Intro copied from various places

thesis/Makefile

@@ -8,14 +8,13 @@ EXTRASTYS = abhepexpt.sty abhep.sty abmath.sty lineno.sty siunitx.sty SIunits.st
 
 default: $(TARGET)
 
-$(TARGET): $(INPUT) extrastyles.zip $(THESIS_STY) Makefile
+$(TARGET): $(INPUT) extrastyles.zip $(THESIS_STY) Makefile chapters/*.tex
 	@rm -f $(EXTRASTYS)
 	@unzip extrastyles.zip
 	@rm -f $(DOCNAME).{aux,toc,lof,lot}
 	pdflatex $< && bibtex $(DOCNAME) && pdflatex $< && pdflatex $<
 	@rm -f $(DOCNAME).{aux,toc,lof,lot}
 	@rm -f $(EXTRASTYS)
-	#pdflatex --enable-write18 $< &&	pdflatex $<
 
 clean:
 	@rm -f $(EXTRASTYS)

thesis/chapters/chap1.tex

@@ -1,20 +1,251 @@
 \chapter{Introduction}
-\label{chap:SomeStuff}
+\label{chap:intro}
 
 %% Restart the numbering to make sure that this is definitely page #1!
 \pagenumbering{arabic}
-\section{$\mu - e$ conversion}
-\label{sec:_mu_e_conversion}
 
-\section{Motivation}
+\section{Muon to electron conversion}
-\label{sec:motivation}
+\label{sec:_mu_e_conversion}
+Charged lepton flavor violation (CLFV) belongs to the class of flavor-changing
+neutral currents, which are suppressed at tree level in the Standard Model
+(SM) where they are mediated by $\gamma$ and $Z^0$ bosons, but arise at loop
+level via weak charged currents mediated by the $W^{\pm}$ boson. Because flavor
+violation requires mixing between generations, CLFV exactly vanishes in the SM
+with massless neutrinos. Even in the framework of the SM with massive neutrinos
+and their mixing, branching ratio of CLFV is still very small - for example, in
+case of \mueg~\cite{marciano}:
+\begin{equation}
+	\mathcal{B}(\mu^{+} \rightarrow e^{+}\gamma) \simeq 
+	10^{-54} \left( \frac{sin^{2}2\theta_{13}}{0.15}\right)
+\end{equation}
+This is an unobservably tiny
+branching ratio so that any experimental evidence of CLFV would be a clear
+sign of new physics beyond the SM.
+
+One of the most prominent CLFV processes is
+a process of coherent muon-to-electron conversion ($\mu
+- e$ conversion) in the field of a nucleus: \muecaz. When muons are stopped in
+a target, they are quickly
+captured by atoms ($~10^{-10}$ s) and cascade down to the 1S orbitals. There,
+they can undergo:
+(a) ordinary decay, (b) weak capture, $\mu^- p \rightarrow \nu_\mu n$, or (c)
+$\mu - e$ conversion, \muec. The last of these reactions is a CLFV process
+where lepton flavor numbers, $L_\mu$ and $L_e$, are violated by one unit.
+
+The $\mu - e $ conversion is attractive both from theoretical and experimental
+points of view. Many extensions of the SM predict that it would has sizeable
+branching ratio~\cite{altman}. One possible supersymmetric contribution to the
+$\mu - e$ conversion is shown in Fig.~\ref{fig:susy_contr}. Experimentally, the
+simplicity and distinctive signal, a mono-energetic electron of energy $E_{e}$:
+$	
+	E_{e} = m_{\mu} - B_{\mu}(Z, A) - R(A) \simeq \textrm{105 MeV},
+$
+where $m_\mu$ is the muon mass, $B_\mu(Z, A)$ is the muonic atom binding
+energy, and $R(A)$ is the nuclear recoil energy, allow experimental searches
+without accidentals and thus in extremely high rates. As a result, one of the
+best upper limits of CLFV searches comes from a search for $\mu - e$ conversion
+in muonic gold done by the SINDRUM--II collaboration:
+\sindrumlimit~\cite{sindrumii}.
+
+\begin{figure}[tbh]
+	\centering
+	\includegraphics[width=\textwidth]{figs/susy_contr}
+	\caption{Possible SUSY contributions to the CLFV processes \mueg
+	(left) and \muec (right).}
+	\label{fig:susy_contr}
+\end{figure}
+
+%\section{Motivation}
+%\label{sec:motivation}
 
