From b21181a08abdc7a3c86720f6bf7edfde9f96e583 Mon Sep 17 00:00:00 2001 From: nam Date: Wed, 29 Oct 2014 19:51:47 +0900 Subject: [PATCH] prog saved --- thesis/chapters/chap2_mu_e_conv.tex | 18 +- thesis/chapters/chap3_comet.tex | 288 ++++++++++++++--------- thesis/figs/{sched.png => old_sched.png} | Bin thesis/thesis.bib | 52 +++- thesis/thesis.tex | 4 +- 5 files changed, 230 insertions(+), 132 deletions(-) rename thesis/figs/{sched.png => old_sched.png} (100%) diff --git a/thesis/chapters/chap2_mu_e_conv.tex b/thesis/chapters/chap2_mu_e_conv.tex index a1a84ed..4363e09 100644 --- a/thesis/chapters/chap2_mu_e_conv.tex +++ b/thesis/chapters/chap2_mu_e_conv.tex @@ -271,11 +271,11 @@ experimental limits on these two decay modes are set respectively by the MEG experiment~\cite{Adam.etal.2013} and the SINDRUM-II experiment~\cite{Bertl.etal.2006}: \begin{equation} - \mathcal{B}(\mu^+ \rightarrow e^+ \gamma) < 5.7 \times 10^{-13}\, + \mathcal{B}(\mu^+ \rightarrow e^+ \gamma) < 5.7 \times 10^{-13}\,, \end{equation} and: \begin{equation} - \mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13}\. + \mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13}\,. \end{equation} %\hl{TODO: mueg and muec relations, Lagrangian \ldots} @@ -307,14 +307,13 @@ In the context of physics beyond the SM, the exotic process of \mueconv where a muon decays to an electron without neutrinos is also expected, but has never been observed: \begin{equation} - \mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)\. + \mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)\,. \end{equation} -The emitted electron in this decay -mode , the \mueconv electron, is mono-energetic at an energy far above the -endpoint +The emitted electron in this decay mode, the \mueconv electron, is +mono-energetic at an energy far above the endpoint of the Michel spectrum (52.8 MeV): \begin{equation} - E_{\mu e} = m_\mu - E_b - \frac{E^2_\mu}{2m_N} + E_{\mu e} = m_\mu - E_b - \frac{E^2_\mu}{2m_N}\,. \end{equation} where $m_\mu$ is the muon mas; $E_b \simeq Z^2\alpha^2 m_\mu/2$ is the binding energy of the muonic atom; and the last term is the nuclear recoil energy @@ -351,7 +350,10 @@ The mean lifetime $\tau = 1/\Gamma$, then: \end{equation} The mean lifetimes of free muons and muons in a material are well-known, therefore the number of captures can be inferred from the number of stops. For -aluminium, $\frac{\Gamma_{\textrm{capture}}}{\Gamma_{\textrm{stop}}} = 0.609$ +aluminium, +\begin{equation} + \frac{\Gamma_{\textrm{capture}}}{\Gamma_{\textrm{stop}}} = 0.609 +\end{equation} and the mean lifetime of stopped muons is 864 ns~\cite{SuzukiMeasday.etal.1987}. diff --git a/thesis/chapters/chap3_comet.tex b/thesis/chapters/chap3_comet.tex index da9979b..a451973 100644 --- a/thesis/chapters/chap3_comet.tex +++ b/thesis/chapters/chap3_comet.tex @@ -5,8 +5,8 @@ This chapter describes the new experimental search for \mueconv, namely COMET - (\textbf{CO}herent \textbf{M}uon to \textbf{E}lectron \textbf{T}ransition). The experiment will be carried out at the Japan Proton Accelerator Research Complex -(J-PARC), aims at a sensitivity of \sn{6}{-17} i.e. 10,000 times better than the -current best limit. +(J-PARC), aims at a single event sensitivity of \num{6E-17}, i.e. 10,000 times +better than the current best limit. %At the Japan Proton Accelerator Research Complex (J-PARC), an experiment to %search for \muec~conversion, which is called @@ -48,8 +48,9 @@ current best limit. The searches for \mueconv has been ongoing for more than 50 years, started in 1952 with cosmic rays~\cite{LagarriguePeyrou.1952} and then moved to -accelerators. The list in the Table~\ref{tab:mueconv_history} is reproduced -from a recent review of Bernstein and Cooper~\cite{BernsteinCooper.2013}. +accelerators. The list of upper limits for \mueconv in +\cref{tab:mueconv_history} is reproduced from a recent review of Bernstein +and Cooper~\cite{BernsteinCooper.2013}. \begin{table}[htb] \begin{center} \begin{tabular}{l l l c} @@ -79,40 +80,43 @@ from a recent review of Bernstein and Cooper~\cite{BernsteinCooper.2013}. \label{tab:mueconv_history} \end{table} -The most recent experiments were the SINDRUM and SINDRUM-II at the Paul -Scherrer Institute (PSI), Switzerland. The SINDRUM-II measured the branching +The latest experiments were the SINDRUM and SINDRUM-II at the Paul +Scherrer Institute (PSI), Switzerland. The SINDRUM-II +(\cref{fig:sindrumII_setup}) measured the branching ratio of \mueconv on a series of heavy targets: Ti, Pb and Au. The proton beam -at PSI is a continuous wave beam, with a time structure of 0.3 ns bursts every -19.75 \si{\nano\second}. An 8-\si{\milli\meter}-thick CH$_2$ degrader was used to reduce -the