From 567b61715bd7bfb406b0e03fe110fd55fd4187e3 Mon Sep 17 00:00:00 2001 From: nam Date: Thu, 30 Oct 2014 18:56:57 +0900 Subject: [PATCH] prog saved --- thesis/chapters/chap1_intro.tex | 4 +- thesis/chapters/chap2_mu_e_conv.tex | 44 ++++++++- thesis/chapters/chap3_comet.tex | 37 +++---- thesis/chapters/chap4_alcap_phys.tex | 24 ++--- thesis/chapters/chap5_alcap_setup.tex | 2 +- thesis/chapters/chap6_analysis.tex | 137 +++++++++++++++++++++++--- thesis/chapters/chap7_results.tex | 120 ++++++++++++---------- thesis/chapters/frontmatter.tex | 22 +++-- thesis/thesis.tex | 14 +-- 9 files changed, 290 insertions(+), 114 deletions(-) diff --git a/thesis/chapters/chap1_intro.tex b/thesis/chapters/chap1_intro.tex index 95a6425..ddae2b1 100644 --- a/thesis/chapters/chap1_intro.tex +++ b/thesis/chapters/chap1_intro.tex @@ -64,7 +64,7 @@ by the SINDRUM-II~\cite{Bertl.etal.2006}. A staging approach is adopted at the COMET to achieve an intermediate physics result, as well as to gain operational experience. The first stage, COMET Phase I, is scheduled to start data taking -in 2016 with the goal single event sensitivity of $3\times 10^{-15}$ after +in 2016 with the goal single event sensitivity of $3.1\times 10^{-15}$ after a three-month running period. A cylindrical drift chamber being developed by the Osaka University group @@ -86,6 +86,6 @@ sensitivities. Details of the study on proton emission are described in Chapters~\ref{cha:alcap_phys},~\ref{cha:the_alcap_run_2013},~\ref{cha:data_analysis}: physics, method, experimental set up, data analysis. The results and impacts of the study on COMET Phase-I design is discussed in -Chapter~\ref{cha:results_and_discussions}. +Chapter~\ref{cha:discussions_on_the_impact_to_the_comet_phase_i}. % chapter introduction (end) diff --git a/thesis/chapters/chap2_mu_e_conv.tex b/thesis/chapters/chap2_mu_e_conv.tex index 4363e09..4fed239 100644 --- a/thesis/chapters/chap2_mu_e_conv.tex +++ b/thesis/chapters/chap2_mu_e_conv.tex @@ -1,7 +1,49 @@ -\chapter{Lepton flavour and $\mu-e$ conversion} +\chapter{Overview} \thispagestyle{empty} \label{cha:clfv} +\section{Introduction} +\label{sec:introduction} +The COMET experiment~\cite{COMET.2007}, proposed at the Japan Proton +Accelerator Research Complex (J-PARC), is a next-generation-experiment that +searches for evidence of charged lepton flavour violation (CLFV) with muons. +The branching ratio of CLFV in the Standard Model, even with massive neutrinos, +is prohibitively small, at the order of $10^{-54}$. Therefore, any experimental +observation of CLFV would be a clear signal of new physics beyond the SM. + +The COMET (\textbf{CO}herent \textbf{M}uon to \textbf{E}lectron +\textbf{T}ransition) Collaboration aims to probe the conversion of a muon to +an electron in a nucleus field at a single event sensitivity of \num{6E-17}, +pushing for a four orders of magnitude improvement from the current limit set +by the +SINDRUM-II~\cite{Bertl.etal.2006}. A staging approach is adopted at the COMET +to achieve an intermediate physics result, as well as to gain operational +experience. The first stage, COMET Phase I, is scheduled to start data taking +in 2016 with the goal single event sensitivity of $3\times 10^{-15}$ after +a three-month running period. + +A cylindrical drift chamber being developed by the Osaka University group +together with the Kyushu University group and the Chinese groups +will be a main tracking detector in the COMET Phase I. It is anticipated that +the chamber will be heavily occupied by protons emitted after nuclear muon +capture in the stopping target, and thus an absorber will be installed to +reduce the proton hit rate to a tolerable level. A study of proton emission +following nuclear muon capture for optimisation of the proton absorber is +presented in this thesis. + +The thesis is structured as follows: +firstly, +the physics motivation of the COMET experiment, with muon's normal decays and +CLFV decays, is described in