picks all pulses occur in a time window of \SI{\pm 10}{\si{\us}} around each candidate to build -a muon event. A muon candidates is a hit on the upstream plastic scintillator +a muon event. A muon candidate is a hit on the upstream plastic scintillator with an amplitude higher than a threshold which was chosen to reject MIPs. The period of \SI{10}{\si{\us}} is long enough compared to the mean life time of muons in the target materials diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index e1d0462..fc18da0 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -1,4 +1,4 @@ -\chapter{Data analysis} +\chapter{Data analysis and results} \label{cha:data_analysis} This chapter presents initial analysis on subsets of the collected data. Purposes of the analysis include: @@ -288,7 +288,7 @@ showed that muons penetrated deeper as the momentum increased, reaching the optimal value at the scale of 1.08, then decreased as punch through happened more often from 1.09. The distributions of stopped muons are illustrated by MC results on the right hand side of \cref{fig:al100_scan_rate}. With the 1.09 -scale beam, the muons stopped \SI{28}{\um} off-centre to the right silicon arm. +scale beam, the muons stopped \SI{28}{\um} off-centred to the right silicon arm. \begin{figure}[htb] \centering \includegraphics[width=0.47\textwidth]{figs/al100_scan_rate} @@ -305,7 +305,7 @@ scale beam, the muons stopped \SI{28}{\um} off-centre to the right silicon arm. As described in the \cref{sec:analysis_framework}, the hits on all detectors are re-organised into muon events: central muons; and all hits within \SI{\pm 10}{\us} from the central muons. The dataset from runs -\numrange{2808}{2873} contains \num{1.17E+9} such muon events. +\numrange{2808}{2873} contains \num{1.17E+9} of such muon events. Selection of proton (and other heavy charged particles) events starts from searching for muon event that has at least one hit on thick silicon. If there @@ -431,6 +431,12 @@ number of protons with those energies could reach the detectors. The jump on the right arm at around \SI{9}{\MeV} can be explained as the punch-through protons were counted as the proton veto counters were not used in this analysis. +\begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/al100_unfolded_lr} + \caption{Unfolded proton spectra from the 100-\si{\um} aluminium target.} + \label{fig:al100_unfold} +\end{figure} %Several studies were conducted to assess the performance of the unfolding %code, including: @@ -467,18 +473,11 @@ The yields of protons from \SIrange{4}{8}{\MeV} are: N_{\textrm{p unfold left}} &= (165.4 \pm 2.7)\times 10^3\\ N_{\textrm{p unfold right}} &= (173.1 \pm 2.9)\times 10^3 \end{align} -Therefore, the number of emitted protons is taken as average value: +The number of emitted protons is taken as average of the two yields: \begin{equation} N_{\textrm{p unfold}} = (169.3 \pm 2.9) \times 10^3 \end{equation} -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/al100_unfolded_lr} - \caption{Unfolded proton spectra from the 100-\si{\um} aluminium target.} - \label{fig:al100_unfold} -\end{figure} - \subsection{Number of nuclear captures} \label{sub:number_of_nuclear_captures} \begin{figure}[htb] @@ -503,16 +502,21 @@ the number of nuclear captures are: \label{sub:proton_emission_rate} The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore: \begin{equation} - R_{\textrm{p}} = \frac{169.3\times 10^3}{9.57\times 10^6} = 1.74\times + R_{\textrm{p}} = \frac{169.3\times 10^3}{9.57\times 10^6} = 1.7\times 10^{-2} \label{eq:proton_rate_al} \end{equation} The total proton emission rate can be estimated by assuming a spectrum shape with the same parameterisation as in \eqref{eqn:EH_pdf}. The fit parameters -are shown in \cref{fig:al100_parameterisation}. With such parameterisation, the -integration in range from \SIrange{4}{8}{\MeV} is 51\% of the total number of -protons. The total proton emission rate is therefore $3.5\times 10^{-2}$. +are shown in \cref{fig:al100_parameterisation} and \cref{tab:al100_fit_pars}. +The average spectrum is obtained by taking the average of the two unfolded +spectra from the left and right arms. The fitted parameters are compatible +with each other within their errors. + +Using the fitted parameters of the average spectrum, the integration in range +from \SIrange{4}{8}{\MeV} is 51\% of the total number of +protons. The total proton emission rate is therefore estimated to be $3.5\times 10^{-2}$. \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/al100_parameterisation} @@ -520,6 +524,27 @@ protons. The total proton emission rate is therefore $3.5\times 10^{-2}$. \label{fig:al100_parameterisation} \end{figure} +\begin{table}[htb] + \begin{center} + \begin{tabular}{l S[separate-uncertainty=true] S[separate-uncertainty=true] + S[separate-uncertainty=true]} + \toprule + \textbf{Parameter} &{\textbf{Left}} & {\textbf{Right}} & {\textbf{Average}}\\ + \midrule + $A \times 10^{-5}$ & 2.0 \pm 0.7 & 1.3 \pm 0.1 & 1.5 \pm 0.3\\ + $T_{th}$ (\si{\keV}) & 1301 \pm 490 & 1966 \pm 68 & 1573 \pm 132\\ + $\alpha$ & 3.2 \pm 0.7 & 1.2 \pm 0.1 & 2.0 \pm 1.2\\ + $T_{th}$ (\si{\keV}) & 2469 \pm 203 & 2641 \pm 106 & 2601 \pm 186\\ + \bottomrule + \end{tabular} + \end{center} + \caption{Parameters of the fits on the unfolded spectra, the average spectrum + is obtained by taking average of the unfolded spectra from left and right + arms.} + \label{tab:al100_fit_pars} +\end{table} + + \subsection{Uncertainties of the emission rate} \label{sub:uncertainties_of_the_emission_rate} The uncertainties of the emission rate come from: @@ -584,4 +609,84 @@ presented in \cref{tab:al100_uncertainties_all}. \label{tab:al100_uncertainties_all} \end{table} -The proton emission rate is then $(3.5 \pm 0.2)$\%. +\section{Results of the initial analysis} +\label{sec:results_of_the_initial_analysis} +\subsection{Verification of the experimental method} +\label{sub:verification_of_the_experimental_method} +The experimental method described in \cref{sub:experimental_method} has been +validated: +\begin{itemize} + \item Number of muon capture normalisation: the number of stopped muons + calculated from the muonic X-ray spectrum is shown to be consistent with + that calculated from the active target spectrum. + \item Particle identification: the particle identification by specific + energy loss has been demonstrated. The banding of different particle + species is clearly visible. The proton extraction method using cut on + likelihood probability has been established. Since the distribution of + $\Delta E$ at a given $E$ is not Gaussian, the fraction of protons that do + not make the cut is 0.5\%, much larger than the threshold at \num{1E-4}. + The fraction of other charged particles being misidentified as protons is + smaller than 0.1\%. These uncertainties from particle identification are + still small in compared with the + uncertainty of the measurement (2.3\%). + \item Unfolding of the proton spectrum: the unfolded spectra inferred from + two measurements at the two silicon arms show good agreement with each + other, and with the muon stopping distribution obtained in the momentum + scanning analysis. +\end{itemize} + +\subsection{Proton emission rates and spectrum} +\label{sub:proton_emission_rates_and_spectrum} +The proton emission spectrum in \cref{sub:proton_emission_rate} peaks around +\SI{4}{\MeV} which is comparable to the Coulomb barrier for proton of +\SI{3.9}{\MeV} calculated using \eqref{eqn:classical_coulomb_barrier}. The +spectrum has a decay constant of \SI{2.6}{\MeV} in higher energy region, +makes the emission probability drop more quickly than silicon charged +particles spectrum of Sobottka and Wills~\cite{SobottkaWills.1968} where the +decay constant was \SI{4.6}{\MeV}. This can be explained as the silicon +spectrum includes other heavier particles which have higher Coulomb barriers, +hence contribute more in the higher energy bins, effectively reduces the decay +rate. + +The partial emission rate measured in the energy range from +\SIrange{4}{8}{\MeV} is: +\begin{equation} + R_{p \textrm{ meas. }} = (1.7 \pm 0.1)\%. + \label{eqn:meas_partial_rate} +\end{equation} + +The total emission rate from aluminium assuming the spectrum shape holds for +all energy is: +\begin{equation} + R_{p \textrm{ total}} = (3.5 \pm 0.2)\%. + \label{eqn:meas_total_rate} +\end{equation} +No direct comparison of this result to existing experimental or +theoretical work is available. Indirectly, it is compatible with the figures +calculated by Lifshitz and +Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980} listed in +\cref{tab:lifshitzsinger_cal_proton_rate}. It is significantly larger than +the rate of 0.97\% for the $(\mu,\nu p)$ channel, and does not +exceed the inclusion rate for all channels $\Sigma(\mu,\nu p(xn))$ at 4\%, +leaving some room for other modes such as $(\mu,\nu d)$ or $(\mu,\nu p2n)$. +Certainly, if the rate of deuterons can be extracted then the combined +emission rate of protons and deuterons could be compared directly with the +inclusive rate. + +The result \eqref{eqn:meas_total_rate} is greater than the +probability of the reaction $(\mu,\nu pn)$ measured by Wyttenbach et +al.~\cite{WyttenbachBaertschi.etal.1978} at 2.8\%. It is expectable because +the contribution from the $(\mu,\nu d)$ channel should be small since it +needs to form a deuteron from a proton and a neutron. +%The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in +%\eqref{eqn:wyttenbach_ratio}. + +Compared with emission rate from silicon, the result +\eqref{eqn:meas_total_rate} is indeed much smaller. It is even lower than +the rate of the no-neutron reaction $(\mu,\nu p)$. This can be explained as +the resulted nucleus from muon capture on silicon, $^{28}$Al, is an odd-odd +nucleus and less stable than that from aluminium, $^{27}$Mg. The proton +separation energy for $^{28}$Al is \SI{9.6}{\MeV}, which is significantly +lower than that of $^{27}$Mg at \SI{15.0}{\MeV}~\cite{AudiWapstra.etal.2003}. + + diff --git a/thesis/chapters/chap7_results.tex b/thesis/chapters/chap7_results.tex index 39b77bd..64da318 100644 --- a/thesis/chapters/chap7_results.tex +++ b/thesis/chapters/chap7_results.tex @@ -1,50 +1,53 @@ -\chapter{Results and discussions} -\label{cha:results_and_discussions} -\section{Verification of the experimental method} -\label{sec:verification_of_the_experimental_method} -\subsection{Number of stopped muons calculation} -\label{sub:number_of_stopped_muons_normalisation} -The number of stopped muons calculated from the muonic X-ray spectrum is shown -to be consistent with that calculated from the active target spectrum. This -proves the validity of normalisation using muon X-ray measurement. -\subsection{Particle identification and unfolding} -\label{sub:particle_identification_and_unfolding} -The particle identification using specific energy loss using cut on -likelihood probability is shown in -\cref{sub:event_selection_for_the_passive_targets}. Since the distribution of -$\Delta E$ at a given $E$ is not Gaussian, the fraction of protons that do not -make the cut is 0.5\%, much larger than the threshold at \num{1E-4}. However, -that missing fraction is small compared to the statistical uncertainty of the -measurement (2.3\%) so the threshold is sufficient. +\chapter{Discussions on the impact to the COMET Phase-I} +\label{cha:discussions_on_the_impact_to_the_comet_phase_i} +The measured proton emission rate of 3.5\% is about 5 times +smaller than the figure using to make the baseline design of the CDC in COMET +Phase-I. The spectrum shape +peaks around \SI{4}{\MeV} rather than at \SI{2.5}{\MeV}, and decays more +quickly in compared with the silicon spectrum(\cref{fig:sobottka_spec}). +Therefore CDC hit rate due to proton should be smaller than the current +estimation. -The observed spectra on the two silicon arms reflect the muon stopping -distribution discussed in \cref{sub:momentum_scan_for_the_100_} where more -muons stopped at the downstream side of the target. The proton yields -calculated from two arms are consistent with each other, and show that the muon -stopping distribution used to generate the response matrices is reasonable. +The CDC proton hit rate is calculated by a toy MC study. The dimensions of the +geometry shown in \cref{fig:cdc_toy_mc} are from \cref{ssub:CDC_configuration}. +The inner wall of the CDC is \SI{0.5}{\mm} thick CFRP. +A proton absorber made +of CFRP is placed \SI{5}{\cm} far from the inner wall of the CDC. The +absorber's thickness is varied from 0 (no absorber) to \SI{1}{\mm}. +\begin{figure}[htb] + \centering + \includegraphics[width=0.55\textwidth]{figs/cdc_toy_mc} + \caption{Geometry of the toy MC study for hit rate study.} + \label{fig:cdc_toy_mc} +\end{figure} -\section{Emission rate of protons and the COMET Phase I's CDC} -\label{sec:emission_rate_of_protons_and_the_comet_phase_i_s_cdc} -The proton emission rate from the 100-\si{\um} aluminium target is -$(3.5 \pm 0.2)$\%. This rate is significantly larger than the calculation rate -of 0.97\% by Lifshitz and Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980}. -The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in -\eqref{eqn:wyttenbach_ratio}. -The rate smaller that the proton emission rate from silicon of -5.3\%~\cite{Measday.2001} which is expected since an odd-odd nucleus as -$^{28}$Al is less stable than an even-odd one. +The protons with the energy spectrum shape as in +\cref{sub:proton_emission_rate} are generated inside the COMET's muon stopping +targets which are 17 200-\si{\um}-thick aluminium discs. The spatial +distribution of protons resembles the stopping distribution of muons inside the +target discs calculated from the full MC simulation of the COMET detectors +(\cref{fig:cdc_toy_mc_init_pos}). +\begin{figure}[htb] + \centering + \includegraphics[width=0.65\textwidth]{figs/cdc_toy_mc_init_pos_xy} + \includegraphics[width=0.60\textwidth]{figs/cdc_toy_mc_init_pos_z} + \caption{Spatial distribution of the generated protons in X, Y (top) and + Z (bottom). Z is the axis of the CDC, X, Y are the horizontal and vertical + axes respectively.} + \label{fig:cdc_toy_mc_init_pos} +\end{figure} -For the COMET Phase I experiment, the emission rate of 3.5\% is about 5 times -smaller than the figure using to design the CDC. The measured spectrum shape -peaks around \SI{4}{\MeV} rather than \SI{2.5}{\MeV} in the silicon -spectrum(\cref{fig:sobottka_spec}). Therefore the proton hit rate on the CDC -should be smaller than the current estimation. +The protons are then tracked in a \SI{1}{\tesla} magnetic field. The protons +reaching the absorber, inner wall and the sensitive volume of the CDC are +recorded (see \cref{fig:cdc_toy_mc_p_spec_500um}). +\begin{figure}[!htb] + \centering + \includegraphics[width=0.75\textwidth]{figs/cdc_toy_mc_p_spec_500um} + \caption{Toy MC study of the CDC hit rate due to protons. The absorber + thickness was set at \SI{0.5}{\mm} in this plot.} + \label{fig:cdc_toy_mc_p_spec_500um} +\end{figure} -The CDC proton hit rate is calculated by a toy MC study. The protons with the -energy spectrum as the parameterisation in \cref{sub:proton_emission_rate} are -generated inside the COMET's muon stopping targets which are 17 -200-\si{\um}-thick aluminium discs. A proton absorber made of CFRP is placed -\SI{5}{\cm} far from the inner wall of the CDC. A muon stopping rate of \SI{1.3E9}{\Hz} is assumed as in the COMET Phase I's TDR. The number of proton emitted is then $\num{1.3E9} \times 0.609 \times 0.035 = \SI{2.8E7}{\Hz}$. The hit rates on a single cell in the inner most @@ -52,13 +55,19 @@ layer due to these protons with different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. \begin{table}[htb] \begin{center} - \begin{tabular}{l r} + \begin{tabular}{S S S S} \toprule - \textbf{Absorber thickness} & \textbf{Hit rate}\\ + {\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& + {\textbf{Proton}}\\ + {\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& + {\textbf{hit rate}}\\ + {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}\\ \midrule - \SI{1}{\mm} & \SI{2}{\Hz}\\ - \SI{0.5}{\mm} & \SI{126}{\Hz}\\ - \SI{0}{\mm} & \SI{1436}{\Hz}\\ + 1 &0.5&1.5 & 2\\ + 0.5 &0.5&1.0 & 126\\ + 0 &0.5&0.5 & 1436\\ + 0 &0.3&0.3 & 8281\\ + 0 &0.1&0.1 & 15011\\ \bottomrule \end{tabular} \end{center} @@ -66,7 +75,14 @@ different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. \label{tab:proton_cdc_hitrate} \end{table} -The proton hit rate even without the absorber is only \SI{1.4}{\kHz}, much -smaller than the current estimation of \SI{11}{\kHz} (using 1-mm-thick -absorber). Therefore a proton absorber is not needed for the COMET Phase I's -CDC. +At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz}, +much smaller than the current estimation at \SI{34}{\kHz}. Even without the +absorber, proton hit rate remains low at \SI{1.4}{\kHz}. Therefore a proton +absorber is not needed for the COMET Phase I's CDC. + +Without the proton absorber, the momentum spread of the signal electron +reduces from \SI{167}{\keV} to \SI{131}{\keV}. If a lower momentum spread is +desired, it is possible to reduce the thickness of the inner wall. The last +two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at +\SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at +manageable levels. diff --git a/thesis/chapters/frontmatter.tex b/thesis/chapters/frontmatter.tex index 4fa23f9..1dabec7 100644 --- a/thesis/chapters/frontmatter.tex +++ b/thesis/chapters/frontmatter.tex @@ -25,11 +25,21 @@ approach in which the first phase, COMET Phase-I [3], starts in 2013 and initial data