radiative pion capture and other prompt backgrounds. Cosmic backgrounds are +at PSI is a continuous beam, with a time structure of 0.3 ns bursts every +19.75 \si{\nano\second}. An 8-\si{\milli\meter}-thick CH$_2$ degrader was used +to reduce the radiative pion capture and other prompt backgrounds. Cosmic +backgrounds are rejected using a combination of -passive shielding, veto counters and reconstruction cuts. The momenta of muons -were 52 \si{\mega\electronvolt\per\cc} and 53 \si{\mega\electronvolt\per\cc}, and the -momentum spread was 2\%. +passive shielding, veto counters and reconstruction cuts. The momenta of beam +muons used in the experiment were \SI{52}{\MeV\per\cc} and +\SI{53}{\MeV\per\cc}, and the momentum spread was 2\%. \begin{figure}[htbp] \centering \includegraphics[width=0.85\textwidth]{figs/sindrumII_setup} \caption{SINDRUM-II set up} \label{fig:sindrumII_setup} \end{figure} -Electrons emitted from the target were tracked in a 0.33 T solenoid field. -Detector system consisted of a superconducting solenoid, two plastic +Electrons emitted from the target were tracked in a 0.33 T solenoidal magnetic +field. Detector system consisted of a superconducting solenoid, two plastic scintillation hodoscopes, a plexiglass Cerenkov hodoscope, and two drift chambers. In the latest measurement, the SINDRUM-II collaboration have not found any conversion electron from captured muons in a gold target, hence set the upper limit for -the branching ratio of \mueconv in gold with 90 \% C.L. at \sn{7.0}{-13}. +the branching ratio of \mueconv in gold with 90 \% C.L. at \num{7.0E-13}. The reconstructed momenta of electrons around the signal region from SINDRUM-II -is shown in the Figure~\ref{fig:sindrumII_result}. It can be seen that the muon +is shown in \cref{fig:sindrumII_result}. It can be seen that the muon decay in orbit background falls steeply near the endpoint as expected, but, the prompt background induced by pions still remains even after the cut in timing and track angle. This indicates the problem of pion contamination is very -important in probing lower sensitivity. +important in probing better sensitivity. \begin{figure}[htbp] \centering \includegraphics[width=0.55\textwidth]{figs/sindrumII_Au_result} - \caption{SINDRUM-II result} + \caption{SINDRUM-II results} +%TODO: explain top and bottom figure \label{fig:sindrumII_result} \end{figure} % subsection experimental_history (end) @@ -124,28 +128,30 @@ A new generation of \mueconv experiments have been proposed with scenarios to overcome pion induced background in the SINDRUM-II. Lobashev and collaborators first suggested the basic idea for new \mueconv at the Moscow Muon Factory; this idea was used to develop the MECO experiment at Brookhaven National -Laboratory. The MECO experiment was cancelled due to budget constraints. The two -modern experiments, COMET at J-PARC and Mu2e at Fermilab use the initial idea +Laboratory. The MECO experiment was cancelled due to budget constraints. Two +recent experiments, COMET at J-PARC and Mu2e at Fermilab, use the initial idea with more upgrades and modifications. -The basic ideas of the modern experiments are: +The basic ideas of the two experiments are: \begin{enumerate} \item Highly intense muon source: the total number of muons needed is of the order of $10^{18}$ in order to achieve a sensitivity of $10^{-16}$. This can be done by producing more pions using a high power proton beam, and having a high efficiency pion collection system; - \item Pulsed proton beam with an appropriate timing: the proton pulse should + \item Pulsed proton beam: the proton pulse should be short compares to the lifetime of muons in the stopping target material, and the period between pulses should be long enough for prompt backgrounds from pion to decay before beginning the measurement. It is also crucial that there is no proton leaks into the measuring interval; \item Curved solenoids for charge and momentum selection: at first, the curved solenoids remove the line of sight backgrounds. A charged particle travels - through a curved solenoidal field will have the centre of the helical - motion drifted up or down depends on the sign of the charge, and the - magnitude of the drift is proportional to its momentum. By using this - effect and placing suitable collimators, charge and momentum selection can - be made. + through a curved solenoidal magnetic field has the centre of the helical + motion drifted up or down with respect to the bending plane depends on the + sign of the charge, and the magnitude of the drift is proportional to its + momentum. By using this effect and placing suitable collimators, charge and + momentum selection can be made. Details of the magnet system