this later part of this chapter. +Chapter~\ref{cha:comet_overview} gives an overview of the +COMET experiment: beam lines, detectors and their requirements, and expected +sensitivities. Details of the study on proton emission are described in +Chapters~\ref{cha:alcap_phys},~\ref{cha:the_alcap_run_2013},~\ref{cha:data_analysis}: +physics, method, experimental set up, data analysis. The results and impacts of +the study on COMET Phase-I design is discussed in +Chapter~\ref{cha:discussions_on_the_impact_to_the_comet_phase_i}. + + \section{Lepton flavour} \label{sec:lepton_flavour} According to the SM, all matter is built from a small set of fundamental diff --git a/thesis/chapters/chap3_comet.tex b/thesis/chapters/chap3_comet.tex index a451973..ae3abc1 100644 --- a/thesis/chapters/chap3_comet.tex +++ b/thesis/chapters/chap3_comet.tex @@ -642,7 +642,7 @@ CyDet. \end{figure} \subsubsection{CDC configuration} -\label{ssub:CDC configuration} +\label{ssub:CDC_configuration} The CDC is the main tracking detector that provides information for reconstruction of charged particle tracks and measuring their momenta. The key parameters for the CDC are listed in the @@ -725,30 +725,33 @@ of protons emitted after muon capture in aluminium. In the design of the COMET Phase-I, we use a conservative estimation of the rate of protons from energy spectrum of charged particles emitted from muon capture in $^{28}$Si~\cite{SobottkaWills.1968}. The baseline design for the proton -absorber is 1.0~\si{\milli\meter}-thick CFRP, making the total thickness -of material before the sensitive region is \SI{1.5}{\mm} in CFRP. In this -configuration, the inner wall and the proton absorber deteriorate the momentum -resolution of the reconstructed track to 195~\si{\kilo\electronvolt\per\cc}. +absorber is 0.5~\si{\milli\meter}-thick CFRP, making the total thickness +of material before the sensitive region is \SI{1.0}{\mm} in CFRP. In this +configuration, the inner wall and the proton absorber contribute a spread of +\SI{167}{\keV\per\cc} to the momentum of a \mueconv signal electron. This +figure is a little below the spread cause by multiple scatterings on the +chamber gas at \SI{197}{\keV\per\cc}. The impact of the proton absorber on the CDC's hit rate and momentum resolution is summarised in \cref{tab:comet_absorber_impact}. \begin{table}[htb] \begin{center} - \begin{tabular}{@{}ccc@{}} + \begin{tabular}{@{}cccc@{}} \toprule - \textbf{Absorber }& \textbf{Proton }& \textbf{Momentum }\\ - \textbf{thickness }& \textbf{hit rate }& \textbf{resolution }\\ - (\si{\um}) & (\si{\kHz}) & (\si{\keV\per\cc}) \\ + \textbf{Absorber }& \textbf{Total CFRP }&\textbf{Proton }& + \textbf{$\Delta p$}\\ + \textbf{thickness }& \textbf{thickness }&\textbf{hit rate }& \\ + (\si{\mm}) &(\si{\mm}) & (\si{\kHz}) & (\si{\keV\per\cc}) \\ \midrule - 0 & 130 & 131 \\ - 0.5 & 34 & 167 \\ - 1.0 & 11 & 195 \\ - 1.5 & 6 & 252 \\ + 0 & 0.5 & 130 & 131 \\ + 0.5 & 1.0 & 34 & 167 \\ + 1.0 & 1.5 & 11 & 195 \\ + 1.5 & 2.0 & 6 & 252 \\ \bottomrule \end{tabular} \end{center} - \caption{Hit rates and contributions to momentum resolution of the proton - absorber and inner wall of the CDC. The intrinsic momentum resolution due - to multiple scattering is \SI{197}{\keV\per\cc}.} + \caption{Hit rates and contributions to momentum spread of the proton + absorber and inner wall of the CDC. The resolutions are calculated for + mono-energetic electrons of \SI{104.96}{\MeV\per\cc}.