diff --git a/AlCapPSI/draft/.DS_Store b/AlCapPSI/draft/.DS_Store index 7a0b1b9..8d6eab0 100644 Binary files a/AlCapPSI/draft/.DS_Store and b/AlCapPSI/draft/.DS_Store differ 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/chap1_intro.tex b/thesis/chapters/chap1_intro.tex index 6c2749e..ddae2b1 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 $3.1\times 10^{-15}$ 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 @@ -83,6 +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: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 6c6166c..404795d 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 @@ -9,7 +51,7 @@ 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 +66,7 @@ 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 +82,25 @@ 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 +163,15 @@ 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 +179,9 @@ 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}. @@ -198,7 +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, @@ -215,14 +267,14 @@ 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 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} @@ -256,16 +308,16 @@ 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 -experimental limits on these two decay modes are set by MEG -experiment~\cite{Adam.etal.2013} and SINDRUM-II +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}: \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} @@ -278,32 +330,32 @@ 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 -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 @@ -322,8 +374,8 @@ 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} @@ -340,7 +392,10 @@ 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..676f869 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} @@ -62,57 +63,63 @@ from a recent review of Bernstein 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} -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} + \caption{SINDRUM-II experimental set up, reprinted from + reference~\cite{Bertl.etal.2006} with permission from Springer.} \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 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} % subsection experimental_history (end) @@ -124,28 +131,30 @@ 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 +165,14 @@ 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 +182,30 @@ 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 +244,7 @@ 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 +253,9 @@ 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 +267,7 @@ 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 +276,7 @@ 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 +302,7 @@ 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 +322,7 @@ 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 +331,44 @@ 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) + respectively. Reprinted figure from + reference~\cite{CiriglianoKitano.etal.2009}. Copyright 2009 by the + American Physical Society.} + \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 +389,7 @@ 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 +406,36 @@ 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 +458,7 @@ 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 +503,7 @@ 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 +547,12 @@ 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 +563,8 @@ 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 +577,11 @@ 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 +590,11 @@ 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 +611,7 @@ 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 +631,7 @@ 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 +646,28 @@ 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 +708,72 @@ 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 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}{@{}cccc@{}} + \toprule + \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 & 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 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} 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 would 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 +784,11 @@ 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/chapters/chap4_alcap_phys.tex b/thesis/chapters/chap4_alcap_phys.tex index a5bd278..71f019c 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] @@ -347,18 +368,18 @@ $n_{avg} = (0.3 \pm 0.02)A^{1/3}$~\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} @@ -382,39 +403,43 @@ 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. \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 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} - \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} 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 -Table~\ref{tab:krane_proton_rate}), a minor contribution to total proton +above \SI{40}{\MeV} are in the \sn{}{-4}--\sn{}{-3} range (see +\cref{tab:krane_proton_rate}), a minor contribution to total proton emission rate. \begin{table}[htb] \begin{center} @@ -438,7 +463,7 @@ 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 @@ -454,24 +479,26 @@ 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 -\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 +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 -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 @@ -480,13 +507,14 @@ 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 \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} @@ -513,42 +541,48 @@ 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 -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}, + 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 -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=0.85\textwidth]{figs/wyttenbach_rate_1p} - \caption{Activation results from Wyttenbach et - al.~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p)$ and - $(\mu^-,\nu pn)$ 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] - \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 +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 \mega\electronvolt~of Coulomb barrier. They -also commented a ratio for different de-excitation channels: +$(\mu^-,\nu pxn)$ is about 1.5 per \si{\MeV}~of Coulomb barrier. They +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} @@ -558,7 +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) @@ -572,33 +606,34 @@ 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 -distribution (curve (III) in the left hand side of -Figure~\ref{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 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 \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} @@ -611,23 +646,25 @@ 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 $10028 \pm 4$ & (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\\ - \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}} - \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 +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}{l S S[separate-uncertainty=true] + S S[separate-uncertainty=true] c} + \toprule + {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 & 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 & {$> 61$}&(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)\\ + \bottomrule + \end{tabular} + \end{center} + \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 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} + For protons with higher energies in the range of -40--90 \mega\electronvolt~observed in the emulsion data as well as in later +40--90 \si{\MeV}~observed in the emulsion data as well as in later experiments~\cite{BudyashovZinov.etal.1971,BalandinGrebenyuk.etal.1978, KraneSharma.etal.1979}, Lifshitz and Singer~\cite{LifshitzSinger.1988} suggested another contribution from capturing on correlated two-nucleon @@ -682,12 +745,12 @@ 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 - \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\\ @@ -699,28 +762,30 @@ 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 $E_p \ge 40$ - \mega\electronvolt~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) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \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 -\mega\electronvolt: +\si{\MeV}: \begin{enumerate} - \item Spectrum wise, only one energy spectrum (Figure~\ref{fig:krane_proton_spec}) - for energies above 40 \mega\electronvolt~is available from Krane et + \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 - $7.5 \pm 0.4$~\mega\electronvolt. At low energy range, the best one can get is + $7.5 \pm 0.4$~\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}). - This charged particle spectrum peaks around 2.5 \mega\electronvolt~and - reduces exponentially with a decay constant of 4.6 \mega\electronvolt. + 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 al.