nam/writeup
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

prog saved

Browse Source
This commit is contained in:
nam
2014-10-30 18:56:57 +09:00
parent 95744773fe
commit 567b61715b
9 changed files with 290 additions and 114 deletions
Download Patch File Download Diff File Expand all files Collapse all files

4
thesis/chapters/chap1_intro.tex
View File

@@ -64,7 +64,7 @@ by the
SINDRUM-II~\cite{Bertl.etal.2006}. A staging approach is adopted at the COMET 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 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 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 three-month running period.
A cylindrical drift chamber being developed by the Osaka University group 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}: 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 physics, method, experimental set up, data analysis. The results and impacts of
the study on COMET Phase-I design is discussed in 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) % chapter introduction (end)

44
thesis/chapters/chap2_mu_e_conv.tex
View File

@@ -1,7 +1,49 @@
\chapter{Lepton flavour and $\mu-e$ conversion} \chapter{Overview}
\thispagestyle{empty} \thispagestyle{empty}
\label{cha:clfv} \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} \section{Lepton flavour}
\label{sec:lepton_flavour} \label{sec:lepton_flavour}
According to the SM, all matter is built from a small set of fundamental According to the SM, all matter is built from a small set of fundamental

37
thesis/chapters/chap3_comet.tex
View File

@@ -642,7 +642,7 @@ CyDet.
\end{figure} \end{figure}
\subsubsection{CDC configuration} \subsubsection{CDC configuration}
\label{ssub:CDC configuration} \label{ssub:CDC_configuration}
The CDC is the main tracking detector that provides information for The CDC is the main tracking detector that provides information for
reconstruction of charged particle tracks and measuring their momenta. The key reconstruction of charged particle tracks and measuring their momenta. The key
parameters for the CDC are listed in the 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 Phase-I, we use a conservative estimation of the rate of protons from energy
spectrum of charged particles emitted from muon capture in spectrum of charged particles emitted from muon capture in
$^{28}$Si~\cite{SobottkaWills.1968}. The baseline design for the proton $^{28}$Si~\cite{SobottkaWills.1968}. The baseline design for the proton
absorber is 1.0~\si{\milli\meter}-thick CFRP, making the total thickness absorber is 0.5~\si{\milli\meter}-thick CFRP, making the total thickness
of material before the sensitive region is \SI{1.5}{\mm} in CFRP. In this of material before the sensitive region is \SI{1.0}{\mm} in CFRP. In this
configuration, the inner wall and the proton absorber deteriorate the momentum configuration, the inner wall and the proton absorber contribute a spread of
resolution of the reconstructed track to 195~\si{\kilo\electronvolt\per\cc}. \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 The impact of the proton absorber on the CDC's hit rate and momentum
resolution is summarised in \cref{tab:comet_absorber_impact}. resolution is summarised in \cref{tab:comet_absorber_impact}.
\begin{table}[htb] \begin{table}[htb]
\begin{center} \begin{center}
\begin{tabular}{@{}ccc@{}} \begin{tabular}{@{}cccc@{}}
\toprule \toprule
\textbf{Absorber }& \textbf{Proton }& \textbf{Momentum }\\ \textbf{Absorber }& \textbf{Total CFRP }&\textbf{Proton }&
\textbf{thickness }& \textbf{hit rate }& \textbf{resolution }\\ \textbf{$\Delta p$}\\
(\si{\um}) & (\si{\kHz}) & (\si{\keV\per\cc}) \\ \textbf{thickness }& \textbf{thickness }&\textbf{hit rate }& \\
(\si{\mm}) &(\si{\mm}) & (\si{\kHz}) & (\si{\keV\per\cc}) \\
\midrule \midrule
0 & 130 & 131 \\ 0 & 0.5 & 130 & 131 \\
0.5 & 34 & 167 \\ 0.5 & 1.0 & 34 & 167 \\
1.0 & 11 & 195 \\ 1.0 & 1.5 & 11 & 195 \\
1.5 & 6 & 252 \\ 1.5 & 2.0 & 6 & 252 \\
\bottomrule \bottomrule
\end{tabular} \end{tabular}
\end{center} \end{center}
\caption{Hit rates and contributions to momentum resolution of the proton \caption{Hit rates and contributions to momentum spread of the proton
absorber and inner wall of the CDC. The intrinsic momentum resolution due absorber and inner wall of the CDC. The resolutions are calculated for
to multiple scattering is \SI{197}{\keV\per\cc}.} mono-energetic electrons of \SI{104.96}{\MeV\per\cc}.}
\label{tab:comet_absorber_impact} \label{tab:comet_absorber_impact}
\end{table} \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. is described in detail in next chapters.
It should be noted that the proton hit rate is not a problem for the COMET 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. protons emitted.
% subsection detectors_for_mueconv_search_in_the_phase_i (end) % subsection detectors_for_mueconv_search_in_the_phase_i (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