} \label{tab:comet_absorber_impact} \end{table} @@ -758,7 +761,7 @@ emission rate and energy spectrum is being carried out at PSI. This experiment is described in detail in next chapters. It should be noted that the proton hit rate is not a problem for the COMET -Phase-II where the additional electron transport solenoid will removed all +Phase-II where the additional electron transport solenoid would removed all protons emitted. % subsection detectors_for_mueconv_search_in_the_phase_i (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/thesis/chapters/chap4_alcap_phys.tex b/thesis/chapters/chap4_alcap_phys.tex index a95e682..cb4a9c3 100644 --- a/thesis/chapters/chap4_alcap_phys.tex +++ b/thesis/chapters/chap4_alcap_phys.tex @@ -540,15 +540,16 @@ Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978} studied $(\mu^-,\nu p)$, $(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$, $(\mu^-,\nu p3n)$ and $(\mu^-,\nu\alpha)$ in a wide range of 18 elements from sodium to bismuth.Their results plotted against the Coulomb barrier for the outgoing protons are given in -\cref{fig:wyttenbach_rate_1p} and \cref{fig:wyttenbach_rate_23p}. The -classical Coulomb barrier $V$ they used are given by: +\cref{fig:wyttenbach_rate_1p}. +%and \cref{fig:wyttenbach_rate_23p}. +The classical Coulomb barrier $V$ they used are given by: \begin{equation} V = \frac{zZe^2}{r_0A^{\frac{1}{3}} + \rho}, \label{eqn:classical_coulomb_barrier} \end{equation} where $z$ and $Z$ are the charges of the outgoing particle and of the residual -nucleus respectively, $r_0 = 1.35 \textrm{ fm}$, and $\rho = 0 \textrm{ fm}$ for -protons were taken. +nucleus respectively, $e^2 = 1.44 \si{\MeV}$, $r_0 = 1.35 \textrm{ fm}$, and +$\rho = 0 \textrm{ fm}$ for protons were taken. \begin{figure}[htb] \centering \includegraphics[width=0.48\textwidth]{figs/wyttenbach_rate_1p} @@ -805,15 +806,14 @@ not of concern because they have lower kinetic energy compared with protons and higher stopping power, thus are harder to escape the muon stopping target. \begin{figure}[htb] \centering - \includegraphics[width=0.85\textwidth]{figs/proton_impact_CDC} - \caption{Momentum kinetic energy relation of protons, deuterons and alphas - below 10\si{\MeV}. Shaded area is the acceptance of the COMET - Phase-I's CDC. Protons with energies in higher than \SI{2.5}{\MeV} are in the - acceptance of the CDC. Deuterons and alphas at low energies should be stopped - inside the muon stopping target.} + \includegraphics[width=0.85\textwidth]{figs/alcap_proton_vs_acceptance} + \caption{Momentum - kinetic energy relation of protons, deuterons and alphas + at low energy region below 20\si{\MeV}. Charged particles in the shaded + area could reach the COMET Phase-I's CDC, for protons that corresponds + kinetic energies higher than \SI{2.5}{\MeV}. Deuterons and alphas at low + energies should be stopped inside the muon stopping target.} \label{fig:proton_impact_CDC} \end{figure} -%%TODO replace a figure without upper limit The COMET plans to introduce a thin, low-$Z$ proton absorber in between the target and the CDC to reduce proton hit rate. The absorber will be effective @@ -846,7 +846,7 @@ cut-off value of $T_{th}$, its rising edge is governed by the parameter $\alpha$. The exponential decay component dominates at higher energy. The baseline design of the proton absorber for the COMET Phase-I based on -above assumptions is a 1-\si{\mm}-thick CFRP layer as has been described in +above assumptions is a 0.5-\si{\mm}-thick CFRP layer as has been described in \cref{ssub:hit_rate_on_the_cdc}. The hit rate estimation is conservative and the contribution of the absorber to the momentum resolution is not negligible, further optimisation is desirable. Therefore a measurement diff --git a/thesis/chapters/chap5_alcap_setup.tex b/thesis/chapters/chap5_alcap_setup.tex index 52e34bd..a5a17ae 100644 --- a/thesis/chapters/chap5_alcap_setup.tex +++ b/thesis/chapters/chap5_alcap_setup.tex @@ -985,7 +985,7 @@ pile-up or double pulses in one \tpulseisland{} in \cref{fig:tap_maxbin_bad}. The TSimpleMuonEvent first picks a muon candidate, then loops through all pulses on all detector channels, and picks all pulses occur in a time window of \SI{\pm 10}{\si{\us}} around each candidate to build -a muon event. A muon candidates is a hit on the upstream plastic scintillator +a muon event. A muon candidate is a hit on the upstream plastic scintillator with an amplitude higher than a threshold which was chosen to reject MIPs. The