taking in around 2017. In order to optimize detector design for the Phase-I, backgrounds from nuclear -muon capture are crucial. We have proposed a dedicated experiment , namely -AlCap, at PSI, Switzerland to study the backgrounds, including: heavy charged -particles, neutrons and photons. The measurements of heavy charged particles -have been carried out in the 2013 run and the preliminary analysis results are -presented in this thesis. +muon capture are crucial. We have proposed a dedicated experiment, namely +AlCap, at PSI, Switzerland to study the backgrounds, including protons, +neutrons and photons. The measurements of proton rate and spectrum on +aluminium have been carried out in the 2013 run. The second run to study +neutrons and photons is planned in 2015. + +The preliminary results from the analysis of the 2013 run are presented in this +thesis. The measured proton spectrum peaks at \SI{4}{\MeV} and decays +exponentially with the decay constant of \SI{2.6}{\MeV}. The emission +rate of protons in the energy range from \SIrange{4}{8}{\MeV} is +$(1.7\pm0.1)\%$. The total proton emission rate is estimated to be +$(3.5\pm0.2)\%$ assuming the spectrum shape holds. +The resulted proton rate and spectrum were used to optimise the tracking +detector hit rate of the COMET Phase-I. + \end{abstract} @@ -58,7 +68,7 @@ presented in this thesis. %\begin{preface} %\thispagestyle{empty} %The thesis is about measurements of products of nuclear muon capture on an - %aluminum target, which is important for optimization of a tracking detector + %aluminium target, which is important for optimization of a tracking detector %of a search for muon to electron conversion, the E21 experiment - so called %COMET - at Japan Proton Accelerator Complex (J-PARC). %\end{preface} diff --git a/thesis/thesis.tex b/thesis/thesis.tex index b980c80..aec31ac 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -29,14 +29,14 @@ for the COMET experiment} \end{frontmatter} \mainmatter -%\input{chapters/chap1_intro} -%\input{chapters/chap2_mu_e_conv} -%\input{chapters/chap3_comet} -%\input{chapters/chap4_alcap_phys} +%%%\input{chapters/chap1_intro} +\input{chapters/chap2_mu_e_conv} +\input{chapters/chap3_comet} +\input{chapters/chap4_alcap_phys} \input{chapters/chap5_alcap_setup} -%\input{chapters/chap6_analysis} -%\input{chapters/chap7_results} -%\input{chapters/chap8_conclusions} +\input{chapters/chap6_analysis} +\input{chapters/chap7_results} +\input{chapters/chap8_conclusions} \begin{backmatter} \input{chapters/backmatter} From 84a3d4ae5962bb6ce15e126c196b483f9817f856 Mon Sep 17 00:00:00 2001 From: nam Date: Thu, 30 Oct 2014 19:00:12 +0900 Subject: [PATCH 20/26] chap8 --- thesis/chapters/chap8_conclusions.tex | 31 +++++++++++++++++++++++++++ 1 file changed, 31 insertions(+) create mode 100644 thesis/chapters/chap8_conclusions.tex diff --git a/thesis/chapters/chap8_conclusions.tex b/thesis/chapters/chap8_conclusions.tex new file mode 100644 index 0000000..ca92006 --- /dev/null +++ b/thesis/chapters/chap8_conclusions.tex @@ -0,0 +1,31 @@ +\chapter{Conclusions} +\label{cha:conclusions} +AlCap is an experiment proposed at PSI to study charged particles, neutrons +and photons emitting after nuclear muon capture on aluminium. These +measurements are important for backgrounds and hit rates estimation of the new +generation of \mueconv experiments, COMET and Mu2e. In the first stage of the +COMET experiment, hit rate on its main tracking detector is anticipated to be +dominated by low energy protons following muon capture on an aluminium target, +which has never been measured. + +The first run of the AlCap which aims for proton measurement has been carried +out in 2013. Data analysis is in progress. An initial analysis on partial data +was done with the main results are: +\begin{enumerate} + \item Demonstration of the analysis chain from raw waveforms to physics + events; + \item Validation of the experimental method including: number of nuclear + capture muons normalisation by muonic X-ray measurement, charged particle + identification by specific energy loss, and unfolding of the proton energy + spectrum using the iterative Bayesian method; + \item Obtaining preliminary results on proton emission rate and spectrum: + the proton spectrum has a peak at \SI{4}{\MeV}, then reduces exponentially + with a decay constant of \SI{2.6}{\MeV}. The partial emission rate in the + energy range from \SIrange{4}{8}{\MeV} is $(1.7 \pm 0.1)\%$, and the total + emission rate assuming the shape holds for the whole spectrum is + $(3.5\pm0.2)$. +\end{enumerate} +The proton rate and spectrum have been used to optimise the planned proton +absorber for the drift chamber of the COMET Phase-I. The resulted proton hit +rate with the baseline configuration is very small compared with the current +figure. It is safe to remove the proton absorber altogether. 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z7(Mcr@KVIcg>0FTzRwy}2o9Cd!YD5?Upp{Q2vsOFg+Kg?jDpz*&>p?kCE5cUP#6U+ zGWlq1q_cWUuB86@aUUw->phAw@XR_jR9UZ$=u(UZUQ7VYNJk z&hbaofG(U2mX5ncobWQB)GFmHuNT*&9Mri9-`kJgXdirAI8{;8zN)Ewq0r7Gym0y= zH(U|8Ke6CcYjrO9aAnHrOQ!CFtN$nx;V~4wIdj=_@z-K2gX2!-(YCnib2UL}XHvTC z6i_!Tgyk0H Date: Thu, 30 Oct 2014 19:11:23 +0900 Subject: [PATCH 22/26] abbr --- thesis/thesis.bib | 22 +++++++++++----------- 1 file changed, 11 insertions(+), 11 deletions(-) diff --git a/thesis/thesis.bib b/thesis/thesis.bib index abc2226..104544c 100644 --- a/thesis/thesis.bib +++ b/thesis/thesis.bib @@ -115,7 +115,7 @@ @Article{Agostinelli.etal.2003, Title = {{GEANT4: A Simulation toolkit}}, Author = {Agostinelli, S. and others}, - Journal = {Nucl.Instrum.Meth.}, + Journal = {Nucl. Instrum. Meth.}, Year = {2003}, Pages = {250-303}, Volume = {A506}, @@ -147,7 +147,7 @@ @Article{AhmadAzuelos.etal.1987, Title = {Searches for muon-electron and muon-positron conversion in titanium}, Author = {Ahmad, S and Azuelos, G and Blecher, M and Bryman, D and Burnham, RA and Clifford, ETH and Depommier, P and Dixit, MS and Gotow, K and Hargrove, CK and others}, - Journal = {Physical review letters}, + Journal = {Phys. Rev. Lett.}, Year = {1987}, Number = {9}, Pages = {970}, @@ -289,7 +289,7 @@ @Article{AndreevBanks.etal.2013a, Title = {Measurement of Muon Capture on the Proton to 1\% Precision and Determination of the Pseudoscalar Coupling g P}, Author = {Andreev, VA and Banks, TI and Carey, RM and Case, TA and Clayton, SM and Crowe, KM and Deutsch, J and Egger, J and Freedman, SJ and Ganzha, VA and others}, - Journal = {Physical review letters}, + Journal = {Phys. Rev. Lett.}, Year = {2013}, Number = {1}, Pages = {012504}, @@ -326,7 +326,7 @@ @Article{AudiWapstra.etal.2003, Title = {The Ame2003 atomic mass evaluation: (II). Tables, graphs and references }, Author = {G. Audi and A.H. Wapstra and C. Thibault}, - Journal = {Nuclear Physics A }, + Journal = {Nucl. Phys. A}, Year = {2003}, Note = {The 2003 \{NUBASE\} and Atomic Mass Evaluations }, Number = {1}, @@ -344,7 +344,7 @@ @Article{BadertscherBorer.etal.1982, Title = {A search for muon-electron and muon-positron conversion in sulfur}, Author = {Badertscher, A and Borer, K and Czapek, G and Fl{\"u}ckiger, A and H{\"a}nni, H and Hahn, B and Hugentobler, E and Markees, A and Marti, T and Moser, U and others}, - Journal = {Nuclear Physics A}, + Journal = {Nucl. Phys. A}, Year = {1982}, Number = {2}, Pages = {406--440}, @@ -1232,7 +1232,7 @@ @Article{Henley.1952, Title = {$\pi$-Meson Production by Protons on Nuclei}, Author = {Henley, Ernest M}, - Journal = {Physical Review}, + Journal = {Phys. Rev.}, Year = {1952}, Number = {2}, Pages = {204}, @@ -1282,7 +1282,7 @@ @Article{Huff.1961, Title = {Decay rate of bound muons }, Author = {Robert W Huff}, - Journal = {Annals of Physics }, + Journal = {Annals of Physics}, Year = {1961}, Number = {2}, Pages = {288 - 317}, @@ -1338,7 +1338,7 @@ ABSORPTION OF STOPPED NEGATIVE PIONS IN NICKEL ISOTOPES}}, Author = {Isaak, H.P. and Engfer, R. and Hartmann, R. and Hermes, E.A. and Pruys, H.S. and others}, - Journal = {Nucl.Phys.}, + Journal = {Nucl. Phys.}, Year = {1983}, Pages = {385}, Volume = {A392}, @@ -1566,7 +1566,7 @@ @Article{KotelchuckTyler.1968, Title = {Search for a Conserved-Vector-Current Mechanism in the Emission of Protons from $\mu$-Stars in Emulsion}, Author = {Kotelchuck, D and Tyler, James V}, - Journal = {Physical Review}, + Journal = {Phys. Rev.}, Year = {1968}, Number = {4}, Pages = {1190}, @@ -1599,7 +1599,7 @@ @Article{KozlowskiZglinski.1974, Title = {{Nuclear muon capture - a simple model}}, Author = {Kozlowski, T. and Zglinski, A.}, - Journal = {Phys.Lett.}, + Journal = {Phys. Lett.}, Year = {1974}, Pages = {222-224}, Volume = {B50}, @@ -2497,7 +2497,7 @@ @Article{SobottkaWills.1968, Title = {Energy Spectrum of Charged Particles Emitted Following Muon Capture in Si 28}, Author = {Sobottka, Stanley E and Wills, Edward L}, - Journal = {Physical Review Letters}, + Journal = {Phys. Rev. Lett.}, Year = {1968}, Number = {12}, Pages = {596}, From befa19706a520d9906fc902b5e76cbd18018f9ca Mon Sep 17 00:00:00 2001 From: nam Date: Fri, 31 Oct 2014 17:23:14 +0900 Subject: [PATCH 23/26] submitted to preevaluation committee --- thesis/chapters/chap4_alcap_phys.tex | 14 ++--- thesis/chapters/chap6_analysis.tex | 76 ++++++++++++++++++--------- thesis/chapters/chap7_results.tex | 50 +++++++++++------- thesis/chapters/chap8_conclusions.tex | 30 +++++++---- thesis/chapters/frontmatter.tex | 2 +- thesis/mythesis.sty | 2 +- 6 files changed, 113 insertions(+), 61 deletions(-) diff --git a/thesis/chapters/chap4_alcap_phys.tex b/thesis/chapters/chap4_alcap_phys.tex index cb4a9c3..0a33eb7 100644 --- a/thesis/chapters/chap4_alcap_phys.tex +++ b/thesis/chapters/chap4_alcap_phys.tex @@ -736,7 +736,7 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr \begin{center} \begin{tabular}{l l c} \toprule - \textbf{Nucleus} & \textbf{Exp.$\times 10^3$} & \textbf{MEC cal.$\times + \textbf{Nucleus} & \textbf{Experiment$\times 10^3$} & \textbf{Calculation$\times 10^3$}\\ \midrule Al & $1.38 \pm 0.09$ & 0.3\\ @@ -748,9 +748,10 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr \bottomrule \end{tabular} \end{center} - \caption{Probability of proton emission with $E_p \ge 40$ - \si{\MeV}~as calculated by Lifshitz and - Singer~\cite{LifshitzSinger.1988} in comparison with available data.} + \caption{Probability of proton emission with $E_p \ge \SI{40}{\MeV}$ + calculated by Lifshitz and + Singer~\cite{LifshitzSinger.1988} with the two-nucleon capture hypothesis + in comparison with available data.} \label{tab:lifshitzsinger_cal_proton_rate_1988} \end{table} % subsection theoretical_models (end) @@ -825,7 +826,7 @@ protons should be affordable. The proton absorber solves the problem of hit rate, but it degrades the reconstructed momentum resolution. Therefore its thickness and geometry should be carefully optimised. The limited information available makes it difficult to -arrive at a conclusive detector design. The proton emission rate could be 0.97\% +arrive at a conclusive detector design. The proton emission rate could be 4\% as calculated by Lifshitz and Singer~\cite{LifshitzSinger.1980}; or 7\% as estimated from the $(\mu^-,\nu pn)$ activation data and the ratio in \eqref{eqn:wyttenbach_ratio}; or as high as 15-20\% from silicon and neon. @@ -836,7 +837,8 @@ are adopted follow the silicon data from Sobottka and Will ~\cite{SobottkaWills.1968}. The spectrum shape is fitted with an empirical function given by: \begin{equation} - p(T) = A\left(1-\frac{T_{th}}{T}\right)^\alpha \exp{-\frac{T}{T_0})}, + p(T) = A\left(1-\frac{T_{th}}{T}\right)^\alpha + \exp{\left(-\frac{T}{T_0}\right)}, \label{eqn:EH_pdf} \end{equation} where $T$ is the kinetic energy of the proton in \si{\MeV}, and the fitted diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index fc18da0..b84f3eb 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -475,21 +475,22 @@ The yields of protons from \SIrange{4}{8}{\MeV} are: \end{align} The number of emitted protons is taken as average of the two yields: \begin{equation} - N_{\textrm{p unfold}} = (169.3 \pm 2.9) \times 10^3 + N_{\textrm{p unfold}} = (169.3 \pm 1.9) \times 10^3 \end{equation} \subsection{Number of nuclear captures} \label{sub:number_of_nuclear_captures} -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/al100_ge_spec} - \caption{X-ray spectrum from the aluminium target, the characteristic - $(2p-1s)$ line shows up at 346.67~keV} -\label{fig:al100_ge_spec} -\end{figure} +%\begin{figure}[!htb] + %\centering + %\includegraphics[width=0.85\textwidth]{figs/al100_ge_spec} + %\caption{X-ray spectrum from the aluminium target, the characteristic + %$(2p-1s)$ line shows up at 346.67~keV} +%\label{fig:al100_ge_spec} +%\end{figure} -The X-ray spectrum on the germanium detector is shown on -\cref{fig:al100_ge_spec}. Fitting the double peaks on top of a first-order +%The X-ray spectrum on the germanium detector is shown on +%\cref{fig:al100_ge_spec}. +Fitting the double peaks on top of a first-order polynomial gives the X-ray peak area of $5903.5 \pm 109.2$. With the same procedure as in the case of the active target, the number stopped muons and the number of nuclear captures are: @@ -508,7 +509,15 @@ The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore: \end{equation} The total proton emission rate can be estimated by assuming a spectrum shape -with the same parameterisation as in \eqref{eqn:EH_pdf}. The fit parameters +with the same parameterisation as in \eqref{eqn:EH_pdf}. The +\eqref{eqn:EH_pdf} function has a power rising edge, and a exponential decay +falling edge. The falling edge has only one decay component and is suitable to +describe the proton spectrum with the equilibrium emission only assumption. +The pre-equilibrium emission contribution should be small for low-$Z$ material, +for aluminium the contribution of this component is 2.2\% according to +Lifshitz and Singer~\cite{LifshitzSinger.1980}. + +The fitted results are shown in \cref{fig:al100_parameterisation} and \cref{tab:al100_fit_pars}. The average spectrum is obtained by taking the average of the two unfolded spectra from the left and right arms. The fitted parameters are compatible @@ -534,7 +543,7 @@ protons. The total proton emission rate is therefore estimated to be $3.5\times $A \times 10^{-5}$ & 2.0 \pm 0.7 & 1.3 \pm 0.1 & 1.5 \pm 0.3\\ $T_{th}$ (\si{\keV}) & 1301 \pm 490 & 1966 \pm 68 & 1573 \pm 132\\ $\alpha$ & 3.2 \pm 0.7 & 1.2 \pm 0.1 & 2.0 \pm 1.2\\ - $T_{th}$ (\si{\keV}) & 2469 \pm 203 & 2641 \pm 106 & 2601 \pm 186\\ + $T_{0}$ (\si{\keV}) & 2469 \pm 203 & 2641 \pm 106 & 2601 \pm 186\\ \bottomrule \end{tabular} \end{center} @@ -597,7 +606,7 @@ presented in \cref{tab:al100_uncertainties_all}. \textbf{Item}& \textbf{Value} \\ \midrule Number of muons & 3.2\% \\ - Statistical from measured spectra & 1.6\% \\ + Statistical from measured spectra & 1.1\% \\ Systematic from unfolding & 5.0\% \\ Systematic from PID & \textless0.5\% \\ \midrule @@ -638,7 +647,7 @@ validated: \subsection{Proton emission rates and spectrum} \label{sub:proton_emission_rates_and_spectrum} The proton emission spectrum in \cref{sub:proton_emission_rate} peaks around -\SI{4}{\MeV} which is comparable to the Coulomb barrier for proton of +\SI{3.7}{\MeV} which is a little below the Coulomb barrier for proton of \SI{3.9}{\MeV} calculated using \eqref{eqn:classical_coulomb_barrier}. The spectrum has a decay constant of \SI{2.6}{\MeV} in higher energy region, makes the emission probability drop more quickly than silicon charged @@ -661,29 +670,48 @@ all energy is: R_{p \textrm{ total}} = (3.5 \pm 0.2)\%. \label{eqn:meas_total_rate} \end{equation} -No direct comparison of this result to existing experimental or -theoretical work is available. Indirectly, it is compatible with the figures -calculated by Lifshitz and + +\subsubsection{Comparison to theoretical and other experimental results} +\label{ssub:comparison_to_theoretical_and_other_experimental_results} +There is no existing experimental or theoretical work that could be directly +compared with the obtained proton emission rate. Indirectly, it is compatible +with the figures calculated by Lifshitz and Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980} listed in \cref{tab:lifshitzsinger_cal_proton_rate}. It is significantly larger than the rate of 0.97\% for the $(\mu,\nu p)$ channel, and does not exceed the inclusion rate for all channels $\Sigma(\mu,\nu p(xn))$ at 4\%, -leaving some room for other modes such as $(\mu,\nu d)$ or $(\mu,\nu p2n)$. -Certainly, if the rate of deuterons can be extracted then the combined -emission rate of protons and deuterons could be compared directly with the -inclusive rate. +leaving some room for other modes such as emission of deuterons or tritons. +Certainly, when the full analysis is available, deuterons and tritons emission +rates could be extracted and the combined emission rate could be compared +directly with the inclusive rate. The result \eqref{eqn:meas_total_rate} is greater than the probability of the reaction $(\mu,\nu pn)$ measured by Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978} at 2.8\%. It is expectable because the contribution from the $(\mu,\nu d)$ channel should be small since it needs to form a deuteron from a proton and a neutron. + +The rate of 3.5\% was estimated with an assumption that all protons are +emitted in equilibrium. With the exponential constant of \SI{2.6}{\MeV}, the +proton yield in the range from \SIrange{40}{70}{\MeV} is negligibly small +($\sim\num{E-8}$). However, Krane and colleagues reported a significant yield +of 0.1\% in that region~\cite{KraneSharma.etal.1979}. The energetic proton +spectrum shape also has a different exponential constant of \SI{7.5}{\MeV}. One +explanation for these protons is that they are emitted by other mechanisms, +such as capture on two-nucleon cluster suggested by Singer~\cite{Singer.1961} +(see \cref{sub:theoretical_models} and +\cref{tab:lifshitzsinger_cal_proton_rate_1988}). Despite being sizeable, the +yield of high energy protons is still small (3\%) in compared with the result +in \eqref{eqn:meas_total_rate}. + %The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in %\eqref{eqn:wyttenbach_ratio}. -Compared with emission rate from silicon, the result -\eqref{eqn:meas_total_rate} is indeed much smaller. It is even lower than -the rate of the no-neutron reaction $(\mu,\nu p)$. This can be explained as +\subsubsection{Comparison to the silicon result} +\label{ssub:comparison_to_the_silicon_result} +The probability of proton emission per nuclear capture of 3.5\% is indeed much +smaller than that of silicon. It is even lower than the rate of the no-neutron +reaction $(\mu,\nu p)$. This can be explained as the resulted nucleus from muon capture on silicon, $^{28}$Al, is an odd-odd nucleus and less stable than that from aluminium, $^{27}$Mg. The proton separation energy for $^{28}$Al is \SI{9.6}{\MeV}, which is significantly diff --git a/thesis/chapters/chap7_results.tex b/thesis/chapters/chap7_results.tex index 64da318..fd471d8 100644 --- a/thesis/chapters/chap7_results.tex +++ b/thesis/chapters/chap7_results.tex @@ -43,9 +43,11 @@ recorded (see \cref{fig:cdc_toy_mc_p_spec_500um}). \begin{figure}[!htb] \centering \includegraphics[width=0.75\textwidth]{figs/cdc_toy_mc_p_spec_500um} - \caption{Toy MC study of the CDC hit rate due to protons. The absorber - thickness was set at \SI{0.5}{\mm} in this plot.