are described + in \cref{sub:pion_production_can_capture_solenoid} and + \cref{sub:pion_and_muon_transportation}. \end{enumerate} % subsection new_generation_of_mueconv_experiments (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -156,13 +162,14 @@ The basic ideas of the modern experiments are: \section{Concepts of the COMET experiment} \label{sec:concepts_of_the_comet_experiment} This section elaborates the design choices of the COMET to realise the basic -ideas mentioned above. Figures and numbers, other than noted, are taken from -the COMET's documentations: +ideas mentioned previously. Figures and numbers, other than noted, are taken +from the COMET's documentations: \begin{itemize} %TODO citations - \item Conceptual design report for the COMET experiment~\cite{COMET.2009} - \item Proposal Phase-I 2012 - \item TDR 2014 + \item Conceptual design report for the COMET experiment~\cite{COMET.2009}, + \item Experimental Proposal for Phase-I of the COMET Experiment at + J-PARC~\cite{COMET.2012}, + \item and COMET Phase-I Technical Design Report~\cite{COMET.2014}. \end{itemize} @@ -172,30 +179,30 @@ A high power pulsed proton beam is of utmost importance to achieve the desired sensitivity of the COMET experiment. A slow-extracted proton beam from the J-PARC main ring (MR), which is designed to deliver \sn{3.6}{15} protons per cycle at a frequency of 0.45 Hz, will be used for the COMET experiment. The -proton beam power of the current design is 8 GeV$\times$7 $\mu$A, or -\sn{4.4}{13} protons/s. The beam energy 8 \si{\giga\electronvolt} helps to minimise -the production of antiprotons. +proton beam power of the current design is $\SI{8}{\GeV}\times \SI{7}{\uA}$, or +\num{4.4E13} protons/s at \SI{8}{\GeV}. The beam energy was chosen to minimise +the production of antiprotons which may introduce background events. The proton pulse width is chosen to be 100 ns, and the pulse period to be -$1 \sim 2 \textrm{ }\mu\textrm{s}$. This time structure is sufficient for the -search for \mueconv in an aluminium target where the lifetime of muons is 864 -ns. A plan of accelerator operation to realise the scheme is shown in -the Figure~\ref{fig:comet_mr_4filled}, where 4 out of 9 MR buckets are filled. +from \SIrange{1}{2}{\us}. This time structure is sufficient for the +search for \mueconv in an aluminium target where the mean lifetime of negative +muons in muonic atoms is \SI{864}{\ns}. One possible plan of accelerator +operation to realise the beam pulsing is shown in \cref{fig:comet_mr_4filled}, +where 4 out of 9 MR buckets are filled. As mentioned, it is very important that there is no stray proton arrives in the measuring period between two proton bunches. An extinction factor is defined as the ratio between number of protons in between two pulses and the number of protons in the main pulse. In order to achieve the goal sensitivity of the -COMET, an extinction factor of \sn{}{-9} is required. +COMET, an extinction factor less than \num{E-9} is required. -Requirements for the proton beam are summarised in the -Table~\ref{tab:comet_proton_beam}. +Requirements for the proton beam are summarised in \cref{tab:comet_proton_beam}. \begin{figure}[htb] \centering \includegraphics[width=0.8\textwidth]{figs/comet_mr_4filled} - \caption{The COMET proton bunch structure in the RCS (rapid cycle - synchrotron) and MR where 4 buckets + \caption{The COMET proton bunch structure in the RCS (Rapid Cycling + Synchrotron) and MR where 4 buckets are filled producing 100 \si{\nano\second} bunches separated by 1.2~\si{\micro\second}.} \label{fig:comet_mr_4filled} @@ -234,7 +241,7 @@ pions, are preferred. It is known from other measurements that backward scattered pions (with respect to proton beam direction) of high energy are suppressed, and the yield of low energy pions in the backward direction is not too low compares to that of the forward direction (see -Figure~\ref{fig:pion_yield}). For these reasons, the COMET +\cref{fig:pion_yield}). For these reasons, the COMET decided to collect backward pions. \begin{figure}[htb] \centering @@ -243,10 +250,9 @@ decided to collect backward pions. target.} \label{fig:pion_yield} \end{figure} - The pion capture system is composed of several superconducting solenoids: capture solenoids and matching solenoids. The magnetic field distribution along -the beam axis of the COMET is shown in the Figure~\ref{fig:comet_Bfield}. The +the beam axis of the COMET is shown in \cref{fig:comet_Bfield}. The peak field of 5 T is created by the capture solenoid, and the matching solenoids provide a smooth transition from that peak field to the 3 T field in the pions/muons transportation region. The superconducting solenoids are @@ -258,6 +264,7 @@ will be installed inside the cryostat to reduce radiation heat load. \caption{Magnetic field distribution along the COMET beam line.