period of \SI{10}{\si{\us}} is long enough compared to the mean life time of muons in the target materials diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index e1d0462..fc18da0 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -1,4 +1,4 @@ -\chapter{Data analysis} +\chapter{Data analysis and results} \label{cha:data_analysis} This chapter presents initial analysis on subsets of the collected data. Purposes of the analysis include: @@ -288,7 +288,7 @@ showed that muons penetrated deeper as the momentum increased, reaching the optimal value at the scale of 1.08, then decreased as punch through happened more often from 1.09. The distributions of stopped muons are illustrated by MC results on the right hand side of \cref{fig:al100_scan_rate}. With the 1.09 -scale beam, the muons stopped \SI{28}{\um} off-centre to the right silicon arm. +scale beam, the muons stopped \SI{28}{\um} off-centred to the right silicon arm. \begin{figure}[htb] \centering \includegraphics[width=0.47\textwidth]{figs/al100_scan_rate} @@ -305,7 +305,7 @@ scale beam, the muons stopped \SI{28}{\um} off-centre to the right silicon arm. As described in the \cref{sec:analysis_framework}, the hits on all detectors are re-organised into muon events: central muons; and all hits within \SI{\pm 10}{\us} from the central muons. The dataset from runs -\numrange{2808}{2873} contains \num{1.17E+9} such muon events. +\numrange{2808}{2873} contains \num{1.17E+9} of such muon events. Selection of proton (and other heavy charged particles) events starts from searching for muon event that has at least one hit on thick silicon. If there @@ -431,6 +431,12 @@ number of protons with those energies could reach the detectors. The jump on the right arm at around \SI{9}{\MeV} can be explained as the punch-through protons were counted as the proton veto counters were not used in this analysis. +\begin{figure}[htb] + \centering + \includegraphics[width=0.85\textwidth]{figs/al100_unfolded_lr} + \caption{Unfolded proton spectra from the 100-\si{\um} aluminium target.} + \label{fig:al100_unfold} +\end{figure} %Several studies were conducted to assess the performance of the unfolding %code, including: @@ -467,18 +473,11 @@ The yields of protons from \SIrange{4}{8}{\MeV} are: N_{\textrm{p unfold left}} &= (165.4 \pm 2.7)\times 10^3\\ N_{\textrm{p unfold right}} &= (173.1 \pm 2.9)\times 10^3 \end{align} -Therefore, the number of emitted protons is taken as average value: +The number of emitted protons is taken as average of the two yields: \begin{equation} N_{\textrm{p unfold}} = (169.3 \pm 2.9) \times 10^3 \end{equation} -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/al100_unfolded_lr} - \caption{Unfolded proton spectra from the 100-\si{\um} aluminium target.} - \label{fig:al100_unfold} -\end{figure} - \subsection{Number of nuclear captures} \label{sub:number_of_nuclear_captures} \begin{figure}[htb] @@ -503,16 +502,21 @@ the number of nuclear captures are: \label{sub:proton_emission_rate} The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore: \begin{equation} - R_{\textrm{p}} = \frac{169.3\times 10^3}{9.57\times 10^6} = 1.74\times + R_{\textrm{p}} = \frac{169.3\times 10^3}{9.57\times 10^6} = 1.7\times 10^{-2} \label{eq:proton_rate_al} \end{equation} The total proton emission rate can be estimated by assuming a spectrum shape with the same parameterisation as in \eqref{eqn:EH_pdf}. The fit parameters -are shown in \cref{fig:al100_parameterisation}. With such parameterisation, the -integration in range from \SIrange{4}{8}{\MeV} is 51\% of the total number of -protons. The total proton emission rate is therefore $3.5\times 10^{-2}$. +are shown in \cref{fig:al100_parameterisation} and \cref{tab:al100_fit_pars}. +The average spectrum is obtained by taking the average of the two unfolded +spectra from the left and right arms. The fitted parameters are compatible +with each other within their errors. + +Using the fitted parameters of the average