} - \label{fig:cdc_toy_mc_p_spec_500um} + \caption{Proton energy spectra at different stages from birth to the + sensitive volume of the CDC. The baseline design of \SI{0.5}{\mm} thick + absorber and \SI{0.5}{\mm} thick inner wall was used to produce this + plot.} + \label{fig:cdc_toy_mc_p_spec_500um} \end{figure} A muon stopping rate of \SI{1.3E9}{\Hz} is assumed as in the COMET Phase I's @@ -55,34 +57,44 @@ layer due to these protons with different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. \begin{table}[htb] \begin{center} - \begin{tabular}{S S S S} + \begin{tabular}{S S S S S} \toprule {\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& - {\textbf{Proton}}\\ + {\textbf{Proton}} & {\textbf{Momentum}}\\ {\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& - {\textbf{hit rate}}\\ - {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}\\ + {\textbf{hit rate}} &{\textbf{spread $\Delta p$}}\\ + {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})} + & {(\si{\keV\per\cc)}}\\ \midrule - 1 &0.5&1.5 & 2\\ - 0.5 &0.5&1.0 & 126\\ - 0 &0.5&0.5 & 1436\\ - 0 &0.3&0.3 & 8281\\ - 0 &0.1&0.1 & 15011\\ + 1 &0.5&1.5 & 2 & 195\\ + 0.5 &0.5&1.0 & 126 & 167\\ + 0 &0.5&0.5 & 1436 & 133\\ + 0 &0.3&0.3 & 8281 & {-}\\ + 0 &0.1&0.1 & 15011& {-}\\ \bottomrule \end{tabular} \end{center} - \caption{CDC proton hit rates} + \caption{CDC proton hit rates at different configuration of proton absorber + and inner wall. The momentum spreads for \SI{0.5}{\mm} thick inner wall are + taken from \cref{tab:comet_absorber_impact}.} \label{tab:proton_cdc_hitrate} \end{table} At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz}, much smaller than the current estimation at \SI{34}{\kHz}. Even without the -absorber, proton hit rate remains low at \SI{1.4}{\kHz}. Therefore a proton -absorber is not needed for the COMET Phase I's CDC. +absorber, proton hit rate remains low at \SI{1.4}{\kHz}. +%Therefore a proton +%absorber is not needed for the COMET Phase I's CDC. -Without the proton absorber, the momentum spread of the signal electron -reduces from \SI{167}{\keV} to \SI{131}{\keV}. If a lower momentum spread is -desired, it is possible to reduce the thickness of the inner wall. The last +If the proton absorber is not used, the momentum spread of the signal electron +reduces from \SI{167}{\keV} to \SI{131}{\keV}. In case a lower momentum spread +is desired, it is possible to reduce the thickness of the inner wall. The last two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at \SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at -manageable levels. +manageable levels. However, reducing the wall thickness would be governed by +other requirements such as mechanical structure and gas-tightness. + +In summary, the toy MC study with the preliminary proton rate and spectrum +shows that a proton absorber is not needed. It confirms the known fact that the +estimation used in COMET Phase-I is conservative, and provides a solid +prediction of the hit rate caused by protons. diff --git a/thesis/chapters/chap8_conclusions.tex b/thesis/chapters/chap8_conclusions.tex index ca92006..4c27f09 100644 --- a/thesis/chapters/chap8_conclusions.tex +++ b/thesis/chapters/chap8_conclusions.tex @@ -1,6 +1,6 @@ \chapter{Conclusions} \label{cha:conclusions} -AlCap is an experiment proposed at PSI to study charged particles, neutrons +The AlCap is an experiment proposed at PSI to study charged particles, neutrons and photons emitting after nuclear muon capture on aluminium. These measurements are important for backgrounds and hit rates estimation of the new generation of \mueconv experiments, COMET and Mu2e. In the first stage of the @@ -9,23 +9,33 @@ dominated by low energy protons following muon capture on an aluminium target, which has never been measured. The first run of the AlCap which aims for proton measurement has been carried -out in 2013. Data analysis is in progress. An initial analysis on partial data -was done with the main results are: +out in 2013. Data analysis is in progress. Before finishing the complete AlCap +analysis, an initial analysis on partial data +was made. The main results are: \begin{enumerate} - \item Demonstration of the analysis chain from raw waveforms to physics - events; - \item Validation of the experimental method including: number of nuclear + \item demonstration of the analysis chain from trigger-less waveforms to + correlated physics events; + \item validation of the experimental method including: number of nuclear capture muons normalisation by muonic X-ray measurement, charged particle identification by specific energy loss, and unfolding of the proton energy spectrum using the iterative Bayesian method; - \item Obtaining preliminary results on proton emission rate and spectrum: - the proton spectrum has a peak at \SI{4}{\MeV}, then reduces exponentially + \item obtaining preliminary results on proton emission rate and spectrum: + the proton spectrum has a peak at \SI{3.7}{\MeV}, then reduces exponentially with a decay constant of \SI{2.6}{\MeV}. The partial emission rate in the energy range from \SIrange{4}{8}{\MeV} is $(1.7 \pm 0.1)\%$, and the total emission rate assuming the shape holds for the whole spectrum is $(3.5\pm0.2)$. \end{enumerate} +The emission rate is consistent with the lower limit of 2.8\% set by +Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978}. It is also compatible +with the theoretical calculation by Lifshitz and +Singer~\cite{LifshitzSinger.1980}. Compared with the emission rate from +silicon, our result is smaller. + The proton rate and spectrum have been used to optimise the planned proton absorber for the drift chamber of the COMET Phase-I. The resulted proton hit -rate with the baseline configuration is very small compared with the current -figure. It is safe to remove the proton absorber altogether. +rate with the baseline configuration is very small compared with the current +figure. It is safe to remove the proton absorber altogether. This would make +a strong impact to the drift chamber design. The AlCap experiment is going to +submit a beam time request for the 2015 run to collect more data and other +measurements for neutrons and gamma rays. diff --git a/thesis/chapters/frontmatter.tex b/thesis/chapters/frontmatter.tex index 1dabec7..f185e9a 100644 --- a/thesis/chapters/frontmatter.tex +++ b/thesis/chapters/frontmatter.tex @@ -32,7 +32,7 @@ aluminium have been carried out in the 2013 run. The second run to study neutrons and photons is planned in 2015. The preliminary results from the analysis of the 2013 run are presented in this -thesis. The measured proton spectrum peaks at \SI{4}{\MeV} and decays +thesis. The measured proton spectrum peaks at \SI{3.7}{\MeV} and decays exponentially with the decay constant of \SI{2.6}{\MeV}. The emission rate of protons in the energy range from \SIrange{4}{8}{\MeV} is $(1.7\pm0.1)\%$. The total proton emission rate is estimated to be diff --git a/thesis/mythesis.sty b/thesis/mythesis.sty index 9bdb285..47b7e24 100644 --- a/thesis/mythesis.sty +++ b/thesis/mythesis.sty @@ -12,7 +12,7 @@ inner=1.25in, outer=1in, twoside]{geometry} %$ Hyper-link .. \RequirePackage[% -colorlinks=true,% color links instead of using boxes +colorlinks=false,% color links instead of using boxes linkcolor=red,% color for internal (intra-document) links citecolor=green,% color for bibliographic links urlcolor=blue,% color for URL links From b99a626448cda5422d526fe549b3d96ee0bb7616 Mon Sep 17 00:00:00 2001 From: nam Date: Thu, 27 Nov 2014 15:46:58 +0900 Subject: [PATCH 24/26] various fixes --- thesis/chapters/chap4_alcap_phys.tex | 38 +++++++++++++-------------- thesis/chapters/chap6_analysis.tex | 4 +-- thesis/chapters/chap7_results.tex | 18 ++++++------- thesis/chapters/chap8_conclusions.tex | 2 +- thesis/chapters/frontmatter.tex | 2 +- thesis/mythesis.sty | 9 ++++--- thesis/thesis.tex | 10 +++---- 7 files changed, 42 insertions(+), 41 deletions(-) diff --git a/thesis/chapters/chap4_alcap_phys.tex b/thesis/chapters/chap4_alcap_phys.tex index 0a33eb7..af630d9 100644 --- a/thesis/chapters/chap4_alcap_phys.tex +++ b/thesis/chapters/chap4_alcap_phys.tex @@ -548,8 +548,8 @@ The classical Coulomb barrier $V$ they used are given by: \label{eqn:classical_coulomb_barrier} \end{equation} where $z$ and $Z$ are the charges of the outgoing particle and of the residual -nucleus respectively, $e^2 = 1.44 \si{\MeV}$, $r_0 = 1.35 \textrm{ fm}$, and -$\rho = 0 \textrm{ fm}$ for protons were taken. +nucleus respectively, $e^2 = 1.44 \si{\MeV}\cdot\textrm{fm}$, $r_0 = 1.35 +\textrm{ fm}$, and $\rho = 0 \textrm{ fm}$ for protons were taken. \begin{figure}[htb] \centering \includegraphics[width=0.48\textwidth]{figs/wyttenbach_rate_1p} @@ -684,25 +684,25 @@ al.~\cite{VilgelmovaEvseev.etal.1971} observed. %nucleus & calculation & experiment & calculation & experiment \\ %\textbf{Col1}\\ \midrule - $^{27}_{13}$Al & 9.7 & {(4.7)} & 40 & {$> 28 \pm 4$} &(70)\\ + $^{27}_{13}$Al & 9.7 & {(4.7)} & 40 & {$> 28 $} &(70)\\ $^{28}_{14}$Si & 32 & 53 \pm 10 & 144 & 150 \pm 30 & \\ - $^{31}_{15}$P & 6.7 & {(6.3)} & 35 & {$> 61 \pm 6$}&(91) \\ + $^{31}_{15}$P & 6.7 & {(6.3)} & 35 & {$> 61$}&(91) \\ $^{39}_{19}$K & 19 & 32 \pm 6 & 67 & {} \\ - $^{41}_{19}$K & 5.1 & {(4.7)} & 30 & {$> 28 \pm 4$} &(70)\\ - $^{51 }_{23}$V &3.7 &2.9 \pm 0.4 &25 &{$>20 \pm 1.8$}& (32)\\ - $^{55 }_{25}$Mn &2.4 &2.8 \pm 0.4 &16 &{$>26 \pm 2.5$}& (35)\\ - $^{59 }_{27}$Co &3.3 &1.9 \pm 0.2 &21 &{$>37 \pm 3.4$}& (50)\\ - $^{60 }_{28}$Ni &8.9 &21.4 \pm 2.3 &49 &40 \pm 5&\\ - $^{63 }_{29}$Cu &4.0 &2.9 \pm 0.6 &25 &{$>17 \pm 3 $}& (36)\\ - $^{65 }_{29}$Cu &1.2 &{(2.3)} &11 &{$>35 \pm 4.5$}& (36)\\ - $^{75 }_{33}$As &1.5 &1.4 \pm 0.2 &14 &{$>14 \pm 1.3$}& (19)\\ - $^{79 }_{35}$Br &2.7 &{} &22 & &\\ - $^{107}_{47}$Ag &2.3 &{} &18 & &\\ - $^{115}_{49}$In &0.63 &{(0.77)} &7.2 &{$>11 \pm 1$} &(12)\\ - $^{133}_{55}$Cs &0.75 &0.48 \pm 0.07 &8.7 &{$>4.9 \pm 0.5$} &(6.7)\\ - $^{165}_{67}$Ho &0.26 &0.30 \pm 0.04 &4.1 &{$>3.4 \pm 0.3$} &(4.6)\\ - $^{181}_{73}$Ta &0.15 &0.26 \pm 0.04 &2.8 &{$>0.7 \pm 0.1$} &(3.0)\\ - $^{208}_{82}$Pb &0.14 &0.13 \pm 0.02 &1.1 &{$>3.0 \pm 0.8$} &(4.1)\\ + $^{41}_{19}$K & 5.1 & {(4.7)} & 30 & {$> 28$} &(70)\\ + %$^{51 }_{23}$V &3.7 &2.9 \pm 0.4 &25 &{$>20 \pm 1.8$}& (32)\\ + %$^{55 }_{25}$Mn &2.4 &2.8 \pm 0.4 &16 &{$>26 \pm 2.5$}& (35)\\ + %$^{59 }_{27}$Co &3.3 &1.9 \pm 0.2 &21 &{$>37 \pm 3.4$}& (50)\\ + %$^{60 }_{28}$Ni &8.9 &21.4 \pm 2.3 &49 &40 \pm 5&\\ + %$^{63 }_{29}$Cu &4.0 &2.9 \pm 0.6 &25 &{$>17 \pm 3 $}& (36)\\ + %$^{65 }_{29}$Cu &1.2 &{(2.3)} &11 &{$>35 \pm 4.5$}& (36)\\ + %$^{75 }_{33}$As &1.5 &1.4 \pm 0.2 &14 &{$>14 \pm 1.3$}& (19)\\ + %$^{79 }_{35}$Br &2.7 &{} &22 & &\\ + %$^{107}_{47}$Ag &2.3 &{} &18 & &\\ + %$^{115}_{49}$In &0.63 &{(0.77)} &7.2 &{$>11 \pm 1$} &(12)\\ + %$^{133}_{55}$Cs &0.75 &0.48 \pm 0.07 &8.7 &{$>4.9 \pm 0.5$} &(6.7)\\ + %$^{165}_{67}$Ho &0.26 &0.30 \pm 0.04 &4.1 &{$>3.4 \pm 0.3$} &(4.6)\\ + %$^{181}_{73}$Ta &0.15 &0.26 \pm 0.04 &2.8 &{$>0.7 \pm 0.1$} &(3.0)\\ + %$^{208}_{82}$Pb &0.14 &0.13 \pm 0.02 &1.1 &{$>3.0 \pm 0.8$} &(4.1)\\ \bottomrule \end{tabular} \end{center} diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index b84f3eb..19c9b66 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -178,7 +178,7 @@ which is consistent with the number of X-rays counted using the active target. \toprule \textbf{Efficiency and intensity} & \textbf{Value} & \textbf{Absolute error} & \textbf{Relative error} \\ \midrule - Detector efficiency & \num{4.40E-4} & \num{0.978E-5} & 0.02 \\ + Detector efficiency & \num{4.40E-4} & \num{0.10E-4} & 0.02 \\ X-ray intensity & 0.803 & 0.008 & 0.009 \\ \vspace{0.03em}\\ \toprule @@ -336,7 +336,7 @@ With the aid from MC study (\cref{fig:pid_sim}), the banding on The band of protons is then extracted by cut on likelihood probability calculated as: \begin{equation} - p_{i} = \dfrac{1}{\sqrt{2\pi}\sigma_{\Delta E}} + P_{i} = \dfrac{1}{\sqrt{2\pi}\sigma_{\Delta E}} \exp{\left[\dfrac{(\Delta E_{meas.} - \Delta E_i)^2} {2\sigma^2_{\Delta E}}\right]} \end{equation} diff --git a/thesis/chapters/chap7_results.tex b/thesis/chapters/chap7_results.tex index fd471d8..359d6b1 100644 --- a/thesis/chapters/chap7_results.tex +++ b/thesis/chapters/chap7_results.tex @@ -57,20 +57,20 @@ layer due to these protons with different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. \begin{table}[htb] \begin{center} - \begin{tabular}{S S S S S} + \begin{tabular}{S S S S S S} \toprule {\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& - {\textbf{Proton}} & {\textbf{Momentum}}\\ + {\textbf{Proton}} & {\textbf{Momentum}} & {\textbf{Integrated charge}}\\ {\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& - {\textbf{hit rate}} &{\textbf{spread $\Delta p$}}\\ + {\textbf{hit rate}} &{\textbf{spread $\Delta p$}} &{\textbf{300 days}}\\ {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})} - & {(\si{\keV\per\cc)}}\\ + & {(\si{\keV\per\cc)}} &{(mC/cm)}\\ \midrule - 1 &0.5&1.5 & 2 & 195\\ - 0.5 &0.5&1.0 & 126 & 167\\ - 0 &0.5&0.5 & 1436 & 133\\ - 0 &0.3&0.3 & 8281 & {-}\\ - 0 &0.1&0.1 & 15011& {-}\\ + 1 &0.5&1.5 & 2 & 195 & 25\\ + 0.5 &0.5&1.0 & 126 & 167 & 60\\ + 0 &0.5&0.5 & 1436 & 133 & 160\\ + %0 &0.3&0.3 & 8281 & {-} & {-}\\ + %0 &0.1&0.1 & 15011& {-} & {-}\\ \bottomrule \end{tabular} \end{center} diff --git a/thesis/chapters/chap8_conclusions.tex b/thesis/chapters/chap8_conclusions.tex index 4c27f09..b61f6cc 100644 --- a/thesis/chapters/chap8_conclusions.tex +++ b/thesis/chapters/chap8_conclusions.tex @@ -24,7 +24,7 @@ was made. The main results are: with a decay constant of \SI{2.6}{\MeV}. The partial emission rate in the energy range from \SIrange{4}{8}{\MeV} is $(1.7 \pm 0.1)\%$, and the total emission rate assuming the shape holds for the whole spectrum is - $(3.5\pm0.2)$. + $(3.5\pm0.2)\%$. \end{enumerate} The emission rate is consistent with the lower limit of 2.8\% set by Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978}. It is also compatible diff --git a/thesis/chapters/frontmatter.tex b/thesis/chapters/frontmatter.tex index f185e9a..fea1b50 100644 --- a/thesis/chapters/frontmatter.tex +++ b/thesis/chapters/frontmatter.tex @@ -14,7 +14,7 @@ Osaka University} violation (CLFV) process, the muon-to-electron conversion in the presence of a nucleus, \muec. The process is forbidden in the Standard Model (SM), however is -predicted to occur in various extensions of SM, such as . Current experimental +predicted to occur in various extensions of SM. Current experimental upper limit of the branching ratio is $BR(\mu^{-} + Au \rightarrow e^{-} + Au) < 7 \times 10^{-13}$, set by the SINDRUM II experiment [2]. diff --git a/thesis/mythesis.sty b/thesis/mythesis.sty index 47b7e24..c4ed552 100644 --- a/thesis/mythesis.sty +++ b/thesis/mythesis.sty @@ -12,10 +12,11 @@ inner=1.25in, outer=1in, twoside]{geometry} %$ Hyper-link .. \RequirePackage[% -colorlinks=false,% color links instead of using boxes -linkcolor=red,% color for internal (intra-document) links -citecolor=green,% color for bibliographic links -urlcolor=blue,% color for URL links +%colorlinks=false,% color links instead of using boxes +%linkcolor=red,% color for internal (intra-document) links +%citecolor=green,% color for bibliographic links +%urlcolor=blue,% color for URL links +hidelinks, hyperfootnotes=false,% disable links to footnotes (because feature broken) hyperindex,% make page numbers in index into hyperlinks pdfstartview={FitH},% startup page view: fit width of page to window diff --git a/thesis/thesis.tex b/thesis/thesis.tex index aec31ac..7c10071 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -30,13 +30,13 @@ for the COMET experiment} \mainmatter %%%\input{chapters/chap1_intro} -\input{chapters/chap2_mu_e_conv} -\input{chapters/chap3_comet} -\input{chapters/chap4_alcap_phys} -\input{chapters/chap5_alcap_setup} +%\input{chapters/chap2_mu_e_conv} +%\input{chapters/chap3_comet} +%\input{chapters/chap4_alcap_phys} +%\input{chapters/chap5_alcap_setup} \input{chapters/chap6_analysis} \input{chapters/chap7_results} -\input{chapters/chap8_conclusions} +%\input{chapters/chap8_conclusions} \begin{backmatter} \input{chapters/backmatter} From 20a3a71211d77dfbd1214cc9e47536f3920440bc Mon Sep 17 00:00:00 2001 From: nam Date: Thu, 27 Nov 2014 16:05:43 +0900 Subject: [PATCH 25/26] various fixes --- thesis/chapters/chap7_results.tex | 40 ++++++++++++++++++++++++++++++ thesis/figs/ge_eff_cal.pdf | Bin 23218 -> 22618 bytes thesis/thesis.tex | 10 ++++---- 3 files changed, 45 insertions(+), 5 deletions(-) diff --git a/thesis/chapters/chap7_results.tex b/thesis/chapters/chap7_results.tex index 359d6b1..cf4fa77 100644 --- a/thesis/chapters/chap7_results.tex +++ b/thesis/chapters/chap7_results.tex @@ -80,6 +80,46 @@ different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. \label{tab:proton_cdc_hitrate} \end{table} +%\begin{table}[htb] + %\begin{center} + %\begin{tabular}{S S S S S} + %\toprule + %{\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& + %{\textbf{Proton hit rate}} & {\textbf{Proton hit rate}}\\ + %{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& + %{\textbf{Phase-I TDR}} & {\textbf{New estimation}}\\ + %{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}& {(\si{\Hz})}\\ + %\midrule + %1 &0.5&1.5 & 4E+3 & 2 \\ + %0.5 &0.5&1.0 & 11E+3& 126 \\ + %0 &0.5&0.5 & 30E+3& 1436 \\ + %\bottomrule + %\end{tabular} + %\end{center} + %\caption{CDC proton hit rates at different configuration of proton absorber + %and inner wall. The momentum spreads for \SI{0.5}{\mm} thick inner wall are + %taken from \cref{tab:comet_absorber_impact}.