~\cite{WyttenbachBaertschi.etal.1978} only gives rate of $^{27}\textrm{Al}(\mu^-,\nu pn)^{25}\textrm{Na}$ reaction, and set a lower @@ -748,25 +813,25 @@ 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 \mega\electronvolt\per\cc. -Figure~\ref{fig:proton_impact_CDC} shows that protons with kinetic energies of -2.5--8 \mega\electronvolt~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 - below 10\mega\electronvolt. Shaded area is the acceptance of the COMET -Phase-I's CDC. Protons with energies in the range of 2.5--8 -\mega\electronvolt~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} 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 +839,11 @@ 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 +be carefully optimised. The limited information available makes it difficult to 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 -\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 @@ -787,58 +851,60 @@ 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{\left(-\frac{T}{T_0}\right)}, \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 \milli\meter~thick -carbon-fibre-reinforced-polymer (CFRP) which contributes -195~\kilo\electronvolt\per\cc~to the momentum resolution. The absorber also -down shifts the conversion peak by 0.7 \mega\electronvolt. 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 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 +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} \label{sub:experimental_method} -We planned to use a low energy, narrow momentum spread available at PSI to +We planned to use a low-energy, narrow-momentum-spread available at PSI to fight the aforementioned difficulties in measuring protons. The beam momentum -is tunable from 28 to 45~\mega\electronvolt\ so that targets at different -thickness from 25 to 100 \micro\meter\ can be studied. The $\pi$E1 beam line -could provide about \sn{}{3} muons\per\second\ at 1\% momentum spread, and -\sn{}{4} muons\per\second\ at 3\% momentum spread. With this tunable beam, the -stopping distribution of the muons is well-defined. +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-tuned using this excellent beam. -The principle of the particle identification used in the AlCap experiment is -that for each species, the function describes the relationship between energy -loss per unit length (dE/dx) and the particle energy E is uniquely defined. -With a simple system of two detectors, dE/dx can be obtained by -measuring energy deposit $\Delta$E in one detector of known thickness -$\Delta$x, and E is the sum of energy deposit in both detector if the particle -is fully stopped. - -In the AlCap, we realise the idea with a pair of silicon detectors: one thin -detector of 65~\micron\ serves as the $\Delta$E counter, and one thick detector -of 1500~\micron\ that can fully stop protons up to about 12~MeV. Since the -$\Delta \textrm{d}=65$~\micron\ is known, the function relates dE/dx to -E reduces to a function between $\Delta$E and E. Figure~\ref{fig:pid_sim} shows -that the function of protons can be clearly distinguished from other charged -particles in the energy range of interest. +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. +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 +\SIrange{2.5}{12}{\MeV} as shown in \cref{fig:pid_sim}. \begin{figure}[htbp] \centering \includegraphics[width=0.75\textwidth]{figs/pid_sim} - \caption{Simulation study of PID using a pair of silicon detectors} + \caption{Simulation study of PID using a pair of silicon detectors. The + detector resolutions follow the calibration results provided by the + manufacturer.} \label{fig:pid_sim} \end{figure} -The AlCap uses two pairs of detector with large area, placed symmetrically with -respect to the target provide a mean to check for muon stopping distribution. -The absolute number of stopped muons are inferred +Two pairs of detectors, placed symmetrically with +respect to the target, provide a mean to check for muon stopping distribution +inside the target. The absolute number of stopped muons is calculated from the number of muonic X-rays recorded by a germanium detector. For -aluminium, the $(2p-1s)$ line is at 346 \kilo\electronvolt. The acceptances of +aluminium, the $(2p-1s)$ line is at \SI{346.828}{\keV}. The acceptances of detectors will be assessed by detailed Monte Carlo study using Geant4. % subsection experimental_method (end) @@ -846,50 +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 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. 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 638aa6b..828ec29 100644 --- a/thesis/chapters/chap5_alcap_setup.tex +++ b/thesis/chapters/chap5_alcap_setup.tex @@ -2,96 +2,105 @@ \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, -2013. The goal of the run was to measure protons rate and spectrum following -muon capture on aluminium. - -\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} +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} 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 +(\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}[htbp] +\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.} \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}. +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}. 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}. -\begin{figure}[htb] - \centering - \includegraphics[width=0.7\textwidth]{figs/psi_piE1_elements} - \caption{The $\pi$E1 beam line} - \label{fig:psi_piE1_elements} -\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 + %\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 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}{\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. 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 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}[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} + \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. 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} 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 -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. +chamber as shown in \cref{fig:alcap_setup_detailed}. The muon beam enters +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. 