} \label{fig:comet_Bfield} \end{figure} +%TODO full comet field % subsection pion_production_can_capture_solenoid (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -266,7 +273,7 @@ will be installed inside the cryostat to reduce radiation heat load. Muons and pions are transported to the muon stopping target through a muon beam line, which includes several curved and straight superconducting solenoid magnets. A schematic layout of the muon beam line, include the capture and -detector sections, is shown in Figure~\ref{fig:comet_beamline_layout}. +detector sections, is shown in \cref{fig:comet_beamline_layout}. \begin{figure}[htb] \centering \includegraphics[width=0.95\textwidth]{figs/comet_beamline_layout} @@ -292,7 +299,7 @@ of the drift is given by: &= \frac{1}{qB} \frac{s}{R} \frac{p}{2} \left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right)\\ &= \frac{1}{qB} \theta_{bend} \frac{p}{2} - \left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right) + \left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right)\,, \end{align} where $q$ is the electric charge of the particle; $B$ is the magnetic field at the axis; $s$ and $R$ are the path length and the radius of the curvature; $p$, @@ -312,7 +319,7 @@ produced by additional coils winded around the solenoid coils. The magnitude of the compensating field is: \begin{equation} B_{\textrm{comp}} = \frac{1}{qR} \frac{p_0}{2} - \left( \textrm{cos}\theta_0 + \frac{1}{\textrm{cos}\theta_0} \right) + \left( \textrm{cos}\theta_0 + \frac{1}{\textrm{cos}\theta_0} \right)\,, \end{equation} where the trajectories of charged particles with momentum $p_0$ and pitch angle $\theta_0$ are corrected to be on-axis. An average dipole field of 0.03 T is @@ -321,23 +328,42 @@ needed to select 40 MeV/$c$ muons as required by the COMET design. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Muon stopping target} \label{sub:muon_stopping_target} -Muon stopping target is place at 180\si{\degree}~bending after the pion production -target (Figure~\ref{fig:comet_beamline_layout}) in its own solenoid. The target +Muon stopping target is place at 180\si{\degree}~bending after the pion +production target (\cref{fig:comet_beamline_layout}) in its own solenoid. The +target is designed to maximise the muon stopping efficiency and minimise the energy loss of signal electrons. %\hl{TODO: Target choice: separation, product, lifetime, energy loss\ldots} It is calculated that the branching ratio of \mueconv increases with atomic -number $Z$, and plateaus above $Z \simeq 30$, then decreases as $Z>60$. The -lifetime of muons inside a material decreases quickly as $Z$ increases. -Tracking wise, lower $Z$ material provides better reconstructed momentum -resolution. Therefore, light material is preferable as muon stopping target. +number $Z$, and plateaus above $Z \simeq 30$, then decreases as $Z>60$ (see +\cref{fig:comet_mueconv_RateVsZ}). Although the sensitivity is better for +higher $Z$ material, the acceptance of the measurement time window decreases +quickly because the average lifetime of negative muons inside a material +decreases as $Z^{-4}$. +%Tracking wise, lower $Z$ material provides better +%reconstructed momentum +%resolution. +Therefore, light material is preferable as muon stopping target. +\begin{figure}[hbp] + \centering + \includegraphics[width=0.60\textwidth]{figs/comet_mueconv_RateVsZ} + \caption{Target dependence of the \mueconv rate in different models + calculated by Cirigliano and colleagues~\cite{CiriglianoKitano.etal.2009}. + The conversion rates are normalised to the rate in aluminium. Four models + were considered and noted with letters: D for dipole-interaction-dominated + model, V for vector and S for scalar interactions. The three vertical lines + from left to right correspond to $Z=13$(Al), $Z=22$(Ti), and $Z=82$(Pb)l + respectively.} + \label{fig:comet_mueconv_RateVsZ} +\end{figure} The first choice for the muon stopping target material in the COMET is -aluminium. A titanium target is also considered. Configuration of the target is -shown in the Table~\ref{tab:comet_al_target}. Monte Carlo studies with this +aluminium. A titanium target is also considered in the future. Configuration of +the target is shown in \cref{tab:comet_al_target}. Monte Carlo studies with +this design showed that net stopping efficiency is 0.29, and average energy loss -of signal electrons is about 400 \si{\kilo\electronvolt}. +of signal electrons is about \SI{400}{\keV}. \begin{table}[htb] \begin{center} \begin{tabular}{l l} @@ -358,7 +384,7 @@ of signal electrons is about 400 \si{\kilo\electronvolt}. \end{table} A graded magnetic field (reduces from 3 T to 1 T) is produced at the -location of the stopping target (see Figure~\ref{fig:comet_target_Bfield}) to +location of the stopping target (see \cref{fig:comet_target_Bfield}) to maximise the acceptance for \mueconv signals, since electrons emitted in the backward direction would be reflected due to magnetic mirroring. The graded field also @@ -375,36 +401,36 @@ transport section. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Electron transportation beam line} \label{sub:electron_transportation_beam_line} -The 180\si{\degree}~bending electron transport solenoids help remove line-of-sight +The \ang{180} bending electron transport solenoids help remove line-of-sight between the target and the detector system. It works similarly to the muon transportation section, but is tuned differently to accept electrons of about -105~\si{\mega\electronvolt\per\cc}. A compensation field of 0.17 T along the -vertical direction will be applied. Electrons with momentum less than 80 -\si{\mega\electronvolt\per\cc} are blocked at the exit of this section by +\SI{105}{\MeV\per\cc}. A compensation field of \SI{0.17}{\tesla} along the +vertical direction will be applied. Electrons with momentum less than +\SI{80}{\MeV\per\cc} are blocked at the exit of this section by a collimator to reduce DIO electrons rate. The net acceptance of signals of \mueconv is about 0.32, and the detector hit rate will be in the order of -1~\si{\kilo\hertz}~for \sn{}{11} stopped muons\si{\per\second}. +\SI{1}{\kHz} for a muon stopping rate of \SI{E11}{\Hz}. % subsection electron_transportation_beam_line (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Electron detectors} \label{sub:electron_detectors} The \mueconv signal electrons is measured by an electron detector system, which consists of straw-tube trackers and an electromagnetic calorimeter - shown in -Figure~\ref{fig:comet_detector_system}. The +\cref{fig:comet_detector_system}. The requirements for the detector system is to distinguish electrons from other particles, and measure their momenta, energy and timings. The whole detector system is in a uniform solenoidal magnetic field under vacuum. Passive and active shielding against cosmic rays is considered. The tracking detector has to provide a momentum resolution less than +%%TODO 350 or 150? 350~\si{\kilo\electronvolt\per\cc} in order to achieve a sensitivity of \sn{3}{-17}. There are five stations of straw-tube gas chambers, each provides -two -dimensional information. Each straw tube is 5~\si{\milli\meter} in diameter and has -a 25~\si{\micro\meter}-thick wall. According to a GEANT4 Monte Carlo simulation, -a position resolution of 250~\si{\micro\meter} can be obtained, which is enough for -350~\si{\kilo\electronvolt\per\cc} momentum resolution. The DIO background of 0.15 -events is estimated. +two dimensional information. Each straw tube is 5~\si{\milli\meter} in diameter +and has a 25-\si{\micro\meter}-thick wall. According to a GEANT4 Monte Carlo +simulation, a position resolution of 250~\si{\micro\meter} can be obtained, +which is enough for 350~\si{\kilo\electronvolt\per\cc} momentum resolution. The +DIO background of 0.15 events is expected. The electromagnetic calorimeter serves three purposes: a) to measure electrons energy with high energy resolution; b) to provide timing information and @@ -427,7 +453,7 @@ The requirements for \mueconv signals are: muons decay in flight; \item timing wise, conversion electrons should arrive in the time window of detection which is about 700~\si{\nano\second}~after each proton pulses - (Figure~\ref{fig:comet_meas_timing}). The acceptance in this detection + (\cref{fig:comet_meas_timing}). The acceptance in this detection window is about 0.39 for aluminium. \end{itemize} @@ -472,7 +498,7 @@ Potential backgrounds for the COMET are: \item Accidental background from cosmic rays \end{enumerate} The expected background rates for the COMET at an SES of -\sn{3}{-17} is summarised in Table~\ref{tab:comet_background_estimation}. +\sn{3}{-17} is summarised in \cref{tab:comet_background_estimation}. \begin{table}[htb] \begin{center} %\begin{tabular}{l l} @@ -516,11 +542,12 @@ are believed to greatly reduce potential backgrounds, by several orders of magnitude, for the \mueconv search. That also means that backgrounds are being extrapolated over four orders of magnitude from existing data. In order to obtain data-driven estimates of backgrounds, and inform the detailed design for -the ultimate COMET experiment, and initial phase is desirable. Also, the 5-year -mid-term plan from 2013 of J-PARC includes the construction of the COMET beam -line. For these