} + %\label{tab:proton_cdc_hitrate} +%\end{table} + +%\begin{table}[htb] + %\begin{center} + %\begin{tabular}{S S S S S S} + %\toprule + %{\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& {\textbf{Proton}} & {\textbf{Momentum}} & {\textbf{Integrated charge}}\\ + %{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& {\textbf{hit rate}} &{\textbf{spread $\Delta p$}} &{\textbf{300 days}}\\ + %{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})} & {(\si{\keV\per\cc)}} &{(mC/cm)}\\ + %\midrule + %1 &0.5&1.5 & 2 & 195 & 25\\ + %0.5 &0.5&1.0 & 126 & 167 & 60\\ + %0 &0.5&0.5 & 1436 & 133 & 160\\ + %\bottomrule + %\end{tabular} + %\end{center} + %\caption{CDC proton hit rates at different configuration of proton absorber + %and inner wall. The momentum spreads for \SI{0.5}{\mm} thick inner wall are + %taken from \cref{tab:comet_absorber_impact}.} +%\end{table} At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz}, much smaller than the current estimation at \SI{34}{\kHz}. 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%%%\input{chapters/chap1_intro} -%\input{chapters/chap2_mu_e_conv} -%\input{chapters/chap3_comet} -%\input{chapters/chap4_alcap_phys} -%\input{chapters/chap5_alcap_setup} +\input{chapters/chap2_mu_e_conv} +\input{chapters/chap3_comet} +\input{chapters/chap4_alcap_phys} +\input{chapters/chap5_alcap_setup} \input{chapters/chap6_analysis} \input{chapters/chap7_results} -%\input{chapters/chap8_conclusions} +\input{chapters/chap8_conclusions} \begin{backmatter} \input{chapters/backmatter} From 1dd6fe68784db252621a24077335d5bd8a60a551 Mon Sep 17 00:00:00 2001 From: nam Date: Mon, 2 May 2016 13:08:13 +0900 Subject: [PATCH 26/26] status saved --- AlCapPSI/draft/.DS_Store | Bin 6148 -> 8196 bytes thesis/chapters/chap2_mu_e_conv.tex | 10 +- thesis/chapters/chap3_comet.tex | 35 +- thesis/chapters/chap4_alcap_phys.tex | 215 ++++++----- thesis/chapters/chap5_alcap_setup.tex | 93 +++-- thesis/chapters/chap6_analysis.tex | 497 ++++++++++++++++++-------- thesis/chapters/chap7_results.tex | 116 +++--- thesis/chapters/chap8_conclusions.tex | 18 +- thesis/chapters/frontmatter.tex | 26 +- thesis/figs/al100_resp.pdf | Bin 24277 -> 24017 bytes thesis/figs/sir2_xray_22.pdf | Bin 28722 -> 155021 bytes thesis/mythesis.sty | 20 ++ thesis/thesis.bib | 170 ++++++++- 13 files changed, 842 insertions(+), 358 deletions(-) diff --git a/AlCapPSI/draft/.DS_Store b/AlCapPSI/draft/.DS_Store index 7a0b1b95e61ee61b478549c41e6ee13316ac7214..8d6eab09660f7e3400059f310eba853f6ce8fd2f 100644 GIT binary patch literal 8196 zcmeHMTWl0n7(QPwFhd8JmKMsg4J*Z9O#`K+6y&zO07W1)Y_EVUvz-A(r!#eD+M;El z`lfil#b`9%@Pf({g1#7okr;VVAto60LE|eX@*ut#|1)QHUAE^M^CU zg$(Nufe?Yo2=Kjo2|LJ4c8Iz8`}fqaWx8HN!xa=2mz2(!Dao^DDfCgxmHQHhow0KBr|Tq zX{6Zs?LE)y9J_zczlC&}st% ztBp4ZRi?yL!x~u!+rbX7G#h76vX|ML>dedj=q1smoPeq%n#-bf5-kw5$Zsn3(dC@}YO(0`X|2m@spws;tl>*REfKxzlntEp z>I~6aqqNGh%0y#Xv`oGgO#Oy<`YW;Y8Xe94gBd78HSQp8uE1JsLLBYH%`Mo4F6>4E zJ=l*VG^C&tGi?mxLAW@IjL*q;#qRJWVUGM>PK?gv{Z`4 ztg89`fAh`H|EJ~L!%2k*gb3Uk1W?kE=xC!@+20d|VfkJ=M%Mwlc;VwFg!Emgy5S&z o+POarNsrM`?h_B>gpg#R^1mMhIChx-!~F06N(gqRw`KnS7hC?1ng9R* delta 211 zcmZp1XfcprU|?W$DortDU=RQ@Ie-{MGjUEV6q~50D9Qwq2Z<$>7Z)Vuo*oI zXPj&x!y?MUkj9Y7kj_wyEIWC(Sh9{pb+xX!k&c3qfn}|ZLbbWMfsTTSu|;hyCnpD| zz;X^zB|RIDki?qWy84F6p5pS1O`DgBB{6PnxWv4eor6P=8E6j>2yg=lSCD%)7Jg@* b%rD~zaxln6EFc=_I*^OOVw>Z6<}d>QY#S=8 diff --git a/thesis/chapters/chap2_mu_e_conv.tex b/thesis/chapters/chap2_mu_e_conv.tex index 4fed239..404795d 100644 --- a/thesis/chapters/chap2_mu_e_conv.tex +++ b/thesis/chapters/chap2_mu_e_conv.tex @@ -250,7 +250,7 @@ flavour was experimentally verified in the Nobel Prize-winning experiment of Danby et al. at Brookhaven National Laboratory (BNL)~\cite{DanbyGaillard.etal.1962}. Then the concepts of generations of particles was developed~\cite{MakiNakagawa.etal.1962}, and integrated into the -SM, in which the lepton flavour conservation is guaranteed by and exact +SM, in which the lepton flavour conservation is guaranteed by an exact symmetry, owing to massless neutrinos. Following the above LFV searches with muons, searches with various particles, @@ -267,11 +267,11 @@ must be modified to accommodate the massive neutrinos. With the massive neutrinos charged lepton flavour violation (CLFV) must occur through oscillations in loops. But, CLFV processes are highly suppressed in the SM. -For example, Marciano and Mori ~\cite{MarcianoMori.etal.2008} calculated the +%\hl{TODO: Feynman diagram} +For example, Marciano and Mori~\cite{MarcianoMori.etal.2008} calculated the branching ratio of the process \mueg to be \brmeg$<10^{-54}$. Other CLFV processes with muons are also suppressed to similar practically -unmeasurable levels.%\hl{TODO: Feynman diagram} -Therefore, any experimental +unmeasurable levels. Therefore, any experimental observation of CLFV would be an unambiguous signal of the physics beyond the SM. Many theoretical models for physics beyond the SM, including supersymmetric (SUSY) models, extra dimensional models, little Higgs models, predict @@ -308,7 +308,7 @@ significantly larger CLFV %It is calculated that there are two CLFV processes that would %occur at large rates by many new physics models, Among the CLFV processes, the \mueg and -the \muec are expected to have large effect by many models. The current +the \muec are expected to have large effect in many models. The current experimental limits on these two decay modes are set respectively by the MEG experiment~\cite{Adam.etal.2013} and the SINDRUM-II experiment~\cite{Bertl.etal.2006}: diff --git a/thesis/chapters/chap3_comet.tex b/thesis/chapters/chap3_comet.tex index ae3abc1..676f869 100644 --- a/thesis/chapters/chap3_comet.tex +++ b/thesis/chapters/chap3_comet.tex @@ -63,20 +63,20 @@ and Cooper~\cite{BernsteinCooper.2013}. 1961 & \sn{4.0}{-6} & Cu & \cite{SardCrowe.etal.1961}\\ 1961 & \sn{5.9}{-6} & Cu & \cite{ConversiLella.etal.1961}\\ 1962 & \sn{2.2}{-7} & Cu & \cite{ConfortoConversi.etal.1962}\\ - 1964 & \sn{2.2}{-7} & Cu & \cite{ConversiLella.etal.1961}\\ - 1972 & \sn{2.6}{-8} & Cu & \cite{ConversiLella.etal.1961}\\ - 1977 & \sn{4.0}{-10} & S & \cite{ConversiLella.etal.1961}\\ - 1982 & \sn{7.0}{-11} & S & \cite{ConversiLella.etal.1961}\\ - 1988 & \sn{4.6}{-12} & Ti & \cite{ConversiLella.etal.1961}\\ - 1993 & \sn{4.3}{-12} & Ti & \cite{ConversiLella.etal.1961}\\ - 1995 & \sn{6.5}{-13} & Ti & \cite{ConversiLella.etal.1961}\\ - 1996 & \sn{4.6}{-11} & Pb & \cite{ConversiLella.etal.1961}\\ - 2006 & \sn{7.0}{-13} & Au & \cite{ConversiLella.etal.1961}\\ + 1964 & \sn{2.2}{-7} & Cu & \cite{BartleyDavies.etal.1964}\\ + 1972 & \sn{2.6}{-8} & Cu & \cite{BrymanBlecher.etal.1972}\\ + 1977 & \sn{4.0}{-10} & S & \cite{BadertscherBorer.etal.1977}\\ + 1982 & \sn{7.0}{-11} & S & \cite{BadertscherBorer.etal.1982a}\\ + 1988 & \sn{4.6}{-12} & Ti & \cite{AhmadAzuelos.etal.1988a}\\ + 1993 & \sn{4.3}{-12} & Ti & \cite{DohmenGroth.etal.1993}\\ + 1996 & \sn{4.6}{-11} & Pb & \cite{HoneckerDohmen.etal.1996}\\ + 2006 & \sn{7.0}{-13} & Au & \cite{Bertl.etal.2006}\\ \bottomrule + %%TODO fix ref \end{tabular} \end{center} - \caption{History of \mueconv experiments, reproduced - from~\cite{BernsteinCooper.2013}} + \caption{History of \mueconv experiments with more and more stringent upper + limit.} \label{tab:mueconv_history} \end{table} @@ -94,7 +94,8 @@ muons used in the experiment were \SI{52}{\MeV\per\cc} and \SI{53}{\MeV\per\cc}, and the momentum spread was 2\%. \begin{figure}[htbp] \centering \includegraphics[width=0.85\textwidth]{figs/sindrumII_setup} - \caption{SINDRUM-II set up} + \caption{SINDRUM-II experimental set up, reprinted from + reference~\cite{Bertl.etal.2006} with permission from Springer.} \label{fig:sindrumII_setup} \end{figure} @@ -115,7 +116,9 @@ important in probing better sensitivity. \begin{figure}[htbp] \centering \includegraphics[width=0.55\textwidth]{figs/sindrumII_Au_result} - \caption{SINDRUM-II results} + \caption{SINDRUM-II results showing background events reaching into the + signal region. Reprinted from reference~\cite{Bertl.etal.2006} with + permission from Springer.} %TODO: explain top and bottom figure \label{fig:sindrumII_result} \end{figure} @@ -353,8 +356,10 @@ Therefore, light material is preferable as muon stopping target. The conversion rates are normalised to the rate in aluminium. Four models were considered and noted with letters: D for dipole-interaction-dominated model, V for vector and S for scalar interactions. The three vertical lines - from left to right correspond to $Z=13$(Al), $Z=22$(Ti), and $Z=82$(Pb)l - respectively.} + from left to right correspond to $Z=13$(Al), $Z=22$(Ti), and $Z=82$(Pb) + respectively. Reprinted figure from + reference~\cite{CiriglianoKitano.etal.2009}. Copyright 2009 by the + American Physical Society.} \label{fig:comet_mueconv_RateVsZ} \end{figure} diff --git a/thesis/chapters/chap4_alcap_phys.tex b/thesis/chapters/chap4_alcap_phys.tex index af630d9..71f019c 100644 --- a/thesis/chapters/chap4_alcap_phys.tex +++ b/thesis/chapters/chap4_alcap_phys.tex @@ -410,10 +410,10 @@ data. There are two reasons for that: \end{enumerate} The first study was done by Morigana and Fry~\cite{MorinagaFry.1953} where 24,000 muon tracks were stopped in their nuclear emulsion which contains silver, -bromine, and other light elements, mainly nitrogen, carbon, hydrogen and +bromine AgBr, and other light elements, mainly nitrogen, carbon, hydrogen and oxygen. The authors identified a capture on a light element as it would leave a recoil -track of the nucleus. They found that for silver bromide AgBr, $(2.2 \pm +track of the nucleus. They found that for silver bromide, $(2.2 \pm 0.2)\%$ of the captures produced protons and $(0.5 \pm 0.1)\%$ produced alphas. For light elements, the emission rate for proton and alpha are respectively $(9.5 \pm 1.1)\%$ and $(3.4 \pm 0.7)\%$. Subsequently, Kotelchuk and @@ -423,9 +423,13 @@ statistics and in fair agreement with Morigana and Fry \begin{figure}[htb] \centering \includegraphics[width=0.65\textwidth]{figs/kotelchuk_proton_spectrum} - \caption{Early proton spectrum after muon capture in silver bromide AgBr - recorded using nuclear emulsion. Image is taken from - Ref.~\cite{KotelchuckTyler.1968}} + \caption{Proton spectrum after muon capture in silver bromide AgBr in + early experiments recorded using nuclear emulsion. The closed circles + are data points from Morigana and Fry~\cite{MorinagaFry.1953}, the + histogram is measurement result of Kotelchuk and + Tyler~\cite{KotelchuckTyler.1968}. Reprinted figure from + reference~\cite{KotelchuckTyler.1968}. Copyright 1968 by the American + Physical Society.} \label{fig:kotelchuk_proton_spectrum} \end{figure} @@ -475,16 +479,18 @@ might be at work in this mass range. target (closed circle) in the energy range above 40 MeV and an exponential fit. The open squares are silicon data from Budyashov et al.~\cite{BudyashovZinov.etal.1971}, the open triangles are magnesium data - from Balandin et al.~\cite{BalandinGrebenyuk.etal.1978}.} + from Balandin et al.~\cite{BalandinGrebenyuk.etal.1978}. Reprinted + figure from reference~\cite{KraneSharma.etal.1979}. Copyright 1979 by + the American Physical Society.} \label{fig:krane_proton_spec} \end{figure} The aforementioned difficulties in charged particle measurements could be solved using an active target, just like nuclear emulsion. Sobottka and Wills~\cite{SobottkaWills.1968} took this approach when using a Si(Li) detector -to stop muons. They obtained a spectrum of charged particles up to 26 -\si{\MeV}~in \cref{fig:sobottka_spec}. The peak below 1.4 -\si{\MeV}~is due to the recoiling $^{27}$Al. The higher energy events +to stop muons. They obtained a spectrum of charged particles up to \SI{26}{\MeV} +in \cref{fig:sobottka_spec}. The peak below \SI{1.4}{\MeV} +is due to the recoiling $^{27}$Al. The higher energy events including protons, deuterons and alphas constitute $(15\pm 2)\%$ of capture events, which is consistent with a rate of $(12.9\pm1.4)\%$ from gelatine observed by Morigana and Fry. This part has an exponential @@ -507,7 +513,8 @@ silicon, and $(17\pm4)\%$ in copper. \centering \includegraphics[width=0.75\textwidth]{figs/sobottka_spec} \caption{Charged particle spectrum from muon capture in a silicon detector, - image taken from Sobottka and Wills~\cite{SobottkaWills.1968}.} + measured by Sobottka and Wills~\cite{SobottkaWills.1968}. The plot is + reproduced from the original figure in reference~\cite{SobottkaWills.1968}.} \label{fig:sobottka_spec} \end{figure} @@ -544,7 +551,7 @@ against the Coulomb barrier for the outgoing protons are given in %and \cref{fig:wyttenbach_rate_23p}. The classical Coulomb barrier $V$ they used are given by: \begin{equation} - V = \frac{zZe^2}{r_0A^{\frac{1}{3}} + \rho}, + V = \frac{zZe^2}{r_0A^{\frac{1}{3}} + \rho}\,, \label{eqn:classical_coulomb_barrier} \end{equation} where $z$ and $Z$ are the charges of the outgoing particle and of the residual @@ -552,11 +559,15 @@ nucleus respectively, $e^2 = 1.44 \si{\MeV}\cdot\textrm{fm}$, $r_0 = 1.35 \textrm{ fm}$, and $\rho = 0 \textrm{ fm}$ for protons were taken. \begin{figure}[htb] \centering - \includegraphics[width=0.48\textwidth]{figs/wyttenbach_rate_1p} - \includegraphics[width=0.505\textwidth]{figs/wyttenbach_rate_23p} - \caption{Activation results from Wyttenbach et - al.~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p)$, - $(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$ and $(\mu^-,\nu p3n)$ reactions.} + \includegraphics[width=0.48\textwidth]{figs/wyttenbach_rate_1p} + \includegraphics[width=0.505\textwidth]{figs/wyttenbach_rate_23p} + \caption{Activation results from Wyttenbach and + colleagues~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p)$, + $(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$ and $(\mu^-,\nu p3n)$ reactions. The + cross section of each individual channels decreases exponentially as the + Coulomb barrier for proton emission increases. + Reprinted figure from reference~\cite{WyttenbachBaertschi.etal.1978} with + permission from Elsevier.} \label{fig:wyttenbach_rate_1p} \end{figure} %\begin{figure}[htb] @@ -568,10 +579,10 @@ nucleus respectively, $e^2 = 1.44 \si{\MeV}\cdot\textrm{fm}$, $r_0 = 1.35 %\label{fig:wyttenbach_rate_23p} %\end{figure} -Wyttenbach et al.\ saw that the cross section of each reaction decreases +Wyttenbach and colleagues saw that the cross section of each reaction decreases exponentially with increasing Coulomb barrier. The decay constant for all $(\mu^-,\nu pxn)$ is about 1.5 per \si{\MeV}~of Coulomb barrier. They -also commented a ratio for different de-excitation channels: +also observed a ratio for different de-excitation channels: \begin{equation} (\mu^-,\nu p):(\mu^-,\nu pn):(\mu^-,\nu p2n):(\mu^-,\nu p3n) = 1:6:4:4, \label{eqn:wyttenbach_ratio} @@ -581,7 +592,7 @@ the results from Vil'gel'mova et al.