24
thesis/chapters/chap4_alcap_phys.tex
View File

@@ -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 $(\mu^-,\nu\alpha)$ $(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$, $(\mu^-,\nu p3n)$ and $(\mu^-,\nu\alpha)$
in a wide range of 18 elements from sodium to bismuth.Their results plotted 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 against the Coulomb barrier for the outgoing protons are given in
\cref{fig:wyttenbach_rate_1p} and \cref{fig:wyttenbach_rate_23p}. The \cref{fig:wyttenbach_rate_1p}.
classical Coulomb barrier $V$ they used are given by: %and \cref{fig:wyttenbach_rate_23p}.
The classical Coulomb barrier $V$ they used are given by:
\begin{equation} \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} \label{eqn:classical_coulomb_barrier}
\end{equation} \end{equation}
where $z$ and $Z$ are the charges of the outgoing particle and of the residual 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 nucleus respectively, $e^2 = 1.44 \si{\MeV}$, $r_0 = 1.35 \textrm{ fm}$, and
protons were taken. $\rho = 0 \textrm{ fm}$ for protons were taken.
\begin{figure}[htb] \begin{figure}[htb]
\centering \centering
\includegraphics[width=0.48\textwidth]{figs/wyttenbach_rate_1p} \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. higher stopping power, thus are harder to escape the muon stopping target.
\begin{figure}[htb] \begin{figure}[htb]
\centering \centering
\includegraphics[width=0.85\textwidth]{figs/proton_impact_CDC} \includegraphics[width=0.85\textwidth]{figs/alcap_proton_vs_acceptance}
\caption{Momentum kinetic energy relation of protons, deuterons and alphas \caption{Momentum - kinetic energy relation of protons, deuterons and alphas
below 10\si{\MeV}. Shaded area is the acceptance of the COMET at low energy region below 20\si{\MeV}. Charged particles in the shaded
Phase-I's CDC. Protons with energies in higher than \SI{2.5}{\MeV} are in the area could reach the COMET Phase-I's CDC, for protons that corresponds
acceptance of the CDC. Deuterons and alphas at low energies should be stopped kinetic energies higher than \SI{2.5}{\MeV}. Deuterons and alphas at low
inside the muon stopping target.} energies should be stopped inside the muon stopping target.}
\label{fig:proton_impact_CDC} \label{fig:proton_impact_CDC}
\end{figure} \end{figure}
%%TODO replace a figure without upper limit
The COMET plans to introduce a thin, low-$Z$ proton absorber in between the 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 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. $\alpha$. The exponential decay component dominates at higher energy.
The baseline design of the proton absorber for the COMET Phase-I based on 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 \cref{ssub:hit_rate_on_the_cdc}. The hit rate estimation is
conservative and the contribution of the absorber to the momentum resolution conservative and the contribution of the absorber to the momentum resolution
is not negligible, further optimisation is desirable. Therefore a measurement is not negligible, further optimisation is desirable. Therefore a measurement

2
thesis/chapters/chap5_alcap_setup.tex
View File

@@ -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 The TSimpleMuonEvent first picks a muon candidate, then loops through all
pulses on all detector channels, and picks all pulses occur in 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 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 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 period of \SI{10}{\si{\us}} is long enough compared to the mean life time of
muons in the target materials muons in the target materials