spectrum, the integration in range +from \SIrange{4}{8}{\MeV} is 51\% of the total number of +protons. The total proton emission rate is therefore estimated to be $3.5\times 10^{-2}$. \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/al100_parameterisation} @@ -520,6 +524,27 @@ protons. The total proton emission rate is therefore $3.5\times 10^{-2}$. \label{fig:al100_parameterisation} \end{figure} +\begin{table}[htb] + \begin{center} + \begin{tabular}{l S[separate-uncertainty=true] S[separate-uncertainty=true] + S[separate-uncertainty=true]} + \toprule + \textbf{Parameter} &{\textbf{Left}} & {\textbf{Right}} & {\textbf{Average}}\\ + \midrule + $A \times 10^{-5}$ & 2.0 \pm 0.7 & 1.3 \pm 0.1 & 1.5 \pm 0.3\\ + $T_{th}$ (\si{\keV}) & 1301 \pm 490 & 1966 \pm 68 & 1573 \pm 132\\ + $\alpha$ & 3.2 \pm 0.7 & 1.2 \pm 0.1 & 2.0 \pm 1.2\\ + $T_{th}$ (\si{\keV}) & 2469 \pm 203 & 2641 \pm 106 & 2601 \pm 186\\ + \bottomrule + \end{tabular} + \end{center} + \caption{Parameters of the fits on the unfolded spectra, the average spectrum + is obtained by taking average of the unfolded spectra from left and right + arms.} + \label{tab:al100_fit_pars} +\end{table} + + \subsection{Uncertainties of the emission rate} \label{sub:uncertainties_of_the_emission_rate} The uncertainties of the emission rate come from: @@ -584,4 +609,84 @@ presented in \cref{tab:al100_uncertainties_all}. \label{tab:al100_uncertainties_all} \end{table} -The proton emission rate is then $(3.5 \pm 0.2)$\%. +\section{Results of the initial analysis} +\label{sec:results_of_the_initial_analysis} +\subsection{Verification of the experimental method} +\label{sub:verification_of_the_experimental_method} +The experimental method described in \cref{sub:experimental_method} has been +validated: +\begin{itemize} + \item Number of muon capture normalisation: the number of stopped muons + calculated from the muonic X-ray spectrum is shown to be consistent with + that calculated from the active target spectrum. + \item Particle identification: the particle identification by specific + energy loss has been demonstrated. The banding of different particle + species is clearly visible. The proton extraction method using cut on + likelihood probability has been established. Since the distribution of + $\Delta E$ at a given $E$ is not Gaussian, the fraction of protons that do + not make the cut is 0.5\%, much larger than the threshold at \num{1E-4}. + The fraction of other charged particles being misidentified as protons is + smaller than 0.1\%. These uncertainties from particle identification are + still small in compared with the + uncertainty of the measurement (2.3\%). + \item Unfolding of the proton spectrum: the unfolded spectra inferred from + two measurements at the two silicon arms show good agreement with each + other, and with the muon stopping distribution obtained in the momentum + scanning analysis. +\end{itemize} + +\subsection{Proton emission rates and spectrum} +\label{sub:proton_emission_rates_and_spectrum} +The proton emission spectrum in \cref{sub:proton_emission_rate} peaks around +\SI{4}{\MeV} which is comparable to the Coulomb barrier for proton of +\SI{3.9}{\MeV} calculated using \eqref{eqn:classical_coulomb_barrier}. The +spectrum has a decay constant of \SI{2.6}{\MeV} in higher energy region, +makes the emission probability drop more quickly than silicon charged +particles spectrum of Sobottka and Wills~\cite{SobottkaWills.1968} where the +decay constant was \SI{4.6}{\MeV}. This can be explained as the silicon +spectrum includes other heavier particles which have higher Coulomb barriers, +hence contribute more in the higher energy bins, effectively reduces the decay +rate. + +The partial emission rate measured in the energy range from +\SIrange{4}{8}{\MeV} is: +\begin{equation} + R_{p \textrm{ meas. }} = (1.7 \pm 0.1)\%. + \label{eqn:meas_partial_rate} +\end{equation} + +The total emission rate from aluminium assuming the spectrum shape holds for +all energy is: +\begin{equation} + R_{p \textrm{ total}} = (3.5 \pm 0.2)\%. + \label{eqn:meas_total_rate} +\end{equation} +No direct comparison of this result to existing experimental or +theoretical work is available. Indirectly, it is compatible with the figures +calculated by Lifshitz and +Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980} listed in +\cref{tab:lifshitzsinger_cal_proton_rate}. It is significantly larger than +the rate of 0.97\% for the $(\mu,\nu p)$ channel, and does not +exceed the inclusion rate for all channels $\Sigma(\mu,\nu p(xn))$ at 4\%, +leaving some room for other modes such as $(\mu,\nu d)$ or $(\mu,\nu p2n)$. +Certainly, if the rate of deuterons can be extracted then the combined +emission rate of protons and deuterons could be compared directly with the +inclusive rate. + +The result \eqref{eqn:meas_total_rate} is greater than the +probability of the reaction $(\mu,\nu pn)$ measured by Wyttenbach et +al.~\cite{WyttenbachBaertschi.etal.1978} at 2.8\%. It is expectable because +the contribution from the $(\mu,\nu d)$ channel should be small since it +needs to form a deuteron from a proton and a neutron. +%The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in +%\eqref{eqn:wyttenbach_ratio}. + +Compared with emission rate from silicon, the result +\eqref{eqn:meas_total_rate} is indeed much smaller. It is even lower than +the rate of the no-neutron reaction $(\mu,\nu p)$. This can be explained as +the resulted nucleus from muon capture on silicon, $^{28}$Al, is an odd-odd +nucleus and less stable than that from aluminium, $^{27}$Mg. The proton +separation energy for $^{28}$Al is \SI{9.6}{\MeV}, which is significantly +lower than that of $^{27}$Mg at \SI{15.0}{\MeV}~\cite{AudiWapstra.etal.2003}. + + diff --git a/thesis/chapters/chap7_results.tex b/thesis/chapters/chap7_results.tex index 39b77bd..64da318 100644 --- a/thesis/chapters/chap7_results.tex +++ b/thesis/chapters/chap7_results.tex @@ -1,50 +1,53 @@ -\chapter{Results and discussions} -\label{cha:results_and_discussions} -\section{Verification of the experimental method} -\label{sec:verification_of_the_experimental_method} -\subsection{Number of stopped muons calculation} -\label{sub:number_of_stopped_muons_normalisation} -The number of stopped muons calculated from the muonic X-ray spectrum is shown -to be consistent with that calculated from the active target spectrum. This -proves the validity of normalisation using muon X-ray measurement. -\subsection{Particle identification and unfolding} -\label{sub:particle_identification_and_unfolding} -The particle identification using specific energy loss using cut on -likelihood probability is shown in -\cref{sub:event_selection_for_the_passive_targets}. Since the distribution of -$\Delta E$ at a given $E$ is not Gaussian, the fraction of protons that do not -make the cut is 0.5\%, much larger than the threshold at \num{1E-4}. However, -that missing fraction is small compared to the statistical uncertainty of the -measurement (2.3\%) so the threshold is sufficient. +\chapter{Discussions on the impact to the COMET Phase-I} +\label{cha:discussions_on_the_impact_to_the_comet_phase_i} +The measured proton emission rate of 3.5\% is about 5 times +smaller than the figure using to make the baseline design of the CDC in COMET +Phase-I. The spectrum shape +peaks around \SI{4}{\MeV} rather than at \SI{2.5}{\MeV}, and decays more +quickly in compared with the silicon spectrum(\cref{fig:sobottka_spec}). +Therefore CDC hit rate due to proton should be smaller than the current +estimation. -The observed spectra on the two silicon arms reflect the muon stopping -distribution discussed in \cref{sub:momentum_scan_for_the_100_} where more -muons stopped at the downstream side of the target. The proton yields -calculated from two arms are consistent with each other, and show that the muon -stopping distribution used to generate the response matrices is reasonable. +The CDC proton hit rate is calculated by a toy MC study. The dimensions of the +geometry shown in \cref{fig:cdc_toy_mc} are from \cref{ssub:CDC_configuration}. +The inner wall of the CDC is \SI{0.5}{\mm} thick CFRP. +A proton absorber made +of CFRP is placed \SI{5}{\cm} far from the inner wall of the CDC. The +absorber's thickness is varied from 0 (no absorber) to \SI{1}{\mm}. +\begin{figure}[htb] + \centering + \includegraphics[width=0.55\textwidth]{figs/cdc_toy_mc} + \caption{Geometry of the toy MC study for hit rate study.