~\cite{VilgelmovaEvseev.etal.1971} as being too high, but Measday~\cite{Measday.2001} noted it it is not necessarily true since there has been suggestion from other experiments that $(\mu^-, \nu p)$ reactions might become more important for light nuclei. -Measday also commented that the ratio~\eqref{eqn:wyttenbach_ratio} holds over +Measday noted that the ratio~\eqref{eqn:wyttenbach_ratio} holds over a broad range of mass, but below $A=40$ the $(\mu^-,\nu p)$ reaction can vary significantly from nucleus to nucleus. % subsection experimental_status (end) @@ -598,24 +609,25 @@ $\rho(p) \sim A/(B^2 + p^2)^2$; (II) Fermi gas at zero temperature; and (III) Fermi gas at a finite temperature ($kT = 9$ \si{\MeV}). A very good agreement with the experimental result for the alpha emission was -obtained with distribution (III), both in the absolute percentage and the energy -distribution (curve (III) in the left hand side of -\cref{fig:ishii_cal_result}). However, the calculated emission of protons -at the same temperature falls short by about 10 -times compares to the data. The author also found that the distribution -(I) is unlikely to be suitable for proton emission, and using that distribution -for alpha emission resulted in a rate 15 times larger than observed. +obtained with distribution (III). +%, both in the absolute percentage and the energy +%distribution (curve (III) in the left hand side of +%\cref{fig:ishii_cal_result}). +However, the calculated emission rate of protons at the same temperature was 10 +times smaller the experimental results from Morigana and Fry. The author +found the distribution (I) is unlikely to be suitable for proton emission, +and using that distribution +for alpha emission resulted in a rate 15 times larger than the observed rate. -\begin{figure}[htb] - \centering - \includegraphics[width=.49\textwidth]{figs/ishii_cal_alpha} - %\hspace{10mm} - \includegraphics[width=.49\textwidth]{figs/ishii_cal_proton} - \caption{Alpha spectrum (left) and proton spectrum (right) from Ishii's - calculation~\cite{Ishii.1959} in comparison with experimental data from - Morigana and Fry. Image is taken from Ishii's paper.} - \label{fig:ishii_cal_result} -\end{figure} +%\begin{figure}[htb] + %\centering + %\includegraphics[width=.49\textwidth]{figs/ishii_cal_alpha} + %\includegraphics[width=.49\textwidth]{figs/ishii_cal_proton} + %\caption{Alpha spectrum (left) and proton spectrum (right) from Ishii's + %calculation~\cite{Ishii.1959} in comparison with experimental data from + %Morigana and Fry. Image is taken from Ishii's paper.} + %\label{fig:ishii_cal_result} +%\end{figure} Singer~\cite{Singer.1974} noted that by assuming a reduced effective mass for the nucleon, the average excitation energy increases, but the proton emission rate is not significantly improved and still could not explain the @@ -650,7 +662,9 @@ spectrum and experimental data is shown in \caption{Proton energy spectrum from muon capture in AgBr, the data in histogram is from Morigana and Fry, calculation by Lifshitz and Singer~\cite{LifshitzSinger.1978} showed contributions from the - pre-equilibrium emission and the equilibrium emission.} + pre-equilibrium emission and the equilibrium emission. Reprinted figure + from reference~\cite{LifshitzSinger.1978}. Copyright 1978 by the American + Physical Society.} \label{fig:lifshitzsinger_cal_proton} \end{figure} @@ -689,20 +703,20 @@ al.~\cite{VilgelmovaEvseev.etal.1971} observed. $^{31}_{15}$P & 6.7 & {(6.3)} & 35 & {$> 61$}&(91) \\ $^{39}_{19}$K & 19 & 32 \pm 6 & 67 & {} \\ $^{41}_{19}$K & 5.1 & {(4.7)} & 30 & {$> 28$} &(70)\\ - %$^{51 }_{23}$V &3.7 &2.9 \pm 0.4 &25 &{$>20 \pm 1.8$}& (32)\\ - %$^{55 }_{25}$Mn &2.4 &2.8 \pm 0.4 &16 &{$>26 \pm 2.5$}& (35)\\ - %$^{59 }_{27}$Co &3.3 &1.9 \pm 0.2 &21 &{$>37 \pm 3.4$}& (50)\\ - %$^{60 }_{28}$Ni &8.9 &21.4 \pm 2.3 &49 &40 \pm 5&\\ - %$^{63 }_{29}$Cu &4.0 &2.9 \pm 0.6 &25 &{$>17 \pm 3 $}& (36)\\ - %$^{65 }_{29}$Cu &1.2 &{(2.3)} &11 &{$>35 \pm 4.5$}& (36)\\ - %$^{75 }_{33}$As &1.5 &1.4 \pm 0.2 &14 &{$>14 \pm 1.3$}& (19)\\ - %$^{79 }_{35}$Br &2.7 &{} &22 & &\\ - %$^{107}_{47}$Ag &2.3 &{} &18 & &\\ - %$^{115}_{49}$In &0.63 &{(0.77)} &7.2 &{$>11 \pm 1$} &(12)\\ - %$^{133}_{55}$Cs &0.75 &0.48 \pm 0.07 &8.7 &{$>4.9 \pm 0.5$} &(6.7)\\ - %$^{165}_{67}$Ho &0.26 &0.30 \pm 0.04 &4.1 &{$>3.4 \pm 0.3$} &(4.6)\\ - %$^{181}_{73}$Ta &0.15 &0.26 \pm 0.04 &2.8 &{$>0.7 \pm 0.1$} &(3.0)\\ - %$^{208}_{82}$Pb &0.14 &0.13 \pm 0.02 &1.1 &{$>3.0 \pm 0.8$} &(4.1)\\ + $^{51 }_{23}$V &3.7 &2.9 \pm 0.4 &25 &{$>20 \pm 1.8$}& (32)\\ + $^{55 }_{25}$Mn &2.4 &2.8 \pm 0.4 &16 &{$>26 \pm 2.5$}& (35)\\ + $^{59 }_{27}$Co &3.3 &1.9 \pm 0.2 &21 &{$>37 \pm 3.4$}& (50)\\ + $^{60 }_{28}$Ni &8.9 &21.4 \pm 2.3 &49 &40 \pm 5&\\ + $^{63 }_{29}$Cu &4.0 &2.9 \pm 0.6 &25 &{$>17 \pm 3 $}& (36)\\ + $^{65 }_{29}$Cu &1.2 &{(2.3)} &11 &{$>35 \pm 4.5$}& (36)\\ + $^{75 }_{33}$As &1.5 &1.4 \pm 0.2 &14 &{$>14 \pm 1.3$}& (19)\\ + $^{79 }_{35}$Br &2.7 &{} &22 & &\\ + $^{107}_{47}$Ag &2.3 &{} &18 & &\\ + $^{115}_{49}$In &0.63 &{(0.77)} &7.2 &{$>11 \pm 1$} &(12)\\ + $^{133}_{55}$Cs &0.75 &0.48 \pm 0.07 &8.7 &{$>4.9 \pm 0.5$} &(6.7)\\ + $^{165}_{67}$Ho &0.26 &0.30 \pm 0.04 &4.1 &{$>3.4 \pm 0.3$} &(4.6)\\ + $^{181}_{73}$Ta &0.15 &0.26 \pm 0.04 &2.8 &{$>0.7 \pm 0.1$} &(3.0)\\ + $^{208}_{82}$Pb &0.14 &0.13 \pm 0.02 &1.1 &{$>3.0 \pm 0.8$} &(4.1)\\ \bottomrule \end{tabular} \end{center} @@ -710,11 +724,11 @@ al.~\cite{VilgelmovaEvseev.etal.1971} observed. reaction $^A_Z X (\mu,\nu p) ^{A-1}_{Z-2}Y$ and for inclusive proton emission compiled by Measday~\cite{Measday.2001}. The calculated values are from Lifshitz and Singer. The experimental data are mostly from - Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978}. For inclusive emission - the experimental figures are lower limits, determined from the - actually measured channels. The figures in crescent parentheses are - estimates for the total inclusive rate derived from the measured exclusive - channels by the use of ratio in \eqref{eqn:wyttenbach_ratio}.} + Wyttenbach and colleagues~\cite{WyttenbachBaertschi.etal.1978}. The + inclusive emission the experimental figures are lower limits because only + a few decay channels could be studied. The figures in crescent parentheses + are estimates for the total inclusive rate derived from the measured + exclusive channels by the use of ratio in \eqref{eqn:wyttenbach_ratio}.} \label{tab:lifshitzsinger_cal_proton_rate} \end{table} @@ -898,50 +912,63 @@ detectors will be assessed by detailed Monte Carlo study using Geant4. \subsection{Goals and plan of the experiment} \label{sub:goals_of_the_experiment} -Our experimental program is organised in three distinct work packages (WP), +The goal of the experiment is measure protons following nuclear muon capture +on aluminium: +\begin{enumerate} + \item emission rate, + \item and spectrum shape in the lower energy region down to \SI{2.5}{\MeV}, + \item with a precision of about 5\%. +\end{enumerate} +The measured proton spectrum and rate will be used to assess the hit rate on +the tracking drift chamber of the COMET Phase-I. + +The measurement of protons itself is part of the AlCap, where +experimental program is organised in three distinct work packages (WP), directed by different team leaders, given in parentheses. \begin{itemize} -\item[WP1:] (Kammel (Seattle), Kuno(Osaka)) \textbf{Charged -Particle Emission after Muon Capture.}\\ Protons emitted after nuclear muon -capture in the stopping target dominate the single-hit rates in the tracking -chambers for both the Mu2e and COMET Phase-I experiments. We plan to measure -both the total rate and the energy spectrum to a precision of 5\% down to -proton energies of \SI{2.5}{\MeV}. -\item[WP2:] (Lynn(PNNL), Miller(BU)) -\textbf{Gamma and X-ray Emission after Muon Capture.}\\ A Ge detector will -be used to measure X-rays from the muonic atomic cascade, in order to provide -the muon-capture normalization for WP1, and is essential for very thin -stopping targets. It is also the primary method proposed for calibrating the -number of muon stops in the Mu2e and COMET experiments. Two additional -calibration techniques will also be explored; (1) detection of delayed gamma -rays from nuclei activated during nuclear muon capture, and (2) measurement -of the rate of photons produced in radiative muon decay. The first of these -would use a Ge detector and the second a NaI detector. The NaI -calorimeter will measure the rate of high energy photons from radiative muon -capture (RMC), electrons from muon decays in orbit (DIO), and photons from -radiative muon decay (RMD), as potential background sources for the -conversion measurement. As these rates are expected to be extremely low near -the conversion electron energy, only data at energies well below 100 MeV will -be obtained. -\item[WP3:] (Hungerford(UH), Winter(ANL)) \textbf{Neutron -Emission after Muon Capture.}\\ Neutron rates and spectra after capture in -Al and Ti are not well known. In particular, the low energy region below 10 -MeV is important for determining backgrounds in the Mu2e/COMET detectors and - veto counters as well as evaluating the radiation damage to electronic -components. Carefully calibrated liquid scintillation detectors, employing -neutron-gamma discrimination and spectrum unfolding techniques, will measure -these spectra. The measurement will attempt to obtain spectra as low or lower -than 1 MeV up to 10 MeV. \\ + \item[WP1:] (P. Kammel (University of Washington), Y. Kuno(Osaka University)) + \textbf{Charged Particle Emission after Muon Capture.}\\ Protons emitted + after nuclear muon + capture in the stopping target dominate the single-hit rates in the tracking + chambers for both the Mu2e and COMET Phase-I experiments. We plan to measure + both the total rate and the energy spectrum to a precision of 5\% down to + proton energies of \SI{2.5}{\MeV}. + \item[WP2:] (J. Miller(Boston University)) + \textbf{Gamma and X-ray Emission after Muon Capture.}\\ A germanium detector + will be used to measure X-rays from the muonic atomic cascade, in order to + provide + the muon-capture normalisation for WP1, and is essential for very thin + stopping targets. It is also the primary method proposed for calibrating the + number of muon stops in the Mu2e and COMET experiments. Two additional + calibration techniques will also be explored; (1) detection of delayed gamma + rays from nuclei activated during nuclear muon capture, and (2) measurement + of the rate of photons produced in radiative muon decay. The first of these + would use a germanium detector and the second a sodium iodine detector. + The sodium iodine + calorimeter will measure the rate of high energy photons from radiative muon + capture (RMC), electrons from muon decays in orbit (DIO), and photons from + radiative muon decay (RMD), as potential background sources for the + conversion measurement. As these rates are expected to be extremely low near + the conversion electron energy, only data at energies well below 100 MeV will + be obtained. + \item[WP3:] (E. Hungerford (University of Houston), P. Winter(Argonne + National Laboratory)) \textbf{Neutron + Emission after Muon Capture.}\\ Neutron rates and spectra after capture in + Al and Ti are not well known. In particular, the low energy region below 10 + MeV is important for determining backgrounds in the Mu2e/COMET detectors and + veto counters as well as evaluating the radiation damage to electronic + components. Carefully calibrated liquid scintillation detectors, employing + neutron-gamma discrimination and spectrum unfolding techniques, will measure + these spectra. The measurement will attempt to obtain spectra as low or lower + than 1 MeV up to 10 MeV. \\ \end{itemize} -WP1 is the most developed -project in this program with most of the associated apparatus has been built and -optimized. We are ready to start this experiment in 2013, while preparing and -completing test measurements and simulations to undertake WP2 and WP3. +WP1 was the most developed project in this program with most of the associated +apparatus had been built and optimised. Therefore the measurement of proton has +been carried out in November and December 2013, while preparing and completing +test measurements and simulations to undertake WP2 and WP3. -The measurement of proton has been carried out in November and December 2013, -the details are described in following chapters. % subsection goals_of_the_experiment (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % section the_alcap_experiment (end) diff --git a/thesis/chapters/chap5_alcap_setup.tex b/thesis/chapters/chap5_alcap_setup.tex index a5a17ae..828ec29 100644 --- a/thesis/chapters/chap5_alcap_setup.tex +++ b/thesis/chapters/chap5_alcap_setup.tex @@ -18,7 +18,7 @@ provide veto signals for the silicon and germanium detectors. Two liquid scintillators for neutron measurements were also tested in this run. \begin{figure}[btp] \centering - \includegraphics[width=0.65\textwidth]{figs/alcap_setup_detailed} + \includegraphics[width=0.95\textwidth]{figs/alcap_setup_detailed} \caption{AlCap detectors: two silicon packages inside the vacuum vessel, muon beam detectors including plastic scintillators and a wire chamber, germanium detector and veto plastic scintillators.} @@ -30,9 +30,11 @@ Muons in the $\pi$E1 beam line are decay products of pions created as a \SI{590}{\mega\electronvolt} proton beam hits a thick carbon target. The beam line was designed to deliver muons with momenta ranging from \SIrange{10}{500}{\mega\electronvolt\per\cc} and momentum spread from -\SIrange{0.26}{8.0}{\percent}~\cite{Foroughli.1997}. These parameters can be -selected by changing various magnets and slits shown in -\cref{fig:psi_piE1_elements}. +\SIrange{0.26}{8.0}{\percent}~\cite{Foroughli.1997}. The beam parameters can +be tuned by adjusting magnets and slits along the beam line. +%These parameters can be +%selected by changing various magnets and slits +%\cref{fig:psi_piE1_elements}. %(E-target in \cref{fig:psi_exp_hall_all}). %\begin{figure}[p] @@ -44,40 +46,46 @@ selected by changing various magnets and slits shown in %\label{fig:psi_exp_hall_all} %\end{figure} -\begin{figure}[btp] - \centering - \includegraphics[width=0.7\textwidth]{figs/psi_piE1_elements} - \caption{The $\pi$E1 beam line} - \label{fig:psi_piE1_elements} -\end{figure} +%\begin{figure}[btp] + %\centering + %\includegraphics[width=0.7\textwidth]{figs/psi_piE1_elements} + %\caption{The $\pi$E1 beam line} + %\label{fig:psi_piE1_elements} +%\end{figure} One of the main requirements of the AlCap experiment was a low energy muon beam with narrow momentum bite in order to achieve a high fraction of stopping muons in the very thin targets. In this Run 2013, muons from -\SIrange{28}{45}{\mega\electronvolt\per\cc} and momentum spread of 1\% and -3\%, respectively, were used. +\SIrange{28}{45}{\MeV\per\cc} and momentum spread of 1\% and +3\% were used. For part of the experiment the target was replaced with one of the silicon detector packages allowed an accurate momentum and range calibration %(via range-energy relations) of the beam at the target. \Cref{fig:Rates} shows the measured muon rates as a function of momentum for two different momentum bites. -\Cref{fig:Beam} shows an example of the resulting energy spectra. +\Cref{fig:Beam} shows an example of the resulting energy spectra recorded by +our silicon detector. \begin{figure}[btp] \centering - \includegraphics[width=0.6\textwidth]{figs/Rates.png} - \caption{Measured muon rate (kHz) at low momenta. Momentum bite of 3 and 1 \% - FWHM, respectively.} + \includegraphics[width=0.65\textwidth]{figs/Rates.png} + \caption{Measured muon rates at low momenta during the Run 2013. Beam rates + at 1 \% FWHM momentum bite were about 3 times smaller than the rates at + 3 \% FWHM.} \label{fig:Rates} \end{figure} \begin{figure}[btp] \centering - \includegraphics[width=0.9\textwidth]{figs/beam.pdf} + \includegraphics[width=1.00\textwidth]{figs/beam.pdf} \caption{Energy deposition at \SI{36.4}{/c} incident muon beam in an \SI{1500}{\micro\meter}-thick active target. The peak at low energy is due to beam electrons, the peaks at higher energies are due to muons. Momentum - bite of 1 and 3\% FWHM on left and right hand side, respectively.} + bite of 1 and 3\% FWHM on left and right hand side, respectively. The + electron peak are the same in both plots as beam electrons are minimum + ionisation particles and passed though the detector easily. The muon peak + at the 3 \% FWHM momentum bite is notably broader than that at 1 \% FWHM + setting.} \label{fig:Beam} \end{figure} @@ -254,19 +262,25 @@ The germanium detector is a GMX20P4-70-RB-B-PL, n-type, coaxial high purity germanium detector produced by ORTEC. The detector was optimised for low energy gamma and X-rays measurement with an ultra-thin entrance window of 0.5-mm-thick beryllium and -a 0.3-\si{\micro\meter}-thick ion implanted contact (\cref{fig:ge_det_dimensions}). -This detector is equipped with a transistor reset preamplifier which, -according to the producer, enables it to work in an ultra-high rate environment +a 0.3-\si{\micro\meter}-thick ion implanted contact. The germanium crystal is +\SI{52.5}{\mm} in diameter, and \SI{55.3}{\mm} in length. The axial well has +a diameter of \SI{9.9}{\mm} and \SI{47.8}{\mm} deep. +%(\cref{fig:ge_det_dimensions}). + +ORTEC quoted the energy resolution of the detector is \SI{1.90}{\keV} at the +\SI{1.73}{\MeV} gamma line. The detector is equipped with a transistor reset +preamplifier which, according to the producer, enables it to work in an +ultra-high rate environment up to $10^6$ counts\si{\per\second} at \SI{1}{\mega\electronvolt}. -\begin{figure}[btp] - \centering - \includegraphics[width=0.9\textwidth]{figs/ge_det_dimensions} - \caption{Dimensions of the germanium detector} - \label{fig:ge_det_dimensions} -\end{figure} +%\begin{figure}[btp] + %\centering + %\includegraphics[width=0.9\textwidth]{figs/ge_det_dimensions} + %\caption{Dimensions of the germanium detector} + %\label{fig:ge_det_dimensions} +%\end{figure} The detector was installed outside of the vacuum chamber at 32 cm from the -target, seeing the target through a 10-mm-thick aluminium window, behind +target, viewing the target through a 10-mm-thick aluminium window, behind a plastic scintillator counter used to veto electrons. Liquid nitrogen necessary for the operation of the detector had to be refilled every 8 hours. A timer was set up in the data acquisition system to remind this. @@ -837,12 +851,12 @@ algorithm that takes the pulse parameters from the peak of the waveform. In parallel, a pulse finding and template fitting code is being developed because it would provide more accurate pulse information. The first iteration of this code has been completed and is being tested. -\begin{figure}[btp] - \centering - \includegraphics[width=0.85\textwidth]{figs/analysis_scheme} - \caption{Concept of the analysis framework in \rootana{}} - \label{fig:rootana_scheme} -\end{figure} +%\begin{figure}[btp] + %\centering + %\includegraphics[width=0.85\textwidth]{figs/analysis_scheme} + %\caption{Concept of the analysis framework in \rootana{}} + %\label{fig:rootana_scheme} +%\end{figure} After obtaining pulse parameters for individual channel, the pairing up of fast and slow pulses from the same physical detector needs to be done. This @@ -1030,10 +1044,15 @@ shown in \cref{fig:lldq}. \includegraphics[width=0.47\textwidth]{figs/lldq_noise} \includegraphics[width=0.47\textwidth]{figs/lldq_tdiff} \caption{Example trend plots used in the low level data quality checking: - noise level in FWHM (left) and time correlation with muon hits (right). The + noise level in FWHM (left) and time correlation with muon hits (right). + The horizontal axis is run number, the vertical axis is the channel name + (left), or the time difference between hit in the germanium + detector and a hit in upstream counter (right). Colors in both plots + indicate the number of events. In the left plot, the noise level was basically stable in in this data set, except for one - channel. On the right hand side, this sanity check helped find out the - sampling frequency was wrongly applied in the first tranche of the data + channel where there was a sudden jump in a range of runs. On the right hand + side, this sanity check helped find out the sampling frequency was wrongly + applied in the first tranche of the data set.