reasons, the COMET collaboration considers a staged approach -with the first stage, so called COMET Phase-I, with a shorter muon -transportation solenoid, up to the first 90\si{\degree}. +the ultimate COMET experiment, a staged approach is desirable. Also, the +KEK/J-PARC 5-year mid-term plan from 2013 includes the construction +of the COMET beam line. For these reasons, the COMET collaboration considers +to carry out the experiment in two stages. The first stage, so called COMET +Phase-I, with a shorter muon transportation solenoid, up to the first +90\si{\degree}. %\begin{wrapfigure}{r}{0.5\textwidth} %\centering @@ -531,8 +558,8 @@ transportation solenoid, up to the first 90\si{\degree}. %\end{wrapfigure} \begin{SCfigure} \centering - \caption{Lay out of the COMET Phase-I, the target and detector solenoid are - placed after the first 90\si{\degree}~bend.} + \caption{Layout of the COMET Phase-I, the target and detector solenoid are + placed after the end of the first \ang{90} bend.} \includegraphics[width=0.4\textwidth]{figs/comet_phase1_layout} \label{fig:comet_phase1_layout} \end{SCfigure} @@ -545,11 +572,11 @@ The COMET Phase-I has two major goals: and physics background from muon DIO. Straw tube trackers and crystal calorimeter with the same technology in the full COMET will be used, thus these detectors can be regarded as the final prototype. - \item Search for \mueconv with an intermediate sensitivity of \sn{3.1}{-15}, - a two orders of magnitude improvement from the SINDRUM-II limit. To realise - this goal, two options for detectors are being considered, either a reused - of the detectors for background measurements, or a dedicated detector. - The latter will be described in detail later. + \item Search for \mueconv with an intermediate single event sensitivity of + \num{3.1E-15}, a two orders of magnitude improvement from the SINDRUM-II + limit. Another dedicated detector system (described in + \cref{sub:detectors_for_mueconv_search_in_the_phase_i}) is considered for + this physics measurement. \end{enumerate} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -558,11 +585,11 @@ The COMET Phase-I has two major goals: Proton beam for the Phase-I differs only in beam power compares to that of the full COMET. It is estimated that a beam power of 3.2~\si{\kilo\watt}~$=$~8~\si{\giga\electronvolt}~$\times$~0.4~\si{\micro\ampere}~(or -\sn{2.5}{12} protons\si{\per\second}) will be enough for beam properties +\sn{2.5}{12} protons per second) will be enough for beam properties study and achieving the physics goal of this stage. Starting from a lower intensity is also suitable for performing accelerator -studies that are needed to realise 8~\si{\giga\electronvolt} beam extraction from -the J-PARC main ring. +studies that are needed to realise 8~\si{\giga\electronvolt} beam extraction +from the J-PARC main ring. % subsection proton_beam_for_the_comet_phase_i (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Pion production and transportation solenoids} @@ -579,7 +606,7 @@ A correction dipole filed of 0.05 T is also applied to improve the pion yield. The pion/muon beam line for COMET Phase-I consists of the pion capture solenoid section (CS), muon transport solenoid section (TS) up to the first 90\si{\degree}~bending, and a set of matching solenoids (see -Figure~\ref{fig:comet_phase1_magnets}). At the end of the muon beam line, the +\cref{fig:comet_phase1_magnets}). At the end of the muon beam line, the detectors and the detector solenoid (DS) are installed. To reduce beam backgrounds, a beam collimator is placed upstream of the detector solenoid. \begin{figure}[htb] @@ -599,7 +626,7 @@ backgrounds, a beam collimator is placed upstream of the detector solenoid. As mentioned, two types of detectors are considered for physics measurements in the Phase-I. The dedicated detector system consists of a cylindrical drift chamber (CDC), a trigger hodoscope, a proton absorber and a detector solenoid -(Figure~\ref{fig:comet_phase1_cydet}). +(\cref{fig:comet_phase1_cydet}). The whole system is referred as cylindrical detector system (CyDet) in the COMET's documentation. The CyDet has advantages that low momentum particles for the stopping target will not reach the detector, thus the hit rates are kept @@ -614,26 +641,28 @@ CyDet. \label{fig:comet_phase1_cydet} \end{figure} +\subsubsection{CDC configuration} +\label{ssub:CDC configuration} The CDC is the main tracking detector that provides information for reconstruction of charged particle tracks and measuring their momenta. The key parameters for the CDC are listed in the -Table~\ref{tab:comet_phase1_cdc_params}. +\cref{tab:comet_phase1_cdc_params}. Trigger hodoscopes are placed at both upstream and