 \subsection{COMET experiment}
+
+At the Japan Proton Accelerator Research Complex (J-PARC), an experiment to
+search for \muec~conversion, which is called COMET (COherent Muon to Electron
+Transition), has been proposed~\cite{comet07}. The experiment received Stage--1
+approval in
+2009. Utilising a proton beam of 56 kW (8 GeV $\times$ 7 $\mu$A) from the
+J-PARC main ring, the COMET aims for a single event sensitivity of $3 \times
+10^{-17}$, which is 10000 times better than the current best
+limit at SINDRUM--II. As of April 2013, the COMET collaboration has 117
+members in 27 institutes from 12 countries.
+
+The COMET experiment is designed to be carried out at the Hadron
+Experimental Facility using a bunched proton beam that is
+slowly-extracted from the J-PARC main ring. The experimental set-up consists of
+a dedicated proton beam line, a muon beam transport section, and a detector
+section. The muon beam section is composed of superconducting magnets: pion
+capture solenoid and a pion/muon transport solenoid. The
+detector section has a multi-layered muon stopping target, an electron
+transport beam line for $\mu - e$ conversion signals,
+followed by detector systems. 
+
+The COMET collaboration has adopted a staging approach with two
+phases~\cite{comet12}. COMET Phase--I  is scheduled to
+have an engineering run in 2016, followed by a physics run in 2017. Phase--I
+should achieve a sensitivity
+of $3 \times 10^{-15}$, 100 times better than that of SINDRUM--II; while
+Phase--II will reach a sensitivity of $2.6 \times 10^{-17}$, which is
+competitive with the Mu2e project at Fermilab~\cite{mu2e08}.
+A schematic layout of the COMET experiment with its two phases is
+shown in Fig.~\ref{fig:comet_phase1}, and a schedule for two phases is shown in
+Fig.~\ref{fig:sched}.
+\begin{figure}[tbh]
+	\centering
+\includegraphics[width=\textwidth]{figs/comet_phase1}
+\caption{Schematic layout of the COMET experiment with two phases: Phase--I
+(left) and Phase--II (right).}
+\label{fig:comet_phase1}
+\end{figure}
+
+\begin{figure}[tbh]
+	\centering
+\includegraphics[width=0.8\textwidth]{figs/sched}
+\caption{The anticipated schedule of the COMET experiment.}
+\label{fig:sched}
+\end{figure}
+
+COMET Phase--I has two major goals:
+\begin{itemize}
+	\item Background study for the COMET Phase--II by using the actual COMET beam
+		line constructed at Phase--I, 
+	\item Search for $\mu-e$ conversion with a single event sensitivity of $3
+		\times 10^{-15}$.
+\end{itemize}
+
+In order to realize the goals, COMET Phase--I proposes to have two systems of
+detector. A straw tube detector and an electromagnetic calorimeter will be used
+for the background study. For the $\mu-e$ conversion search, a cylindrical
+drift chamber (CDC) will be built.
+
 \subsection{Proton emission issue}
+We, as a jointed force between Mu2e and COMET, would like to measure rates and
+energy spectrum of charged particle emission after nuclear muon capture on
+aluminum. The rates and spectra of charged particle emission, in particular
+protons, is very important to optimize the detector configuration both for the
+Mu2e and COMET Phase-I experiments. 
+
+\noindent The tracking chambers of COMET Phase-I and Mu2e are designed to be
+measure charged particles of their momenta greater than 70 MeV/$c$ and 53
+MeV/$c$ respectively. In that momentum ranges, it turns out that single hit
+rates of the tracking chambers would be dominated by protons after nuclear muon
+capture.
+The second source of the hit rate will be electrons from muon decays in orbit
+(DIO). In order to limit the single hit rate of the tracking chamber to an
+acceptable level, both experiments are considering to place proton absorbers in
+front of the tracking chambers to reduce proton hit rates. However, the proton
+absorber would deteriorate the reconstructed momentum resolution of electrons
+at birth. And similarly the rate of proton emission is important to determine
+thickness of the muon stopping target made of aluminum. Therefore it is
+important to know the rate so that the detector system can be optimized in
+terms of both hit rate and momentum resolution.
+
+\noindent Unfortunately the yield, energy spectrum and composition of the
+charged particles emitted in muon capture on Al and Ti have not been measured
+in the relevant energy range for COMET Phase-I and Mu2e.
+Figure~\ref{fg:silicon-proton} shows the spectrum of charged particle emission
+from muons being stopped and captured in a silicon detector \cite{sobo68}. The
+peak below 1.4 MeV is from the recoiling heavy ions, mainly $^{27}$Al, when no
+charged particles were emitted. Hungerford~\cite{hung34} fitted the silicon
+spectrum in Fig.~\ref{fg:silicon-proton} with an empirical function given by
+%