137
thesis/chapters/chap6_analysis.tex
View File

@@ -1,4 +1,4 @@
\chapter{Data analysis} \chapter{Data analysis and results}
\label{cha:data_analysis} \label{cha:data_analysis}
This chapter presents initial analysis on subsets of the collected data. This chapter presents initial analysis on subsets of the collected data.
Purposes of the analysis include: 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 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 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 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] \begin{figure}[htb]
\centering \centering
\includegraphics[width=0.47\textwidth]{figs/al100_scan_rate} \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 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 are re-organised into muon events: central muons; and all hits within
\SI{\pm 10}{\us} from the central muons. The dataset from runs \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 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 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 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 protons were counted as the proton veto counters were not used in this
analysis. 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 %Several studies were conducted to assess the performance of the unfolding
%code, including: %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 left}} &= (165.4 \pm 2.7)\times 10^3\\
N_{\textrm{p unfold right}} &= (173.1 \pm 2.9)\times 10^3 N_{\textrm{p unfold right}} &= (173.1 \pm 2.9)\times 10^3
\end{align} \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} \begin{equation}
N_{\textrm{p unfold}} = (169.3 \pm 2.9) \times 10^3 N_{\textrm{p unfold}} = (169.3 \pm 2.9) \times 10^3
\end{equation} \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} \subsection{Number of nuclear captures}
\label{sub:number_of_nuclear_captures} \label{sub:number_of_nuclear_captures}
\begin{figure}[htb] \begin{figure}[htb]
@@ -503,16 +502,21 @@ the number of nuclear captures are:
\label{sub:proton_emission_rate} \label{sub:proton_emission_rate}
The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore: The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore:
\begin{equation} \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} 10^{-2}
\label{eq:proton_rate_al} \label{eq:proton_rate_al}
\end{equation} \end{equation}
The total proton emission rate can be estimated by assuming a spectrum shape The total proton emission rate can be estimated by assuming a spectrum shape
with the same parameterisation as in \eqref{eqn:EH_pdf}. The fit parameters with the same parameterisation as in \eqref{eqn:EH_pdf}. The fit parameters
are shown in \cref{fig:al100_parameterisation}. With such parameterisation, the are shown in \cref{fig:al100_parameterisation} and \cref{tab:al100_fit_pars}.
integration in range from \SIrange{4}{8}{\MeV} is 51\% of the total number of The average spectrum is obtained by taking the average of the two unfolded
protons. The total proton emission rate is therefore $3.5\times 10^{-2}$. 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] \begin{figure}[htb]
\centering \centering
\includegraphics[width=0.85\textwidth]{figs/al100_parameterisation} \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} \label{fig:al100_parameterisation}
\end{figure} \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} \subsection{Uncertainties of the emission rate}
\label{sub:uncertainties_of_the_emission_rate} \label{sub:uncertainties_of_the_emission_rate}
The uncertainties of the emission rate come from: The uncertainties of the emission rate come from:
@@ -584,4 +609,84 @@ presented in \cref{tab:al100_uncertainties_all}.
\label{tab:al100_uncertainties_all} \label{tab:al100_uncertainties_all}
\end{table} \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}.

120
thesis/chapters/chap7_results.tex
View File

@@ -1,50 +1,53 @@
\chapter{Results and discussions} \chapter{Discussions on the impact to the COMET Phase-I}
\label{cha:results_and_discussions} \label{cha:discussions_on_the_impact_to_the_comet_phase_i}
\section{Verification of the experimental method} The measured proton emission rate of 3.5\% is about 5 times
\label{sec:verification_of_the_experimental_method} smaller than the figure using to make the baseline design of the CDC in COMET
\subsection{Number of stopped muons calculation} Phase-I. The spectrum shape
\label{sub:number_of_stopped_muons_normalisation} peaks around \SI{4}{\MeV} rather than at \SI{2.5}{\MeV}, and decays more
The number of stopped muons calculated from the muonic X-ray spectrum is shown quickly in compared with the silicon spectrum(\cref{fig:sobottka_spec}).
to be consistent with that calculated from the active target spectrum. This Therefore CDC hit rate due to proton should be smaller than the current
proves the validity of normalisation using muon X-ray measurement. estimation.
\subsection{Particle identification and unfolding}
\label{sub:particle_identification_and_unfolding}
The particle identification using specific energy loss using cut on
likelihood probability is shown in
\cref{sub:event_selection_for_the_passive_targets}. Since the distribution of
$\Delta E$ at a given $E$ is not Gaussian, the fraction of protons that do not
make the cut is 0.5\%, much larger than the threshold at \num{1E-4}. However,
that missing fraction is small compared to the statistical uncertainty of the
measurement (2.3\%) so the threshold is sufficient.
The observed spectra on the two silicon arms reflect the muon stopping The CDC proton hit rate is calculated by a toy MC study. The dimensions of the
distribution discussed in \cref{sub:momentum_scan_for_the_100_} where more geometry shown in \cref{fig:cdc_toy_mc} are from \cref{ssub:CDC_configuration}.
muons stopped at the downstream side of the target. The proton yields The inner wall of the CDC is \SI{0.5}{\mm} thick CFRP.
calculated from two arms are consistent with each other, and show that the muon A proton absorber made
stopping distribution used to generate the response matrices is reasonable. 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} The protons with the energy spectrum shape as in
\label{sec:emission_rate_of_protons_and_the_comet_phase_i_s_cdc} \cref{sub:proton_emission_rate} are generated inside the COMET's muon stopping
The proton emission rate from the 100-\si{\um} aluminium target is targets which are 17 200-\si{\um}-thick aluminium discs. The spatial
$(3.5 \pm 0.2)$\%. This rate is significantly larger than the calculation rate distribution of protons resembles the stopping distribution of muons inside the
of 0.97\% by Lifshitz and Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980}. target discs calculated from the full MC simulation of the COMET detectors
The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in (\cref{fig:cdc_toy_mc_init_pos}).
\eqref{eqn:wyttenbach_ratio}. \begin{figure}[htb]
The rate smaller that the proton emission rate from silicon of \centering
5.3\%~\cite{Measday.2001} which is expected since an odd-odd nucleus as \includegraphics[width=0.65\textwidth]{figs/cdc_toy_mc_init_pos_xy}
$^{28}$Al is less stable than an even-odd one. \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 The protons are then tracked in a \SI{1}{\tesla} magnetic field. The protons
smaller than the figure using to design the CDC. The measured spectrum shape reaching the absorber, inner wall and the sensitive volume of the CDC are
peaks around \SI{4}{\MeV} rather than \SI{2.5}{\MeV} in the silicon recorded (see \cref{fig:cdc_toy_mc_p_spec_500um}).
spectrum(\cref{fig:sobottka_spec}). Therefore the proton hit rate on the CDC \begin{figure}[!htb]
should be smaller than the current estimation. \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 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 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 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}. different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}.
\begin{table}[htb] \begin{table}[htb]
\begin{center} \begin{center}
\begin{tabular}{l r} \begin{tabular}{S S S S}
\toprule \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 \midrule
\SI{1}{\mm} & \SI{2}{\Hz}\\ 1 &0.5&1.5 & 2\\
\SI{0.5}{\mm} & \SI{126}{\Hz}\\ 0.5 &0.5&1.0 & 126\\
\SI{0}{\mm} & \SI{1436}{\Hz}\\ 0 &0.5&0.5 & 1436\\
0 &0.3&0.3 & 8281\\
0 &0.1&0.1 & 15011\\
\bottomrule \bottomrule
\end{tabular} \end{tabular}
\end{center} \end{center}
@@ -66,7 +75,14 @@ different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}.
\label{tab:proton_cdc_hitrate} \label{tab:proton_cdc_hitrate}
\end{table} \end{table}
The proton hit rate even without the absorber is only \SI{1.4}{\kHz}, much At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz},
smaller than the current estimation of \SI{11}{\kHz} (using 1-mm-thick much smaller than the current estimation at \SI{34}{\kHz}. Even without the
absorber). Therefore a proton absorber is not needed for the COMET Phase I's absorber, proton hit rate remains low at \SI{1.4}{\kHz}. Therefore a proton
CDC. 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.