downstream ends of the CDC. -An absorber is placed concentrically with respect to the CDC axis to +A proton absorber is placed concentrically with respect to the CDC axis to reduce potential high rates caused by protons emitted after nuclear muon capture in the stopping target. The CDC covers the region from \SIrange{500}{831}{\milli\meter}~in the radial direction. The length of the CDC is 1500~\si{\milli\meter}. The inner wall is made of -a 100~\si{\micro\meter}-thick aluminised Mylar. The end-plates will be conical -in shape and about 10~\si{\milli\meter}-thick to support the feedthroughs. The outer -wall is -made of 5~\si{\milli\meter}~carbon fibre reinforced plastic (CFRP). +a 500-\si{um}-thick carbon fibre reinforced plastic (CFRP, density +\SI{1.57}{\gram\per\cubic\m}). The end-plates will +be conical in shape and about 10-\si{\mm}-thick to support the +feedthroughs. The outer wall is made of 5-\si{\mm} CFRP. The CDC is arranged in 20 concentric sense layers with alternating positive and negative stereo angles. The sense wires are made of gold-plated tungsten, -30~\si{\micro\meter} in diameter, tensioned to 50~\si{\gram}. The field wires +\SI{25}{\um} in diameter, tensioned to \SI{50}{\gram}. The field wires are uncoated aluminium wires with a diameter of 80~\si{\micro\meter}, at the same tension of \SI{50}{\gram}. A high voltage of $1700\sim1900$~\si{\volt} will be applied to the sense wires with the field wires at ground potential, giving an @@ -674,37 +703,69 @@ these configurations, an intrinsic momentum resolution of \label{tab:comet_phase1_cdc_params} \end{table} -The maximum usable muon beam intensity will be limited by the detector hit +\subsubsection{Hit rate on the CDC} +\label{ssub:hit_rate_on_the_cdc} +The maximal usable muon beam intensity will be limited by the detector hit occupancy. Charge particles with transversal momentum greater than 70 -\si{\mega\electronvolt\per\cc} are expected to reach the CDC. Those particles are: +\si{\mega\electronvolt\per\cc} are expected to reach the CDC. Those include: protons emitted from nuclear muon capture, and electrons from muon decay in -orbit. It is calculated that the hit rate due to proton emission dominates, -where the highest rate is 11~\si{\kilo\hertz\per}cell compares to -5~\si{\kilo\hertz\per} -cell contributing from DIO electrons. Another potential issue caused by protons -is the ageing effect on the CDC as they leave about a 100 times larger +orbit (DIO). It is calculated that the hit rate due to proton emission dominates, +where the highest rate is \SI{11}{\kHz\per}cell compares to +\SI{5}{\kHz\per}cell contributing from DIO electrons. Another potential issue +%%TODO check the hit rates against TDR +caused by protons is the ageing effect on the CDC as they leave about a 100 +times larger energy deposit than the minimum ionisation particles. +%%TODO integration charge ... -For those reasons, we plan to install an absorber to reduce the rate of protons -reaching the CDC. However, there is no experimental data available for the rate +For those reasons, we plan to install a proton absorber to reduce the rate of +protons reaching the CDC. However, there is no experimental data available for +the rate of protons emitted after muon capture in aluminium. In the design of the COMET Phase-I, we use a conservative estimation of the rate of protons from energy spectrum of charged particles emitted from muon capture in $^{28}$Si~\cite{SobottkaWills.1968}. The baseline design for the proton -absorber is 1.0~\si{\milli\meter}-thick CFRP, which contributes -195~\si{\kilo\electronvolt\per\cc} to the momentum resolution of reconstructed -track. +absorber is 1.0~\si{\milli\meter}-thick CFRP, making the total thickness +of material before the sensitive region is \SI{1.5}{\mm} in CFRP. In this +configuration, the inner wall and the proton absorber deteriorate the momentum +resolution of the reconstructed track to 195~\si{\kilo\electronvolt\per\cc}. +The impact of the proton absorber on the CDC's hit rate and momentum +resolution is summarised in \cref{tab:comet_absorber_impact}. +\begin{table}[htb] + \begin{center} + \begin{tabular}{@{}ccc@{}} + \toprule + \textbf{Absorber }& \textbf{Proton }& \textbf{Momentum }\\ + \textbf{thickness }& \textbf{hit rate }& \textbf{resolution }\\ + (\si{\um}) & (\si{\kHz}) & (\si{\keV\per\cc}) \\ + \midrule + 0 & 130 & 131 \\ + 0.5 & 34 & 167 \\ + 1.0 & 11 & 195 \\ + 1.5 & 6 & 252 \\ + \bottomrule + \end{tabular} + \end{center} + \caption{Hit rates and contributions to momentum resolution of the proton + absorber and inner wall of the CDC. The intrinsic momentum resolution due + to multiple scattering is \SI{197}{\keV\per\cc}.