+\begin{equation} p(T) = A(1-{T_{th} \over T})^{\alpha} e^{-(T/T_0)}
+	\label{eq:protons} \end{equation}
+%
+where $T$ is the kinetic energy and the fitted parameters are $A=0.105$
+MeV$^{-1}$, $T_{th}$ = 1.4 MeV, $\alpha$=1.328 and $T_0$ = 3.1 MeV. The
+spectrum is normalized to 0.1 per muon capture. Some other results in the past
+experiments are summarized in Table~\ref{tb:proton}. 
+
+%\begin{figure}[htb] 
+	%\centering
+	%\includegraphics[width=0.7\textwidth]{figs/si-proton.pdf} 
+	%\caption{Charged particle spectrum from muons stopping and being captured in
+	%a silicon detector~\cite{sobo68}.} 
+	%\label{fg:silicon-proton} 
+%\end{figure}
+
+
+\begin{table}[htb] 
+	\centering \caption{Probabilities in unites of $10^{-3}$ per
+	muon capture for inclusive proton emission calculated by Lifshitz and
+	Singer~\cite{lifshitz80}.
+	The numbers in crescent parenthesis are estimates for the total inclusive
+	rate derived from the measured exclusive channels by the use of the
+	approximate regularity, such as $(\mu, \nu p):(\mu, \nu p n):(\mu, \nu p
+	2n):(\mu, \nu p 3n) = 1:6:4:4$.}
+	\label{tb:proton} 
+	\vskip 3mm
+	\begin{tabularx}{\textwidth}{ccccX}
+		\toprule
+		Target nucleus & Calculation & Experiment & Estimate & Comments \\ 
+		\midrule
+		%$_{10}$Ne 			& 		& $200\pm 40$ & 			& \\
+		$^{27}_{13}$Al 	& 40 	& $>28 \pm 4$ & (70) 	& 7.5 for $T>40$ MeV \\
+		$^{28}_{14}$Si 	& 144 & $150\pm30$ 	& 			& 3.1 and 0.34 $d$ for $T>18$ MeV \\ 
+		$^{31}_{15}$P 	& 35 	& $>61\pm6$ 	& (91) 	& \\ 
+		$^{46}_{22}$Ti 	& 		& 						& 			& \\
+		$^{51}_{23}$V 	& 25 	& $>20\pm1.8$ & (32) 	& \\ 
+		\bottomrule
+	\end{tabularx}
+\end{table}
+
+\noindent The limited information available at present makes it difficult to
+draw quantitative conclusive detector design. From Table~\ref{tb:proton}, the
+yield for Al can be taken from experiment to be $>$3\% for $T>40$ MeV, or from
+theory to be 4\%, or estimated based on the ratio of exclusive channels from
+other nuclei to be 7\%, or speculated to be as high as Si 
+%or Ne
+, namely 15-20\%. The
+energy spectrum can only be inferred from the Si data or from
+Ref.~\cite{bala67}. At this moment, for both COMET Phase-I and Mu2e, this
+analytical spectrum has been used to estimate proton emission. And also the $p,
+d, \alpha$ composition is not known. The Ti proton yield can only be estimated
+from V to be around 3\%.
+
+\noindent It might be worth to present how proton emission affects a single
+rate of the tracking chambers.  As an example for COMET Phase-I, single rates
+of the tracking chamber (cylindrical drift chamber) have been simulated based
+on the spectrum given in Eq.(\ref{eq:protons}). To reduce protons entering the
+tracking chamber, in addition to the inner wall of the drift chamber (of 400
+$\mu$m) a cylindrical proton absorber of different thickness is located in
+front of the tracking chamber. Monte Carlo simulations were done with three
+different thickness of proton degrader, namely 0~mm, 5~mm, and 7.5~mm.
+%Figure~\ref{fig:protongenerated} shows a proton momentum spectrum generated
+(larger than 50 MeV/$c$) in the simulation study, and regions in red show
+protons reaching the first layer.  The results are summarized in
+Table~\ref{tb:protonhits}, where the proton emission rate of 0.15 per muon
+capture is assumed. If we assume the number of muons stopped in the
+muon-stopping target is $5.8 \times 10^{9}$/s, the number of muon capture on
+aluminum is about $3.5 \times 10^{9}$/s since the fraction of muon capture in
+aluminum is $f_{cap}=0.61$. Therefore the total number of hits in all the cells
+in the first layer is estimated to be 530 kHz (1.3 MHz) for the case of a
+proton degrader of 5 mm (0 mm) thickness. This example present the importance
+to understand the proton emission, rate and spectrum, from nuclear muon capture
+on aluminum for COMET Phase-I and Mu2e.
+%
+\begin{table}[htb] 
+	\begin{center} 
+		\caption{Total numbers of hits in the first
+	layer by protons emitted from muon capture for different trigger counter
+	thickness. 100 k proton events were generated for COMET Phase-I. 15 \%
+	protons per muon capture is assumed.} 
+	\label{tb:protonhits} 
+	\vspace{5mm}
+	\begin{tabular}{lccc} 
+		\toprule
+		Proton degrader thickness & 0 mm & 5 mm& 7.5 mm\\
+		\midrule
+%		number of 1 hit events & 2467 & 87 & 28 \cr\hline number of 2 hit events &
+%		73 & 8 & 1 \cr\hline number of 3 hit events & 9 & 0 & 0 \cr\hline\hline
+%		number of 4 hit events & 1 & 0 & 0 \cr\hline\hline
+		Hits & 2644 & 103 & 30 \cr
+		Hits per proton emission & 2.6 \% & 0.1 \% & 0.03 \% \cr
+		Hits per muon capture & $3.9\times10^{-3}$  & $1.5\times10^{-4}$ & $4.5\times10^{-5}$ \cr
+		\bottomrule
+	\end{tabular}
+	\end{center} 
+\end{table} 
 \subsection{Any physics implication??}
 