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 +111,25 @@ 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 +141,11 @@ 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 +158,8 @@ 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 @@ -195,15 +207,15 @@ 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 +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 @@ -214,7 +226,7 @@ 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 +237,9 @@ 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 @@ -250,19 +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-\micron-thick ion implanted contact (Figure~\ref{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] - \centering - \includegraphics[width=0.9\textwidth]{figs/ge_det_dimensions} - \caption{Dimensions of the germanium detector} - \label{fig:ge_det_dimensions} -\end{figure} +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} 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. @@ -285,15 +303,16 @@ 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 -(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} @@ -304,34 +323,34 @@ 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 + 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 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 +366,7 @@ 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 +374,14 @@ 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 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 @@ -375,7 +394,7 @@ 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 @@ -397,18 +416,329 @@ 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 -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). +{\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. 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. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\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}{\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}); + + \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; and + + \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 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}. + +\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}, + %%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} + }, + 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 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: +\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} + +Following corrections for the peak areas are considered: +\begin{enumerate} + \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 (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 a dead time. + \item True coincidence summing correction: two cascade gamma rays hit the + 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} + +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. + +\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. 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 +\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 (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} +\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[ + % 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} + +% 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} @@ -431,14 +761,14 @@ 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 -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 -was chosen to maximise the number of stopped muons. The collected data sets are -shown in Table~\ref{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}[htb!] +\begin{table}[btp!] \begin{center} \vspace{0.15cm} \begin{tabular}{l c c c} @@ -446,38 +776,39 @@ 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} & 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} % 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 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 +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. -\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 @@ -487,9 +818,9 @@ 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. @@ -520,12 +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}[htb] - \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 @@ -545,7 +876,7 @@ 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 +889,8 @@ 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 @@ -604,35 +935,142 @@ 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} \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 (Figure~\ref{fig:muX}), and to help in choosing optimal -momenta which maximised the number of stopped muons. -\begin{figure}[htbp] - \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 - 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. +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 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 +(\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 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 +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 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 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} % 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 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 helped make a sense of the 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 75f46bb..2c4b61e 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -1,355 +1,84 @@ -\chapter{Data analysis} +\chapter{Data analysis and results} \label{cha:data_analysis} +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 and spectrum of proton emission from + aluminium. +\end{itemize} -\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 -thanks to the modularity of the analysis framework. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\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}, which contains \num{6.43E7} muon events. +%\num[fixed-exponent=2, scientific-notation = fixed]{6.4293720E7} muon events. -\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, takes -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 -pile up or double pulses in one \tpulseisland{} in -Figure~\ref{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{\micro\second}} 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}} -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{\micro\second}} 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 -%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}). -%\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 \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 -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}. -\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) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\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. -%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}). -\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 -Table~\ref{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 Figure~\ref{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 Table~\ref{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 -%Table~\ref{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 Figure~\ref{fig:lldq}. The data set contains \sn{6.43}{7} -muon events. -%64293720 - -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. - -\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 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 Figure~\ref{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. +is shown in \cref{fig:sir2f_Et_corr}. -\begin{figure}[htb] +\begin{figure}[tbp] \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} + \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 hits on the silicon active target after 1200~ns are mainly secondary +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 limitation of the current pulse +parameter extraction method where no pile up or double pulses is accounted for. + +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 Figure~\ref{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} @@ -357,134 +86,29 @@ 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: + \item and the first hit on the target has energy of that of the muons: \begin{equation} - 3.4 \textrm{ MeV}