} + \label{tab:comet_absorber_impact} +\end{table} In order to obtain a better understanding of the protons emission, and then further optimisation of the CDC, a dedicated experiment to measure proton emission rate and energy spectrum is being carried out at PSI. This experiment is described in detail in next chapters. + +It should be noted that the proton hit rate is not a problem for the COMET +Phase-II where the additional electron transport solenoid will removed all +protons emitted. % subsection detectors_for_mueconv_search_in_the_phase_i (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Sensitivity of the \mueconv search in the Phase-I} \label{sub:sensitivity_of_the_mueconv_search_in_the_phase_i} The SES for the Phase-I is given by -the Equation~\ref{eq:mue_sensitivity}. Using $N_{\mu} = 1.3\times 10^{16}$, +the \eqref{eq:mue_sensitivity}. Using $N_{\mu} = 1.3\times 10^{16}$, $f_{\textrm{cap}} = 0.61$, and $A_e = 0.043$ from MC study for the Phase-I, the SES becomes: \begin{equation} @@ -715,10 +776,11 @@ SES becomes: \subsection{Time line of the COMET Phase-I and Phase-II} \label{sub:time_line_of_the_phase_i} We are now in the construction stage of the COMET Phase-I, which is planned to -be finished by the end of 2016. We will carry out engineering run in 2016, +be finished in the middle of 2016. We will carry out engineering run in the +second half of 2016, and subsequently, physics run in 2017. A beam time of 90 days is expected to achieve the goal sensitivity of the Phase-I. An anticipated schedule for the -COMET, both Phase-I and Phase-II, is shown in Figure~\ref{fig:sched}. +COMET, both Phase-I and Phase-II, is shown in \cref{fig:sched}. \begin{figure}[tbh] \centering \includegraphics[width=0.8\textwidth]{figs/sched} diff --git a/thesis/figs/sched.png b/thesis/figs/old_sched.png similarity index 100% rename from thesis/figs/sched.png rename to thesis/figs/old_sched.png diff --git a/thesis/thesis.bib b/thesis/thesis.bib index 6b34593..abc2226 100644 --- a/thesis/thesis.bib +++ b/thesis/thesis.bib @@ -161,11 +161,11 @@ } @TechReport{COMET.2012, - Title = {Experimental Proposal for Phase-I of the COMET - Experiment at J-PARC}, + Title = {Experimental Proposal for Phase-I of the COMET Experiment at J-PARC}, Author = {R. Akhmetshin and A. Bondar and L. Epshteyn and G. Fedotovich and D. Grigoriev and V. Kazanin and A. Ryzhenenkov and D. Shemyakin and Yu. Yudin and others}, + Institution = {KEK}, Year = {2012}, Month = {7}, Number = {KEK/J-PARC-PAC 2012-10}, @@ -334,6 +334,7 @@ Volume = {729}, Doi = {http://dx.doi.org/10.1016/j.nuclphysa.2003.11.003}, + File = {Published version:AudiWapstra.etal.2003.pdf:PDF}, ISSN = {0375-9474}, Owner = {NT}, Timestamp = {2014-10-26}, @@ -657,16 +658,49 @@ Timestamp = {2014-04-03} } -@Article{COMET.2009, - Title = {Conceptual design report for experimental search for lepton flavor violating $\mu$-- e- conversion at sensitivity of 10^{-16} with a slow-extracted bunched proton beam}, - Author = {COMET}, - Journal = {KEK Report}, +@Article{CiriglianoKitano.etal.2009, + Title = {Model discriminating power of $\mu\rightarrow e$ conversion in nuclei}, + Author = {Cirigliano, Vincenzo and Kitano, Ryuichiro and Okada, Yasuhiro and Tuzon, Paula}, + Journal = {Phys. Rev. D}, Year = {2009}, - Pages = {2009}, - Volume = {10}, + + Month = {Jul}, + Pages = {013002}, + Volume = {80}, + + Doi = {10.1103/PhysRevD.80.013002}, + File = {Published version:CiriglianoKitano.etal.2009.pdf:PDF}, + Issue = {1}, + Numpages = {13}, + Owner = {NT}, + Publisher = {American Physical Society}, + Timestamp = {2014-10-29}, + Url = {http://link.aps.org/doi/10.1103/PhysRevD.80.013002} +} + +@TechReport{COMET.2014, + Title = {COMET Phase-I Technical Design Report}, + Author = {COMET}, + Institution = {KEK}, + Year = {2014}, + Month = {9}, + Type = {Report}, Owner = {NT}, - Timestamp = {2014-07-13} + Timestamp = {2014-10-29} +} + +@TechReport{COMET.2009, + Title = {Conceptual Design Report for experimental search for lepton flavor violating $\mu^- - e^-$ conversion at sensitivity of $10^{-16}$ with a slow-extracted bunched proton beam}, + Author = {COMET}, + Institution = {KEK}, + Year = {2009}, + Type = {Report}, + + Owner = {NT}, + Pages = {2009}, + Timestamp = {2014-07-13}, + Volume = {10} } @Article{ConfortoConversi.etal.1962, diff --git a/thesis/thesis.tex b/thesis/thesis.tex index 2c4a93b..6ae020a 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -30,8 +30,8 @@ for the COMET experiment} \mainmatter %\input{chapters/chap1_intro} -\input{chapters/chap2_mu_e_conv} -%\input{chapters/chap3_comet} +%\input{chapters/chap2_mu_e_conv} +\input{chapters/chap3_comet} %\input{chapters/chap4_alcap_phys} %\input{chapters/chap5_alcap_setup} %\input{chapters/chap6_analysis}