-% section motivation (end)
-
-
-
 % section _mu_e_conversion (end)

thesis/chapters/frontmatter.tex

@@ -1,46 +1,46 @@
 %% Title
-\titlepage[of Churchill College]%
+\titlepage[of Graduate School of Science]%
-{A dissertation submitted to the University of Cambridge\\
+{A dissertation submitted to the Osaka University\\
-  for the degree of Doctor of Philosophy}
+for the degree of Doctor of Philosophy}
 
 %% Abstract
 \begin{abstract}%[\smaller \thetitle\\ \vspace*{1cm} \smaller {\theauthor}]
-  %\thispagestyle{empty}
+	%\thispagestyle{empty}
-  \LHCb is a \bphysics detector experiment which will take data at
+	\LHCb is a \bphysics detector experiment which will take data at
-  the \unit{14}{\TeV} \LHC accelerator at \CERN from 2007 onward\dots
+	the \unit{14}{\TeV} \LHC accelerator at \CERN from 2007 onward\dots
 \end{abstract}
 
 
 %% Declaration
 \begin{declaration}
-  This dissertation is the result of my own work, except where explicit
+	This dissertation is the result of my own work, except where explicit
-  reference is made to the work of others, and has not been submitted
+	reference is made to the work of others, and has not been submitted
-  for another qualification to this or any other university. This
+	for another qualification to this or any other university. This
-  dissertation does not exceed the word limit for the respective Degree
+	dissertation does not exceed the word limit for the respective Degree
-  Committee.
+	Committee.
-  \vspace*{1cm}
+	\vspace*{1cm}
-  \begin{flushright}
+	\begin{flushright}
-    Andy Buckley
+		Andy Buckley
-  \end{flushright}
+	\end{flushright}
 \end{declaration}
 
 
 %% Acknowledgements
 \begin{acknowledgements}
-  Of the many people who deserve thanks, some are particularly prominent,
+	Of the many people who deserve thanks, some are particularly prominent,
-  such as my supervisor\dots
+	such as my supervisor\dots
 \end{acknowledgements}
 
 
 %% Preface
 \begin{preface}
-  This thesis describes my research on various aspects of the \LHCb
+	This thesis describes my research on various aspects of the \LHCb
-  particle physics program, centred around the \LHCb detector and \LHC
+	particle physics program, centred around the \LHCb detector and \LHC
-  accelerator at \CERN in Geneva.
+	accelerator at \CERN in Geneva.
 