} \label{fig:lldq} \end{figure} diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index 19c9b66..2c4b61e 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -1,13 +1,18 @@ \chapter{Data analysis and results} \label{cha:data_analysis} -This chapter presents initial analysis on subsets of the collected data. +This chapter presents the first analysis on subsets of the collected data for +the aluminium 100-\si{\um}-thick target. The analysis use information from +silicon, germanium, and upstream muon detectors. Pulse parameters were +extracted from waveforms by the simplest method of peak sensing (as mentioned +in \cref{sub:offline_analyser}). Purposes of the analysis include: \begin{itemize} \item testing the analysis chain; \item verification of the experimental method, specifically the normalisation of number of stopped muons, and particle identification using specific energy loss; - \item extracting a preliminary rate of proton emission from aluminium. + \item extracting a preliminary rate and spectrum of proton emission from + aluminium. \end{itemize} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -22,10 +27,8 @@ methods: \item inferred from number of X-rays recorded by the germanium detector. \end{itemize} This analysis was done on a subset of the active target runs -\numrange{2119}{2140} because of the problem of wrong clock frequency found in -the data quality checking shown in \cref{fig:lldq}. The data set contains +\numrange{2119}{2140}, which contains \num{6.43E7} muon events. %\num[fixed-exponent=2, scientific-notation = fixed]{6.4293720E7} muon events. -\num{6.43E7} muon events. \subsection{Number of stopped muons from active target counting} \label{sub:event_selection} @@ -33,40 +36,49 @@ Because of the active target, a stopped muon would cause two coincident hits on the muon counter and the target. The energy of the muon hit on the active target is also well-defined as the narrow-momentum-spread beam was used. The correlation between the energy and timing of all the hits on the active target -is shown in \cref{fig:sir2f_Et_corr}. The most intense spot at zero time +is shown in \cref{fig:sir2f_Et_corr}. + +\begin{figure}[tbp] + \centering + \includegraphics[width=0.85\textwidth]{figs/sir2_sir2f_E_t_corr} + \includegraphics[width=0.85\textwidth]{figs/sir2_sir2f_amp_1us_slices} + \caption{Energy - timing correlation of hits on the active target (top), + and the projections onto the energy axis in 1000-\si{\ns}-long slices + from \SI{1500}{\ns} (bottom). The prompt peak at roughly \SI{5}{\MeV} in + the top plot is muon peak. In the delayed energy spectra, the Michel + electrons dominate at early time, then the beam electrons are more + clearly seen in longer delay.} + \label{fig:sir2f_Et_corr} +\end{figure} + +The prompt hits on the active silicon detector are mainly beam particles: +muons and electrons. The most intense spot at time zero and about \SI{5}{\MeV} energy corresponds to stopped muons in the thick target. The band below \SI{1}{\MeV} is due to electrons, either in the beam or from muon decay in orbits, or emitted during the cascading of muon to the muonic 1S -state. The valley between time zero and 1200~ns shows the minimum distance in -time between two pulses. It is the mentioned limitation of the current pulse +state. The valley between time zero and 1200~ns shows the minimum distance in +time between two pulses. It is the limitation of the current pulse parameter extraction method where no pile up or double pulses is accounted for. -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/sir2_sir2f_E_t_corr} - \caption{Energy - timing correlation of hits on the active target.} - \label{fig:sir2f_Et_corr} -\end{figure} - -The hits on the silicon active target after 1200~ns are mainly secondary +The delayed hits on the active target after 1200~ns are mainly secondary particles from the stopped muons: \begin{itemize} - \item electrons from muon decay in the 1S orbit + \item electrons from muon decay in the 1S orbit, \item products emitted after nuclear muon capture, including: gamma, neutron, - heavy charged particles and recoiled nucleus + heavy charged particles and recoiled nucleus. \end{itemize} It can be seen that there is a faint stripe of muons in the time larger than 1200~ns region, they are scattered muons by other materials without hitting the muon counter. The electrons in the beam caused the constant band below 1 MeV and -$t > 5000$ ns (see \cref{fig:sir2_1us_slices}). -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/sir2_sir2f_amp_1us_slices} - \caption{Energy deposit on the active target in 1000 ns time slices from the - muon hit. The peaks at about 800 keV in large delayed time are from - the beam electrons.} - \label{fig:sir2_1us_slices} -\end{figure} +$t > 5000$ ns (see \cref{fig:sir2f_Et_corr} bottom). +%\begin{figure}[htb] + %\centering + %\includegraphics[width=0.85\textwidth]{figs/sir2_sir2f_amp_1us_slices} + %\caption{Energy deposit on the active target in 1000 ns time slices from the + %muon hit. The peaks at about 800 keV in large delayed time are from + %the beam electrons.} + %\label{fig:sir2_1us_slices} +%\end{figure} From the energy-timing correlation above, the cuts to select stopped muons are: \begin{enumerate} @@ -74,19 +86,20 @@ From the energy-timing correlation above, the cuts to select stopped muons are: and the first hit on the silicon active target is in coincidence with that muon counter hit: \begin{equation} - \lvert t_{\textrm{target}} - t_{\mu\textrm{ counter}}\rvert \le \SI{50}{\ns} + \lvert t_{\textrm{target}} - t_{\mu\textrm{ counter}}\rvert \le + \SI{50}{\ns}\,, \label{eqn:sir2_prompt_cut} \end{equation} - \item the first hit on the target has energy of that of the muons: + \item and the first hit on the target has energy of that of the muons: \begin{equation} - \SI{3.4}{\MeV} \le E_{\textrm{target}} \le \SI{5.6}{\MeV} + \SI{3.4}{\MeV} \le E_{\textrm{target}} \le \SI{5.6}{\MeV}\,. \label{eqn:sir2_muE_cut} \end{equation} \end{enumerate} The two cuts~\eqref{eqn:sir2_prompt_cut} and~\eqref{eqn:sir2_muE_cut} give a number of stopped muons counted by the active target: \begin{equation} - N_{\mu \textrm{ active Si}} = 9.32 \times 10^6 + N_{\mu \textrm{ active Si}} = 9.32 \times 10^6 \pm 3.0\times10^3\,. \label{eqn:n_stopped_si_count} \end{equation} @@ -123,11 +136,19 @@ additional timing cut is applied for the germanium detector hits: \lvert t_{\textrm{Ge}} - t_{\mu\textrm{ counter}} \rvert < \SI{500}{\ns} \label{eqn:sir2_ge_cut} \end{equation} +\begin{figure}[!htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/sir2_xray_22} + \caption{Prompt muonic X-rays spectrum from the active silicon target. The + $(2p-1s)$ X-ray shows up at \SI{400}{\keV}; higher transitions can also + be identified.} + \label{fig:sir2_xray} +\end{figure} The germanium spectrum after three cuts~\eqref{eqn:sir2_prompt_cut},~\eqref{eqn:sir2_muE_cut} and~\eqref{eqn:sir2_ge_cut} is plotted in \cref{fig:sir2_xray}. The $(2p-1s)$ -line clearly showed up at \SI{400}{\keV} with very low background. A peak at +line clearly showed up at \SI{400}{\keV} on a very low background. A peak at \SI{476}{\keV} is identified as the $(3p-1s)$ transition. Higher transitions such as $(4p-1s)$, $(5p-1s)$ and $(6p-1s)$ can also be recognised at \SI{504}{\keV}, \SI{516}{\keV} and \SI{523}{\keV}, respectively. @@ -137,25 +158,24 @@ such as $(4p-1s)$, $(5p-1s)$ and $(6p-1s)$ can also be recognised at %and the calculated efficiency is $(4.549 \pm 0.108)\times 10^{-5}$ -- a 0.15\% %increasing from that of the 400.177~keV line, so no attempt for recalibration %or correction was made. -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/sir2_xray_22} - \caption{Prompt muonic X-rays spectrum from the active silicon target. - } - \label{fig:sir2_xray} -\end{figure} The net area of the $(2p-1s)$ is found to be 2929.7 by fitting a Gaussian -peak on top of a first-order polynomial from \SIrange{395}{405}{\keV}. +peak on top of a linear background from \SIrange{395}{405}{\keV}. Using the same procedure of correcting described in \cref{sub:germanium_detector}, and taking detector acceptance and X-ray intensity into account (see \cref{tab:sir2_xray_corr}), the number of muon stopped is: \begin{equation} - N_{\mu \textrm{ stopped X-ray}} = (9.16 \pm 0.28)\times 10^6, + N_{\mu \textrm{ stopped X-ray}} = (9.16 \pm 0.28)\times 10^6\,, \label{eqn:n_stopped_xray_count} \end{equation} which is consistent with the number of X-rays counted using the active target. + +The uncertainty of the number of muons inferred from the X-ray +has equal contributions from statistical uncertainty in peak +area and systematic uncertainty from efficiency calibration. The relative +uncertainty in number of muons is 3\%, good enough for the normalisation in +this measurement. \begin{table}[btp] \begin{center} \begin{tabular}{@{}llll@{}} @@ -221,10 +241,10 @@ In this analysis, a subset of runs from \numrange{2808}{2873} with the \begin{itemize} \item it was easier to stop and adjust the muon stopping distribution in this thicker target; - \item a thicker target means more stopped muons due to higher muon rate - available at higher momentum and less scattering. + \item a thicker target gives better statistics because of a higher + muon rate available at a higher momentum and less scattering. \end{itemize} -Muons momentum of \SI{30.52}{\MeV\per\cc}, 3\%-FWHM spread (scaling factor of +Muons with momentum of \SI{30.52}{\MeV\per\cc}, 3\%-FWHM spread (scaling factor of 1.09, normalised to \SI{28}{\MeV\per\cc}) were used for this target after a momentum scanning as described in the next subsection. @@ -232,8 +252,8 @@ a momentum scanning as described in the next subsection. \label{sub:momentum_scan_for_the_100_} Before deciding to use the momentum scaling factor of 1.09, we have scanned with momentum scales ranging from 1.04 to 1.12 to maximise the -observed X-rays rate(and hence maximising the rate of stopped muons). The X-ray -spectrum at each momentum point was accumulated in more than 30 minutes to +observed X-rays rate (and maximising the rate of stopped muons). The X-ray +spectrum at each momentum point was accumulated in about 30 minutes to assure a sufficient amount of counts. Details of the scanning runs are listed in \cref{tab:al100_scan}. \begin{table}[htb] @@ -259,44 +279,48 @@ in \cref{tab:al100_scan}. The on-site quick analysis suggested the 1.09 scaling factor was the optimal value so it was chosen for all the runs on this aluminium target. But the offline analysis later showed that the actual optimal factor was 1.08. -There were two reasons for the mistake: +There were two reasons for the discrepancy: \begin{enumerate} \item the X-ray rates were normalised to run length, which is biased - since there are more muons available at higher momentum; + since there are more muons available at higher momenta; \item the $(2p-1s)$ peaks of aluminium at \SI{346.828}{\keV} were not fitted properly. The peak is interfered by a background peak at \SI{351}{\keV} from $^{214}$Pb, but the X-ray peak area was obtained simply by subtracting an automatically estimated background. \end{enumerate} In the offline analysis, the X-ray peak and the background peak are fitted by -two Gaussian peaks on top of a first-order polynomial background. The X-ray peak +two Gaussian peaks on top of a linear background. The X-ray peak area is then normalised to the number of muons hitting the upstream detector (\cref{fig:al100_xray_fit}). \begin{figure}[htb] \centering - \includegraphics[width=0.47\textwidth]{figs/al100_xray_fit} - \includegraphics[width=0.47\textwidth]{figs/al100_xray_musc} - \caption{Fitting of the $(2p-1s)$ muonic X-ray of aluminium and the background - peak at \SI{351}{\keV} (left). The number of muons is integral of the - upstream scintillator spectrum (right) from \numrange{400}{2000} ADC - channels.} + \includegraphics[width=0.50\textwidth]{figs/al100_xray_fit} + \includegraphics[width=0.50\textwidth]{figs/al100_xray_musc} + \caption{Fitting of the $(2p-1s)$ muonic X-ray of aluminium (red) and the + interfered peak at \SI{351}{\keV} (brown) with a linear background (left). + The number of muons is integral of the upstream scintillator spectrum + (right) from \numrange{400}{2000} ADC channels.} \label{fig:al100_xray_fit} \end{figure} + The ratio between the number of X-rays and the number of muons as a function of momentum scaling factor is plotted on \cref{fig:al100_scan_rate}. The trend showed that muons penetrated deeper as the momentum increased, reaching the optimal value at the scale of 1.08, then decreased as punch through happened -more often from 1.09. The distributions of stopped muons are illustrated by -MC results on the right hand side of \cref{fig:al100_scan_rate}. With the 1.09 -scale beam, the muons stopped \SI{28}{\um} off-centred to the right silicon arm. -\begin{figure}[htb] +more often from scales of 1.09 and above. The distributions of stopped muons +are illustrated by MC results on the bottom plot in +\cref{fig:al100_scan_rate}. At the 1.09 +scale beam, the muons stopped \SI{18}{\um} off-centred to the right silicon +arm, the standard deviation of the depth distribution is \SI{29}{\um}. +\begin{figure}[!htb] \centering - \includegraphics[width=0.47\textwidth]{figs/al100_scan_rate} - \includegraphics[width=0.47\textwidth]{figs/al100_mu_stop_mc} + \includegraphics[width=0.77\textwidth]{figs/al100_scan_rate} + \includegraphics[width=0.77\textwidth]{figs/al100_mu_stop_mc} \caption{Number of X-rays per incoming muon as a function of momentum - scaling factor (left); and muon stopping distributions from MC simulation - (right). The depth of muons is measured normal to surface of the target - facing the muon beam.} + scaling factor (top); and muon stopping distributions with scaling factors + from 1.04 to 1.12 obtained by MC simulation + (bottom). The depth of muon stopping positions are measured normal to + the surface of the target facing the muon beam.} \label{fig:al100_scan_rate} \end{figure} @@ -307,24 +331,35 @@ are re-organised into muon events: central muons; and all hits within \SI{\pm 10}{\us} from the central muons. The dataset from runs \numrange{2808}{2873} contains \num{1.17E+9} of such muon events. +\subsubsection{Particle banding identification} +\label{ssub:particle_banding_identification} + Selection of proton (and other heavy charged particles) events starts from searching for muon event that has at least one hit on thick silicon. If there is a thin silicon hit within a coincidence window of $\pm 0.5$~\si{\us}\ around the thick silicon hit, the two hits are considered to belong to one particle. -The specific energy loss spectra recorded by the two silicon arms are plotted -on \cref{fig:al100_dedx}. -\begin{figure}[htb] +The thresholds for energy deposited in all silicon channels, except the thin +silicon on the left arm, are set at \SI{100}{\keV} in this analysis. The +threshold on the left $\Delta E$ counter was higher, at roughly +\SI{400}{\keV}, due to higher noise in that channel and it was decided at the +run time to rise its threshold to reduce the triggering rate. +The specific energy loss as a function of total energy of the charged +particles are plotted on \cref{fig:al100_dedx}. +\begin{figure}[p] \centering - \includegraphics[width=0.85\textwidth]{figs/al100_dedx} + \includegraphics[width=0.85\textwidth]{figs/al100_EdE_left} + \includegraphics[width=0.85\textwidth]{figs/al100_EdE_right} \caption{Energy loss in thin silicon detectors as a function of total energy - recorded by both thin and thick detectors.} + recorded by both thin and thick detectors on the left arm (top) and the + right arm (bottom).