} + \label{fig:cdc_toy_mc} +\end{figure} -\section{Emission rate of protons and the COMET Phase I's CDC} -\label{sec:emission_rate_of_protons_and_the_comet_phase_i_s_cdc} -The proton emission rate from the 100-\si{\um} aluminium target is -$(3.5 \pm 0.2)$\%. This rate is significantly larger than the calculation rate -of 0.97\% by Lifshitz and Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980}. -The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in -\eqref{eqn:wyttenbach_ratio}. -The rate smaller that the proton emission rate from silicon of -5.3\%~\cite{Measday.2001} which is expected since an odd-odd nucleus as -$^{28}$Al is less stable than an even-odd one. +The protons with the energy spectrum shape as in +\cref{sub:proton_emission_rate} are generated inside the COMET's muon stopping +targets which are 17 200-\si{\um}-thick aluminium discs. The spatial +distribution of protons resembles the stopping distribution of muons inside the +target discs calculated from the full MC simulation of the COMET detectors +(\cref{fig:cdc_toy_mc_init_pos}). +\begin{figure}[htb] + \centering + \includegraphics[width=0.65\textwidth]{figs/cdc_toy_mc_init_pos_xy} + \includegraphics[width=0.60\textwidth]{figs/cdc_toy_mc_init_pos_z} + \caption{Spatial distribution of the generated protons in X, Y (top) and + Z (bottom). Z is the axis of the CDC, X, Y are the horizontal and vertical + axes respectively.} + \label{fig:cdc_toy_mc_init_pos} +\end{figure} -For the COMET Phase I experiment, the emission rate of 3.5\% is about 5 times -smaller than the figure using to design the CDC. The measured spectrum shape -peaks around \SI{4}{\MeV} rather than \SI{2.5}{\MeV} in the silicon -spectrum(\cref{fig:sobottka_spec}). Therefore the proton hit rate on the CDC -should be smaller than the current estimation. +The protons are then tracked in a \SI{1}{\tesla} magnetic field. The protons +reaching the absorber, inner wall and the sensitive volume of the CDC are +recorded (see \cref{fig:cdc_toy_mc_p_spec_500um}). +\begin{figure}[!htb] + \centering + \includegraphics[width=0.75\textwidth]{figs/cdc_toy_mc_p_spec_500um} + \caption{Toy MC study of the CDC hit rate due to protons. The absorber + thickness was set at \SI{0.5}{\mm} in this plot.} + \label{fig:cdc_toy_mc_p_spec_500um} +\end{figure} -The CDC proton hit rate is calculated by a toy MC study. The protons with the -energy spectrum as the parameterisation in \cref{sub:proton_emission_rate} are -generated inside the COMET's muon stopping targets which are 17 -200-\si{\um}-thick aluminium discs. A proton absorber made of CFRP is placed -\SI{5}{\cm} far from the inner wall of the CDC. A muon stopping rate of \SI{1.3E9}{\Hz} is assumed as in the COMET Phase I's TDR. The number of proton emitted is then $\num{1.3E9} \times 0.609 \times 0.035 = \SI{2.8E7}{\Hz}$. The hit rates on a single cell in the inner most @@ -52,13 +55,19 @@ layer due to these protons with different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. \begin{table}[htb] \begin{center} - \begin{tabular}{l r} + \begin{tabular}{S S S S} \toprule - \textbf{Absorber thickness} & \textbf{Hit rate}\\ + {\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& + {\textbf{Proton}}\\ + {\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& + {\textbf{hit rate}}\\ + {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}\\ \midrule - \SI{1}{\mm} & \SI{2}{\Hz}\\ - \SI{0.5}{\mm} & \SI{126}{\Hz}\\ - \SI{0}{\mm} & \SI{1436}{\Hz}\\ + 1 &0.5&1.5 & 2\\ + 0.5 &0.5&1.0 & 126\\ + 0 &0.5&0.5 & 1436\\ + 0 &0.3&0.3 & 8281\\ + 0 &0.1&0.1 & 15011\\ \bottomrule \end{tabular} \end{center} @@ -66,7 +75,14 @@ different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. \label{tab:proton_cdc_hitrate} \end{table} -The proton hit rate even without the absorber is only \SI{1.4}{\kHz}, much -smaller than the current estimation of \SI{11}{\kHz} (using 1-mm-thick -absorber). Therefore a proton absorber is not needed for the COMET Phase I's -CDC. +At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz}, +much smaller than the current estimation at \SI{34}{\kHz}. Even without the +absorber, proton hit rate remains low at \SI{1.4}{\kHz}. Therefore a proton +absorber is not needed for the COMET Phase I's CDC. + +Without the proton absorber, the momentum spread of the signal electron +reduces from \SI{167}{\keV} to \SI{131}{\keV}. If a lower momentum spread is +desired, it is possible to reduce the thickness of the inner wall. The last +two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at +\SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at +manageable levels. diff --git a/thesis/chapters/frontmatter.tex b/thesis/chapters/frontmatter.tex index 4fa23f9..1dabec7 100644 --- a/thesis/chapters/frontmatter.tex +++ b/thesis/chapters/frontmatter.tex @@ -25,11 +25,21 @@ approach in which the first phase, COMET Phase-I [3], starts in 2013 and initial data taking in around 2017. In order to optimize detector design for the Phase-I, backgrounds from nuclear -muon capture are crucial. We have proposed a dedicated experiment , namely -AlCap, at PSI, Switzerland to study the backgrounds, including: heavy charged -particles, neutrons and photons. The measurements of heavy charged particles -have been carried out in the 2013 run and the preliminary analysis results are -presented in this thesis. +muon capture are crucial. We have proposed a dedicated experiment, namely +AlCap, at PSI, Switzerland to study the backgrounds, including protons, +neutrons and photons. The measurements of proton rate and spectrum on +aluminium have been carried out in the 2013 run. The second run to study +neutrons and photons is planned in 2015. + +The preliminary results from the analysis of the 2013 run are presented in this +thesis. The measured proton spectrum peaks at \SI{4}{\MeV} and decays +exponentially with the decay constant of \SI{2.6}{\MeV}. The emission +rate of protons in the energy range from \SIrange{4}{8}{\MeV} is +$(1.7\pm0.1)\%$. The total proton emission rate is estimated to be +$(3.5\pm0.2)\%$ assuming the spectrum shape holds. +The resulted proton rate and spectrum were used to optimise the tracking +detector hit rate of the COMET Phase-I. + \end{abstract} @@ -58,7 +68,7 @@ presented in this thesis. %\begin{preface} %\thispagestyle{empty} %The thesis is about measurements of products of nuclear muon capture on an - %aluminum target, which is important for optimization of a tracking detector + %aluminium target, which is important for optimization of a tracking detector %of a search for muon to electron conversion, the E21 experiment - so called %COMET - at Japan Proton Accelerator Complex (J-PARC). %\end{preface} diff --git a/thesis/thesis.tex b/thesis/thesis.tex index b980c80..aec31ac 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -29,14 +29,14 @@ for the COMET experiment} \end{frontmatter} \mainmatter -%\input{chapters/chap1_intro} -%\input{chapters/chap2_mu_e_conv} -%\input{chapters/chap3_comet} -%\input{chapters/chap4_alcap_phys} +%%%\input{chapters/chap1_intro} +\input{chapters/chap2_mu_e_conv} +\input{chapters/chap3_comet} +\input{chapters/chap4_alcap_phys} \input{chapters/chap5_alcap_setup} -%\input{chapters/chap6_analysis} -%\input{chapters/chap7_results} -%\input{chapters/chap8_conclusions} +\input{chapters/chap6_analysis} +\input{chapters/chap7_results} +\input{chapters/chap8_conclusions} \begin{backmatter} \input{chapters/backmatter}