-  \noindent
+	\noindent
-  For this example, I'll just mention \ChapterRef{chap:SomeStuff}
+	For this example, I'll just mention \ChapterRef{chap:SomeStuff}
-  and \ChapterRef{chap:MoreStuff}.
+	and \ChapterRef{chap:MoreStuff}.
 \end{preface}
 
 %% ToC
@@ -49,6 +49,6 @@
 
 %% Strictly optional!
 \frontquote{%
-  Writing in English is the most ingenious torture\\
+	Writing in English is the most ingenious torture\\
-  ever devised for sins committed in previous lives.}%
+ever devised for sins committed in previous lives.}%
-  {James Joyce}
+{James Joyce}

thesis/custom_macro.tex

@@ -0,0 +1,10 @@
+
+\newcommand{\lagr}{\cal{L}}
+\newcommand{\mueg}{$\mu^{+} \rightarrow e^{+}\gamma$}
+\newcommand{\meee}{$\mu \rightarrow eee$}
+\newcommand{\muenn}{$\mu \rightarrow e \nu \overline{\nu}$}
+\newcommand{\muenng}{$\mu \rightarrow e \nu \overline{\nu} \gamma$}
+\newcommand{\muec}{$\mu^{-} N \rightarrow e^{-} N$}
+\newcommand{\muecaz}{$\mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)$}
+\newcommand{\sindrumlimit}
+{$\mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13}$}

thesis/mythesis.sty

@@ -1,4 +1,4 @@
-\ProvidesPackage{thesis}[2005/07/28]
+\ProvidesPackage{mythesis}[2005/07/28]
 %\RequirePackage{timing}
 \RequirePackage{hepnicenames,abhep}
 % \RequirePackage{siunitx}

thesis/thesis.tex

@@ -1,6 +1,11 @@
 \documentclass{mythesis}
 \usepackage{mythesis}
+\usepackage{hyperref}
+\usepackage{booktabs}
+\usepackage{tabularx}
+\usepackage{color}
 
+\input{custom_macro.tex}
 %% You can set the line spacing this way
 %\setallspacing{double}
 %% or a section at a time like this
@@ -10,17 +15,18 @@
 \makeatletter
 \@ifpackageloaded{hyperref}{%
 \hypersetup{%
-pdftitle = {Studying B to K pi decays with LHCb},
+	pdftitle = {A Study of Muon Capture for Muon to Electron Conversion
-pdfsubject = {Andy Buckley's PhD thesis},
+	Experiments},
-pdfkeywords = {LHCb, B, physics, LHC, heavy flavour},
+	pdfsubject = {Nam H Tran's PhD thesis},
-pdfauthor = {\textcopyright\ Andy Buckley}
+	pdfkeywords = {muon capture, muon to electron conversion, COMET},
+	pdfauthor = {\textcopyright\ Nam Hoai Tran}
 }
 }{}
 \makeatother
 
 %% Define the thesis title and author
-\title{A study of \BToKPi decays with\\ the \LHCb experiment}
+\title{A Study of Muon Capture for \\Muon to Electron Conversion Experiments}
-\author{Andrew Gordon Buckley}
+\author{Nam Hoai Tran}
 
 %% Start the document
 \begin{document}
@@ -34,11 +40,11 @@ pdfauthor = {\textcopyright\ Andy Buckley}
 \begin{mainmatter}
   %% Actually, more semantic chapter filenames are better, like "chap-bgtheory.tex"
   \input{chapters/chap1}
-  \input{chapters/chap2}
+  %\input{chapters/chap2}
-  \input{chapters/chap3}
+  %\input{chapters/chap3}
-  \input{chapters/chap4}
+  %\input{chapters/chap4}
-  \input{chapters/chap5}
+  %\input{chapters/chap5}
-  \input{chapters/chap6}
+  %\input{chapters/chap6}
   %% To ignore a specific chapter while working on another,
   %% making the build faster, comment it out like this:
   %\input{chapters/chap4}