} \label{fig:al100_dedx} \end{figure} -With the aid from MC study (\cref{fig:pid_sim}), the banding on +With the aid from MC simulation (\cref{fig:pid_sim}), the banding on \cref{fig:al100_dedx} can be identified as follows: \begin{itemize} - \item the densest spot at the lower left conner belonged to electron hits; - \item the small blurry cloud just above the electron region was muon hits; + \item the spot at the lower left conner belonged to electron hits; + \item the scattered muons formed the small blurry cloud just above the + electron region; \item the most intense band was due to proton hits; \item the less intense, upper band caused by deuteron hits; \item the highest band corresponded to alpha hits; @@ -332,36 +367,186 @@ With the aid from MC study (\cref{fig:pid_sim}), the banding on hits, which is consistent with a relatively low probability of emission of tritons. \end{itemize} +\begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/al100_dedx_overlay} + \caption{Identifying of charged particles banding: the dots are measured + points, the histograms are expected bands of protons (red), deuterons + (green) and tritons (blue), respectively. The MC bands are calculated + for a pair of 58-\si{\um}-thick and 1535-\si{\um}-thick silicon + detectors. The error bars on MC bands show the standard deviation of + $\Delta E$ in E respective bins. + } + \label{fig:dummylabel} +\end{figure} -The band of protons is then extracted by cut on likelihood probability -calculated as: +It is not clearly seen in the $\Delta E-E$ plots because of the rather high +thresholds on $\Delta E$, but protons with higher energy would punch through +both silicon detectors. Those events have low $\Delta E$ and $E$, making the +proton bands to go backward to the origin of the $\Delta E-E$ plots. For the +configuration of 58-\si{\um} thin, and 1535-\si{\um} thick detectors, the +effect shows up for protons with energy larger than \SI{16}{\MeV}. The +returning part of the proton band would make the cut described in +the next subsection to include protons with higher energy into lower energy +region. The effect of punch through protons could be eliminate using the veto +plastic scintillators at the back of each silicon arm. But in this initial +analysis, the veto information is not used, therefore the upper limit of +proton energy is set at \SI{8}{\MeV} where there is clear separation between +the protons at lower and higher energies with the same measured total energy +deposition $E$. + +\subsubsection{Proton-like probability cut} +\label{ssub:proton_like_probability_cut} +Since protons of interested are at low kinetic energy, their $\Delta E$ +distributions do not have long tails as that of the Landau distribution. +For a given $E$, the distribution of $\Delta E$ is more like a Gaussian, and +with slightly deformed high energy tail (see \cref{fig:dE_distribution}). + +\begin{figure}[htb] + \centering + \includegraphics[width=0.75\textwidth]{figs/dE_distribution} + \caption{Distributions of $\Delta E$ of protons in a 58-\si{\um}-thick + silicon detector for given $E$ in various energy ranges.} + \label{fig:dE_distribution} +\end{figure} + +%In order to select protons, a proton likelihood probability is defined as: +%The band of protons is therefore by cut on likelihood probability +%calculated as: +For a measured event, a proton likelihood probability is defined as: \begin{equation} P_{i} = \dfrac{1}{\sqrt{2\pi}\sigma_{\Delta E}} \exp{\left[\dfrac{(\Delta E_{meas.} - \Delta E_i)^2} {2\sigma^2_{\Delta - E}}\right]} + E}}\right]}\,, \end{equation} -where $\Delta E_{\textrm{meas.}}$ is energy deposition measured by the thin -silicon detector by a certain proton at energy $E_i$, $\Delta E_i$ and -$\sigma_{\Delta E}$ are the expected and standard deviation of the energy loss -caused by the proton calculated by MC study. A threshold is set at \num{1E-4} to -extract protons, the resulted band of protons is shown in -(\cref{fig:al100_protons}). +where $\Delta E_{\textrm{meas.}}$ and $E_i$ are measured energy deposition in +thin silicon detector and in both detectors, respectively; $\Delta E_i$ and +$\sigma_{\Delta E}$ are the expected value and standard deviation of the energy +loss in the thin detector of protons with energy $E$, calculated by the +MC simulation. A measured event with higher $P_i$ is more likely to be +a proton event. + +The lower threshold of proton-like probability, the more protons will be +selected, but also more contamination from other charged particles would be +classified as protons. The number of protons on the left and right arms at +different cuts on $P_i$ are listed in \cref{tab:nprotons_vs_pcut}. The proton +yields are integrated in the energy range from \SIrange{2.2}{8}{\MeV}. The +lower limit comes from the requirement of having at least one hit on the thick +counter. The upper limit is to avoid the inclusion of punch through particles +as explained in the previous session. + +The cut efficiency depends on actual shape of the proton spectrum, other +charged particles spectra, relative ratio between the yields of different +particle species. The fraction of protons missed out, and the fraction of +contamination from other charged particles at different probability +thresholds, with two different assumptions on spectrum shape: flat distribution +and Sobottka and Wills silicon shape (see \eqref{eqn:EH_pdf}), +are listed in the four last columns of \cref{tab:nprotons_vs_pcut}. The +relative ratio of proton:deuteron:triton:alpha:muon is assumed to be +5:2:1:2:2. The probability threshold is therefore chosen to be \num{1.0E-4} in +in order to have both relatively low missing and contamination fractions +compare to the statistical uncertainty of the measurement. The resulted band of +protons is shown in (\cref{fig:al100_protons}). + +\begin{table}[htb] + \begin{center} + \begin{tabular}{c c c c S S S S} + \toprule + \textbf{$P_i$} & \textbf{Equiv.} & \multirow{2}{*}{\textbf{Left}} & + \multirow{2}{*}{\textbf{Right}} & {\textbf{Miss.}} & \textbf{Contam.} + & {\textbf{Miss.}} & \textbf{Contam.}\\ + + \textbf{threshold} & \textbf{$\sigma$} & & + &{\textbf{flat}} & {\textbf{flat}} + &{\textbf{expo.}} & {\textbf{expo.}}\\ + \midrule + \num{4.5E-2} & 2 & 1720 & 2214 & 1.9 \%& 0.03 \%&6.1 \%& 0.06 \%\\ + \num{2.7E-3} & 3 & 1801 & 2340 & 0.7 \%& 0.05 \%&2.8 \%& 0.1 \%\\ + \num{1.0E-4} & 3.89 & 1822 & 2373 & 0.5 \%& 0.1 \%&1.2 \%& 0.3 \%\\ + \num{5.7E-7} & 5 & 1867 & 2421 & 0.4 \%& 0.7 \%&0.7 \%& 0.9 \%\\ + \bottomrule + \end{tabular} + \end{center} + \caption{Proton yields in energy range from \SIrange{2.2}{8}{\MeV} on the two + silicon arms with different thresholds on proton-like probability $P_i$, + and the MC calculated missing fractions and contamination levels with two + different assumptions on spectrum shape: flatly distributed, and + exponential decay spectrum (see \eqref{eqn:EH_pdf}).} + \label{tab:nprotons_vs_pcut} +\end{table} + \begin{figure}[htb] \centering \includegraphics[width=0.47\textwidth]{figs/al100_protons} \includegraphics[width=0.47\textwidth]{figs/al100_protons_px_r} - \caption{Protons (green) selected using the likelihood probability cut - (left). The proton spectrum (right) is obtained by projecting the proton - band onto the total energy axis.} + \caption{Protons (green) selected using the likelihood probability cut of + \num{1.0E-4} (left). The proton spectrum (right) is obtained by projecting + the proton band onto the total energy axis.} \label{fig:al100_protons} \end{figure} -The cut efficiency in the energy range from \SIrange{2}{12}{\MeV} is estimated -by MC study. The fraction of protons that do not satisfy the probability cut -is 0.5\%. The number of other charged particles that are misidentified as -protons depends on the ratios between those species and protons. Assuming -a proton:deuteron:triton:alpha:muon ratio of 5:2:1:2:2, the number of -misidentified hits is 0.1\% of the number of protons. +\subsubsection{Possible backgrounds} +\label{ssub:possible_backgrounds} + +There are several sources of potential backgrounds in this proton measurement: +\begin{enumerate} + \item Protons emitted after capture of scattered muons in the lead + shield: the incoming muons could be scattered to other materials + surrounding the target, emitting protons to the silicon detectors. In + order to avoid complication of estimating this background, we used lead + sheets to collimate and shield around the target and detectors. If + a scattered muon is captured by the lead shielding, the proton from lead + would be emitted shortly after the muon hit because of the short average + lifetime of muons in lead (\SI{78.4}{\ns}~\cite{Measday.2001}). In + comparison, average lifetime of muons in aluminium is + \SI{864}{\ns}~\cite{Measday.2001}, therefore a simple cut in timing could + eliminate background of this kind.\\ + The timing of events classified as protons are plotted in + \cref{fig:al100_proton_timing}. The spectra show no significant fast + decaying component, which should show up if the background from lead + shielding were sizeable. A fit of an exponential function on top of a flat + background gives the average lifetimes of muons as: + \begin{align} + \tau_{\textrm{left}} &= \SI{870 \pm 25}{\ns} \,,\\ + \tau_{\textrm{right}} &= \SI{868 \pm 21}{\ns} \,. + \end{align} + + \begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/al100_proton_timing} + \caption{Timing of protons relative to muon hit. The spectra show the + characteristic one-component decay shape.} + \label{fig:al100_proton_timing} + \end{figure} + The consistency between fitted lifetimes and the reference value of average + lifetime of muons in aluminium at \SI{864\pm 2}{\ns} suggests the background + from the lead shielding is negligible. This smallness can be explained as + a combination of the two facts: (i) only + a minority fraction of muons punched through the target and reached the + downstream lead shield as illustrated in + \cref{fig:al100_scan_rate}; and (ii) the probability of emitting protons from + lead is very low compare to that of aluminium, about 0.4\% per + capture (see \cref{tab:lifshitzsinger_cal_proton_rate}). + + \item The protons emitted after scattered muons stopped at the surface of + the thin silicon detectors: these protons could mimic the signal if they + appear within \SI{1}{\us} around the time muon hit the upstream counter. + The $\Delta E$ and $E$ in this case would be sum of energy of a muon and + energy of the resulted proton. The average energy of scattered muons can be + seen in \cref{fig:al100_dedx} to be about \SI{1.4}{\MeV}. The measured + $\Delta E$ and $E$ then would be shifted by \SI{1.4}{\MeV}, makes the + measured data point move far away from the expected proton band. Therefore + this kind of background should be small with the current probability cut. + + \item The random background: this kind of background can be + examined by the same timing spectrum in + \cref{fig:al100_proton_timing}. The random events show up at negative time + difference and large delay time regions and give a negligible contribution + to the total number of protons. +\end{enumerate} + +It is concluded from above arguments that the backgrounds of this proton +measurement is negligibly small. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Proton emission rate from aluminium} \label{sec:proton_emission_rate_from_aluminium} @@ -376,8 +561,8 @@ of protons is normalised to the number of nuclear muon captures. The numbers of protons in the energy range from \SIrange{2.2}{8.5}{\MeV} after applying the probability cut are: \begin{align} - N_{\textrm{p meas. left}} = 1822\\% \pm 42.7\\ - N_{\textrm{p meas. right}} = 2373% \pm 48.7 + N_{\textrm{p meas. left}} = 1822 \pm 42.7 \,,\\ + N_{\textrm{p meas. right}} = 2373 \pm 48.7 \,. \end{align} The right arm received significantly more protons than the left arm did, which is expected as in \cref{sub:momentum_scan_for_the_100_} where it is shown that @@ -405,15 +590,18 @@ the parameters of the initial protons are: the upstream face of the target; \item energy: flatly distributed from \SIrange{1.5}{15}{\MeV}. \end{itemize} -The resulting response matrices for the two arms are presented in -\cref{fig:al100_resp_matrices}. These are then used as MC truth to train and -test the unfolding code. The code uses an existing ROOT package -called RooUnfold~\cite{Adye.2011} where the iterative Bayesian unfolding -method is implemented. +The calculated response matrices for the two arms are presented in +\cref{fig:al100_resp_matrices}. The different path lengths inside the target +to the two silicon arms causes the difference in the two matrices. The +response matrices are then used as MC truth to train and test the unfolding +code. The code uses an existing ROOT package called RooUnfold~\cite{Adye.2011} +where the iterative Bayesian unfolding method is implemented. \begin{figure}[htb] \centering - \includegraphics[width=0.85\textwidth]{./figs/al100_resp} - \caption{Response functions for the two silicon arms.} + \includegraphics[width=0.99\textwidth]{./figs/al100_resp} + \caption{Response functions for the two silicon arms, showing the relation + between protons energy at birth and as detected by the silicon detector + arms.} \label{fig:al100_resp_matrices} \end{figure} %After training, the unfolding code is applied on the measured spectra from the @@ -425,15 +613,18 @@ method is implemented. %which is \SI{4.1}{\MeV} for protons emitted from $^{27}$Mg. The unfolded spectra using the two observed spectra at the two arms as input are shown in \cref{fig:al100_unfold}. The two unfolded spectra generally agree -with each other, except for a few first and last bins. The discrepancy and -large uncertainties at the low energy region are because of only a small -number of protons with those energies could reach the detectors. The jump on -the right arm at around \SI{9}{\MeV} can be explained as the punch-through -protons were counted as the proton veto counters were not used in this -analysis. -\begin{figure}[htb] +with each other, except for a few first and last bins. +In the lower energy region, there is a small probability for such protons to +escape and reach the detectors, therefore the unfolding is generally unstable +and the uncertainties are large. +At the higher end, the jump on the right arm at around \SI{9}{\MeV} can be +explained as the punch-through protons were counted as the proton veto counters +were not used in this analysis. The lower threshold on the thin silicon +detector at the right arm compared with that at the left arm makes this +misidentification worse. +\begin{figure}[!htb] \centering - \includegraphics[width=0.85\textwidth]{figs/al100_unfolded_lr} + \includegraphics[width=0.80\textwidth]{figs/al100_unfolded_lr} \caption{Unfolded proton spectra from the 100-\si{\um} aluminium target.} \label{fig:al100_unfold} \end{figure} @@ -445,27 +636,37 @@ analysis. %\item comparison between the two arms; %\item and unfolding of a MC-generated spectrum. %\end{itemize} -The stability of the unfolding code is tested by varying the lower cut-off -energy of the input spectrum. \cref{fig:al100_cutoff_study} show that the -shapes of the unfolded spectra are stable. The lower cut-off energy of the -output increases as that of the input increases, and the shape is generally -unchanged after a few bins. -\begin{figure}[htb] +The stability of the unfolding code is tested by varying the lower and upper +cut-off energies of the input spectrum. Plots in \cref{fig:al100_cutoff_study} +show that the shapes of the unfolded spectra are stable after a few first or +last bins. +%The +%lower cut-off energy of the +%output increases as that of the input increases, and the shape is generally +%unchanged after a few bins. +\begin{figure}[!htb] \centering \includegraphics[width=0.85\textwidth]{figs/al100_cutoff_study} - \caption{Unfolded spectra with different cut-off energies.} + \includegraphics[width=0.85\textwidth]{figs/al100_up_cut_off_reco} + \caption{Unfolded spectra with different lower (top) and upper (bottom) + cut-off energies.} \label{fig:al100_cutoff_study} \end{figure} + The proton yields calculated from observed spectra in two arms are compared in \cref{fig:al100_integral_comparison} where the upper limit of the integrals -is fixed at \SI{8}{\MeV}, and the lower limit is varied in \SI{400}{\keV} step. -The difference is large at cut-off energies less than \SI{4}{\MeV} due to -large uncertainties at the first bins. Above \SI{4}{\MeV}, the two arms show -consistent numbers of protons. +is fixed at \SI{8}{\MeV}, and the lower limit is varied in \SI{400}{\keV} +step. The upper limit was chosen to avoid the effects of punched through +protons. The difference is large at cut-off energies less than \SI{4}{\MeV} +due to large uncertainties at the first bins. Above \SI{4}{\MeV}, the two arms +show consistent numbers of protons. \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/al100_integral_comparison} - \caption{Proton yields calculated from two arms.} + \caption{Proton yields calculated from two arms. The upper limit of + integrations is fixed at \SI{8}{\MeV}, the horizontal axis is the lower + limit of the integrations. The proton yields on the two arm agree well + with each other from above \SI{4}{\MeV}.} \label{fig:al100_integral_comparison} \end{figure} The yields of protons from \SIrange{4}{8}{\MeV} are: @@ -490,13 +691,13 @@ The number of emitted protons is taken as average of the two yields: %The X-ray spectrum on the germanium detector is shown on %\cref{fig:al100_ge_spec}. -Fitting the double peaks on top of a first-order -polynomial gives the X-ray peak area of $5903.5 \pm 109.2$. With the same +Fitting the double peaks on top of a linear background +gives the X-ray peak area of $5903.5 \pm 109.2$. With the same procedure as in the case of the active target, the number stopped muons and the number of nuclear captures are: \begin{align} - N_{\mu \textrm{ stopped}} &= (1.57 \pm 0.05)\times 10^7\\ - N_{\mu \textrm{ nucl. cap.