20
thesis/chapters/frontmatter.tex
View File

@@ -26,10 +26,20 @@ initial data taking in around 2017.
In order to optimize detector design for the Phase-I, backgrounds from nuclear In order to optimize detector design for the Phase-I, backgrounds from nuclear
muon capture are crucial. We have proposed a dedicated experiment, namely muon capture are crucial. We have proposed a dedicated experiment, namely
AlCap, at PSI, Switzerland to study the backgrounds, including: heavy charged AlCap, at PSI, Switzerland to study the backgrounds, including protons,
particles, neutrons and photons. The measurements of heavy charged particles neutrons and photons. The measurements of proton rate and spectrum on
have been carried out in the 2013 run and the preliminary analysis results are aluminium have been carried out in the 2013 run. The second run to study
presented in this thesis. 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} \end{abstract}
@@ -58,7 +68,7 @@ presented in this thesis.
%\begin{preface} %\begin{preface}
%\thispagestyle{empty} %\thispagestyle{empty}
%The thesis is about measurements of products of nuclear muon capture on an %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 %of a search for muon to electron conversion, the E21 experiment - so called
%COMET - at Japan Proton Accelerator Complex (J-PARC). %COMET - at Japan Proton Accelerator Complex (J-PARC).
%\end{preface} %\end{preface}

14
thesis/thesis.tex
View File

@@ -29,14 +29,14 @@ for the COMET experiment}
\end{frontmatter} \end{frontmatter}
\mainmatter \mainmatter
%\input{chapters/chap1_intro} %%%\input{chapters/chap1_intro}
%\input{chapters/chap2_mu_e_conv} \input{chapters/chap2_mu_e_conv}
%\input{chapters/chap3_comet} \input{chapters/chap3_comet}
%\input{chapters/chap4_alcap_phys} \input{chapters/chap4_alcap_phys}
\input{chapters/chap5_alcap_setup} \input{chapters/chap5_alcap_setup}
%\input{chapters/chap6_analysis} \input{chapters/chap6_analysis}
%\input{chapters/chap7_results} \input{chapters/chap7_results}
%\input{chapters/chap8_conclusions} \input{chapters/chap8_conclusions}
\begin{backmatter} \begin{backmatter}
\input{chapters/backmatter} \input{chapters/backmatter}