}} &= (9.57\pm 0.31)\times 10^6 + N_{\mu \textrm{ stopped}} &= (1.57 \pm 0.05)\times 10^7\,,\\ + N_{\mu \textrm{ nucl. cap.}} &= (9.57\pm 0.31)\times 10^6\,. \end{align} \subsection{Proton emission rate} @@ -504,7 +705,7 @@ the number of nuclear captures are: The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore: \begin{equation} R_{\textrm{p}} = \frac{169.3\times 10^3}{9.57\times 10^6} = 1.7\times - 10^{-2} + 10^{-2}\,. \label{eq:proton_rate_al} \end{equation} @@ -514,9 +715,9 @@ with the same parameterisation as in \eqref{eqn:EH_pdf}. The falling edge. The falling edge has only one decay component and is suitable to describe the proton spectrum with the equilibrium emission only assumption. The pre-equilibrium emission contribution should be small for low-$Z$ material, -for aluminium the contribution of this component is 2.2\% according to -Lifshitz and Singer~\cite{LifshitzSinger.1980}. - +for aluminium the contribution of this component is 2.2\% of total number of +protons according to Lifshitz and Singer~\cite{LifshitzSinger.1980}. +%%TODO: draw the function and integral The fitted results are shown in \cref{fig:al100_parameterisation} and \cref{tab:al100_fit_pars}. The average spectrum is obtained by taking the average of the two unfolded @@ -526,10 +727,16 @@ with each other within their errors. Using the fitted parameters of the average spectrum, the integration in range from \SIrange{4}{8}{\MeV} is 51\% of the total number of protons. The total proton emission rate is therefore estimated to be $3.5\times 10^{-2}$. -\begin{figure}[htb] +\begin{figure}[!p] \centering \includegraphics[width=0.85\textwidth]{figs/al100_parameterisation} - \caption{Fitting of the unfolded spectra.} + \includegraphics[width=0.85\textwidth]{figs/al100_fit_avgspec} + \includegraphics[width=0.85\textwidth]{figs/al100_fitted_func_integral} + \caption{Fitting of the unfolded spectra on the left and right arms (top), + and on the average spectrum (middle). The bottom plot shows the fitted + function of the average spectrum in the energy range from + \SIrange{1}{50}{\MeV}. The proton yield in the region from + \SIrange{4}{8}{\MeV} (shaded) is 51\% of the whole spectral integral.} \label{fig:al100_parameterisation} \end{figure} @@ -587,9 +794,13 @@ The last item is studied by MC method using the parameterisation in \centering \includegraphics[width=0.48\textwidth]{figs/al100_MCvsUnfold} \includegraphics[width=0.48\textwidth]{figs/al100_unfold_truth_ratio} - \caption{Comparison between an unfolded spectrum and MC truth: spectra - (left), and yields (right). The ratio is defined as $\textrm{(Unfold - MC - truth)/(MC truth)}$} + \caption{Comparison between an unfolded spectrum and MC truth. On the left + hand side, the solid, red line is MC truth, the blue histogram is the + unfoldede spectrum. The ratio between the two yields is compared in the + right hand side plot with the upper end of integration is fixed at + \SI{8}{\MeV}, and a moving lower end of integration. The discrepancy + is genenerally smaller than 5\% if the lower end energy is smaller than + \SI{6}{\MeV}.} \label{fig:al100_MCvsUnfold} \end{figure} \Cref{fig:al100_MCvsUnfold} shows that the yield obtained after unfolding is @@ -608,7 +819,7 @@ presented in \cref{tab:al100_uncertainties_all}. Number of muons & 3.2\% \\ Statistical from measured spectra & 1.1\% \\ Systematic from unfolding & 5.0\% \\ - Systematic from PID & \textless0.5\% \\ + Systematic from PID & \textless1.0\% \\ \midrule Total & 6.1\%\\ \bottomrule @@ -649,13 +860,7 @@ validated: The proton emission spectrum in \cref{sub:proton_emission_rate} peaks around \SI{3.7}{\MeV} which is a little below the Coulomb barrier for proton of \SI{3.9}{\MeV} calculated using \eqref{eqn:classical_coulomb_barrier}. The -spectrum has a decay constant of \SI{2.6}{\MeV} in higher energy region, -makes the emission probability drop more quickly than silicon charged -particles spectrum of Sobottka and Wills~\cite{SobottkaWills.1968} where the -decay constant was \SI{4.6}{\MeV}. This can be explained as the silicon -spectrum includes other heavier particles which have higher Coulomb barriers, -hence contribute more in the higher energy bins, effectively reduces the decay -rate. +spectrum has a decay constant of \SI{2.6}{\MeV} in higher energy region. The partial emission rate measured in the energy range from \SIrange{4}{8}{\MeV} is: @@ -717,4 +922,16 @@ nucleus and less stable than that from aluminium, $^{27}$Mg. The proton separation energy for $^{28}$Al is \SI{9.6}{\MeV}, which is significantly lower than that of $^{27}$Mg at \SI{15.0}{\MeV}~\cite{AudiWapstra.etal.2003}. +The proton spectrum from aluminium is softer than silicon charged +particles spectrum of Sobottka and Wills~\cite{SobottkaWills.1968} where the +decay constant was \SI{4.6}{\MeV}. Two possible reasons can explain this +difference in shape: +\begin{enumerate} + \item The higher proton separation energy of $^{27}$Mg gives less + phase space for protons at higher energies than that in the case of + $^{28}$Al if the excitation energies of the two compound nuclei are similar. + \item The silicon spectrum includes other heavier + particles which have higher Coulomb barriers, hence contribute more in the + higher energy bins, effectively reduces the decay rate. +\end{enumerate} diff --git a/thesis/chapters/chap7_results.tex b/thesis/chapters/chap7_results.tex index cf4fa77..5125cc1 100644 --- a/thesis/chapters/chap7_results.tex +++ b/thesis/chapters/chap7_results.tex @@ -1,12 +1,11 @@ -\chapter{Discussions on the impact to the COMET Phase-I} +\chapter{Impact to the COMET Phase-I} \label{cha:discussions_on_the_impact_to_the_comet_phase_i} The measured proton emission rate of 3.5\% is about 5 times smaller than the figure using to make the baseline design of the CDC in COMET -Phase-I. The spectrum shape -peaks around \SI{4}{\MeV} rather than at \SI{2.5}{\MeV}, and decays more -quickly in compared with the silicon spectrum(\cref{fig:sobottka_spec}). -Therefore CDC hit rate due to proton should be smaller than the current -estimation. +Phase-I. The spectrum shape is softer than that of silicon, +peaks around \SI{4}{\MeV} rather than at \SI{2.5}{\MeV} +(\cref{fig:sobottka_spec}). Therefore CDC hit rate due to proton should be +smaller than the current estimation. The CDC proton hit rate is calculated by a toy MC study. The dimensions of the geometry shown in \cref{fig:cdc_toy_mc} are from \cref{ssub:CDC_configuration}. @@ -54,54 +53,31 @@ A muon stopping rate of \SI{1.3E9}{\Hz} is assumed as in the COMET Phase I's TDR. The number of proton emitted is then $\num{1.3E9} \times 0.609 \times 0.035 = \SI{2.8E7}{\Hz}$. The hit rates on a single cell in the inner most layer due to these protons with -different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. +different absorber configurations are listed in +\cref{tab:proton_cdc_hitrate_comp}. + \begin{table}[htb] \begin{center} - \begin{tabular}{S S S S S S} + \begin{tabular}{S S S S S} \toprule {\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& - {\textbf{Proton}} & {\textbf{Momentum}} & {\textbf{Integrated charge}}\\ + {\textbf{Proton hit rate}} & {\textbf{Proton hit rate}}\\ {\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& - {\textbf{hit rate}} &{\textbf{spread $\Delta p$}} &{\textbf{300 days}}\\ - {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})} - & {(\si{\keV\per\cc)}} &{(mC/cm)}\\ + {\textbf{Phase-I TDR}} & {\textbf{New estimation}}\\ + {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}& {(\si{\Hz})}\\ \midrule - 1 &0.5&1.5 & 2 & 195 & 25\\ - 0.5 &0.5&1.0 & 126 & 167 & 60\\ - 0 &0.5&0.5 & 1436 & 133 & 160\\ - %0 &0.3&0.3 & 8281 & {-} & {-}\\ - %0 &0.1&0.1 & 15011& {-} & {-}\\ + 1 &0.5&1.5 & 4E+3 & 2 \\ + 0.5 &0.5&1.0 & 11E+3& 126 \\ + 0 &0.5&0.5 & 30E+3& 1436 \\ \bottomrule \end{tabular} \end{center} - \caption{CDC proton hit rates at different configuration of proton absorber - and inner wall. The momentum spreads for \SI{0.5}{\mm} thick inner wall are - taken from \cref{tab:comet_absorber_impact}.} - \label{tab:proton_cdc_hitrate} + \caption{CDC proton hit rates in this study in comparison with the expected + rates in COMET Phase-I's Technical Design Report~\cite{COMET.2014} at + different configurations of proton absorber and inner wall.} + \label{tab:proton_cdc_hitrate_comp} \end{table} -%\begin{table}[htb] - %\begin{center} - %\begin{tabular}{S S S S S} - %\toprule - %{\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& - %{\textbf{Proton hit rate}} & {\textbf{Proton hit rate}}\\ - %{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& - %{\textbf{Phase-I TDR}} & {\textbf{New estimation}}\\ - %{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}& {(\si{\Hz})}\\ - %\midrule - %1 &0.5&1.5 & 4E+3 & 2 \\ - %0.5 &0.5&1.0 & 11E+3& 126 \\ - %0 &0.5&0.5 & 30E+3& 1436 \\ - %\bottomrule - %\end{tabular} - %\end{center} - %\caption{CDC proton hit rates at different configuration of proton absorber - %and inner wall. The momentum spreads for \SI{0.5}{\mm} thick inner wall are - %taken from \cref{tab:comet_absorber_impact}.} - %\label{tab:proton_cdc_hitrate} -%\end{table} - %\begin{table}[htb] %\begin{center} %\begin{tabular}{S S S S S S} @@ -121,19 +97,57 @@ different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. %taken from \cref{tab:comet_absorber_impact}.} %\end{table} At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz}, -much smaller than the current estimation at \SI{34}{\kHz}. Even without the -absorber, proton hit rate remains low at \SI{1.4}{\kHz}. +much smaller than the current estimation at \SI{11}{\kHz}. Even without the +absorber, proton hit rate remains lower than that level at \SI{1.4}{\kHz}. +Therefore the absorber is not necessary as far as the hit rate is concerned. %Therefore a proton %absorber is not needed for the COMET Phase I's CDC. If the proton absorber is not used, the momentum spread of the signal electron -reduces from \SI{167}{\keV} to \SI{131}{\keV}. In case a lower momentum spread -is desired, it is possible to reduce the thickness of the inner wall. The last -two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at -\SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at -manageable levels. However, reducing the wall thickness would be governed by -other requirements such as mechanical structure and gas-tightness. +reduces from \SI{167}{\keV\per\cc} to \SI{131}{\keV\per\cc} (\cref{tab:proton_cdc_hitrate}). +This is a small improvement since the momentum resolution is dominated by +intrinsic spread of \SI{197}{\keV\per\cc} due to multiple scattering in gas +and wires. +The last column of \cref{tab:proton_cdc_hitrate} shows the integrated charge +per unit length of a wire. The TDR deems an integrated charge level of +\SI{200}{\milli\coulomb\per\cm} safe. So even with the pessimistic estimation using +silicon rate and spectrum and without the proton absorber, the integrated +charge level in the CDC is still below the requirement. Therefore removing the +absorber will not worsen the ageing process of the wires. +\begin{table}[htb] + \begin{center} + \begin{tabular}{S S S S S} + \toprule + {\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& + {\textbf{Momentum}} & {\textbf{Integrated charge}}\\ + {\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& + {\textbf{spread $\Delta p$}} &{\textbf{300 days}}\\ + {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} + & {(\si{\keV\per\cc)}} &{(mC/cm)}\\ + \midrule + 1 &0.5&1.5 & 195 & 25\\ + 0.5 &0.5&1.0 & 167 & 60\\ + 0 &0.5&0.5 & 133 & 160\\ + %0 &0.3&0.3 & 8281 & {-} & {-}\\ + %0 &0.1&0.1 & 15011& {-} & {-}\\ + \bottomrule + \end{tabular} + \end{center} + \caption{Momentum spreads due to the inner wall and absorber, and integrated + charge per unit length of wire as calculated in the COMET Phase-I's TDR. + The momentum spreads were calculated for signal electrons at + \SI{104.96}{\MeV\per\cc}. The integrated charge is estimated assuming 300 + days of operation.} + \label{tab:proton_cdc_hitrate} +\end{table} + +%In case a lower momentum spread is desired, it is possible to reduce the +%thickness of the inner wall. The last +%two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at +%\SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at +%manageable levels. However, reducing the wall thickness would be governed by +%other requirements such as mechanical structure and gas-tightness. In summary, the toy MC study with the preliminary proton rate and spectrum shows that a proton absorber is not needed. It confirms the known fact that the estimation used in COMET Phase-I is conservative, and provides a solid diff --git a/thesis/chapters/chap8_conclusions.tex b/thesis/chapters/chap8_conclusions.tex index b61f6cc..f84b772 100644 --- a/thesis/chapters/chap8_conclusions.tex +++ b/thesis/chapters/chap8_conclusions.tex @@ -22,20 +22,26 @@ was made. The main results are: \item obtaining preliminary results on proton emission rate and spectrum: the proton spectrum has a peak at \SI{3.7}{\MeV}, then reduces exponentially with a decay constant of \SI{2.6}{\MeV}. The partial emission rate in the - energy range from \SIrange{4}{8}{\MeV} is $(1.7 \pm 0.1)\%$, and the total + energy range from \SIrange{4}{8}{\MeV} is $(1.7 \pm 0.1)\%$ per nuclear + muon capture, and the total emission rate assuming the shape holds for the whole spectrum is - $(3.5\pm0.2)\%$. + $(3.5\pm0.2)\%$ per nuclear muon capture. \end{enumerate} The emission rate is consistent with the lower limit of 2.8\% set by Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978}. It is also compatible with the theoretical calculation by Lifshitz and -Singer~\cite{LifshitzSinger.1980}. Compared with the emission rate from -silicon, our result is smaller. +Singer~\cite{LifshitzSinger.1980}. Compared with the existing result on +silicon~\cite{SobottkaWills.1968}, the emission rate from aluminium is +significantly smaller and the spectrum is softer. The proton rate and spectrum have been used to optimise the planned proton absorber for the drift chamber of the COMET Phase-I. The resulted proton hit rate with the baseline configuration is very small compared with the current -figure. It is safe to remove the proton absorber altogether. This would make -a strong impact to the drift chamber design. The AlCap experiment is going to +figure.The recommendation to the COMET Phase-I is to remove the proton +absorber altogether. The momentum resolution of the drift chamber will be +slightly improved, and the level of integrated charge will still remain below +the safe level for the chamber. + +The AlCap experiment is going to submit a beam time request for the 2015 run to collect more data and other measurements for neutrons and gamma rays. diff --git a/thesis/chapters/frontmatter.tex b/thesis/chapters/frontmatter.tex index fea1b50..099a0f3 100644 --- a/thesis/chapters/frontmatter.tex +++ b/thesis/chapters/frontmatter.tex @@ -57,11 +57,27 @@ detector hit rate of the COMET Phase-I. % Acknowledgements -%\begin{acknowledgements} - %\thispagestyle{empty} - %Of the many people who deserve thanks, some are particularly prominent, - %such as my supervisor Professor Yoshitaka Kuno. -%\end{acknowledgements} +\begin{acknowledgements} + \thispagestyle{empty} + First and foremost I would like to thank my supervisor Yoshitaka + Kuno, for his great support and almost infinite patience in last four years. + I am also grateful to all members of the Kuno group, Department of + Physics, Osaka University. Thanks to Akira Sato, Hideyuki Sakamoto for the + knowledge and supervision they have provided. And to Takahisa Itahashi + for the advice and allowing me to practice on his expensive silicon detectors. + + The measurement described in this thesis is the product of effort of all + members of the AlCap Collaboration. Special thanks to Peter Kammel for + always pushing the experiment forward and your very helpful advices. + I enjoyed the stays at your group at University of Washington in Seattle + a lot. I would also like to thank the + fellow graduate students in the collaboration Andy, John, Ben, Damien for + all the hard work in the beam time, in the analysis phase, and also for + the beers. I wish you all success with your work. + + Finally, I would like to thank my family and friends. Without your love and + support I wouldn't make it through these long years of graduate school. +\end{acknowledgements} %% Preface diff --git a/thesis/figs/al100_resp.pdf b/thesis/figs/al100_resp.pdf index 963ea3a9f81834ae5b05954b6b97613c1d7a7be1..f3c0540c314d4fb1af69498782760b2174ef4540 100644 GIT binary patch delta 11843 zcma*tWmH>D)F|LWp|}@{Yti6V+}(o{+#QNLr&zJz!3q?oxD}^BaR^qlSfO~KxLe`o z{l2^I@B1ffa%N|eGkf-0bDqh37t(YmQgS&44=*=2H;)i6cS8dgD=-*hTE`)*y<@(V z^g;L7J5-2|1`UOwBnAH$qra5c>xr7Og1`D+RRiC9@=qsYl=j5;n}b_49e)>|cyL7b z6F5gndY-JF@r*nV4`*Eux3MR!Ki@uHOnCVw9f)LSp#25`^A!y+PJ2k#kHdSHYd*T&dLhcPi#16GqfT3Y2#gEJy;Bz)7+D3 zZJ%}zKedVFb58P9ugHPDvWDfr&ZINld~?(bLcDXlA03TYoB-U1Ztxu21Ork)n|9W$ zN`DlXgfoV`&wtmgsVM+o**rHGkGE-4dWZ#!SHUrvZY1JclsGQ`2&wIVmzd@Bv@NCI zhIp`vjr@p1BP-?~!H3ykuJlP2!$?TPRDTlMV$O<2d{MRu!AKGq?3-{@+ss733{vg*&+bRB24a^#lmi?n@s&x!Kwb9uyrkIWiw#%Wg z7Th6#G`@kV4eRf9?;_rjQ0u;fb)eli+C@+NSE829)nS&M(7j7_svppbml3*XT-!7A zNDm?pJn+RN@KER`$MhD{qk7%Mk^rm^f2;36Od*?u_J9gf;EO+I3d&n+gA`C1sAf); 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