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61
thesis/chapters/chap2_mu_e_conv.tex
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@@ -9,7 +9,7 @@ spin one-half particles, called fermions: six quarks and six leptons.
The six leptons form three generations (or flavours), namely: The six leptons form three generations (or flavours), namely:
\begin{equation*} \begin{equation*}
\binom{\nu_e}{e^-}, \quad \binom{\nu_\mu}{\mu^-} \quad \textrm{ and } \quad \binom{\nu_e}{e^-}, \quad \binom{\nu_\mu}{\mu^-} \quad \textrm{ and } \quad
\binom{\nu_\tau}{\tau^-} \binom{\nu_\tau}{\tau^-}.
\end{equation*} \end{equation*}
Each lepton is assigned a lepton flavour quantum number, $L_e$, $L_\mu$, Each lepton is assigned a lepton flavour quantum number, $L_e$, $L_\mu$,
@@ -24,7 +24,7 @@ or, the interaction of an electron-type antineutrino with a proton (inverse
beta decay): beta decay):
\begin{align*} \begin{align*}
&\quad \overline{\nu}_e + p \rightarrow e^+ + n \\ &\quad \overline{\nu}_e + p \rightarrow e^+ + n \\
L_e \quad &-1 \quad \textrm{ }0 \quad -1 \textrm{ } \quad 0 L_e \quad &-1 \quad \textrm{ }0 \quad -1 \textrm{ } \quad 0
\end{align*} \end{align*}
The decay of a muon to an electron and a photon, where lepton flavour numbers The decay of a muon to an electron and a photon, where lepton flavour numbers
@@ -40,15 +40,25 @@ are violated by one unit or more, is forbidden:
\end{aligned} \end{aligned}
\label{eq:mueg} \label{eq:mueg}
\end{equation} \end{equation}
However, it is observed that neutrinos do change flavour in the so-called
neutrino oscillations where a neutrino of a certain lepton flavour
can be measured to have a different flavour as it travels in space-time. The
phenomenon has been confirmed in many experiments with solar neutrinos,
atmospheric neutrinos, reactor neutrinos and beam neutrinos. The observation
of neutrino oscillations means that the lepton flavour is not strictly
conserved and neutrinos are massive. The massive neutrinos allow lepton
flavour violation in the charged leptons, but at an unmeasurably small level
as described in \cref{sec:lepton_flavour_violation}.
%One more decay? %One more decay?
%\hl{TODO: Why massless neutrinos help lepton flavour conservation??} %\hl{TODO: Why massless neutrinos help lepton flavour conservation??}
%\hl{TODO: copied from KunoOkada} %\hl{TODO: copied from KunoOkada}
%In the minimal version of the SM, where only one Higgs doublet is included and %In the minimal version of the SM, where only one Higgs doublet is included and
%massless neutrinos are assumed, lepton flavor conservation is an automatic %massless neutrinos are assumed, lepton conservation is an automatic
%consequence of gauge invariance and the renormalizability of the SM %consequence of gauge invariance and the renormalizability of the SM
%Lagrangian. It is the basis of a natural explanation for the smallness of %Lagrangian. It is the basis of a natural explanation for the smallness of
%lepton flavor violation (LFV) in charged lepton processes. %lepton violation (LFV) in charged lepton processes.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Muon and its decays in the Standard Model} \section{Muon and its decays in the Standard Model}
@@ -111,15 +121,15 @@ or with an associated $e^+ e^-$ pair:
\label{eq:mu3e2nu} \label{eq:mu3e2nu}
\end{equation} \end{equation}
The dominant process, \micheldecay is commonly called Michel decay. It can be The dominant process, \micheldecay is commonly called the Michel decay. It can
described by the V-A interaction which is a special case of a local, be described by the V-A interaction which is a special case of a local,
derivative-free, lepton-number-conserving four-fermion interaction. derivative-free, lepton-number-conserving four-fermion interaction.
%using $V-A$ %using $V-A$
%inteaction, a special case of four-fermion interaction, by Louis %inteaction, a special case of four-fermion interaction, by Louis
%Michel~\cite{Michel.1950}. %Michel~\cite{Michel.1950}.
The model contains independent real parameters that can be determined from The model contains independent real parameters that can be determined from
measurements of muon life time, muon decay and inverse muon measurements of muon life time, muon decay and inverse muon
decay. Experimental results from extensive measurements of Michel parameters decay. Experimental results from extensive measurements of the Michel parameters
are consistent with the predictions of the V-A are consistent with the predictions of the V-A
theory~\cite{Michel.1950,FetscherGerber.etal.1986,BeringerArguin.etal.2012}. theory~\cite{Michel.1950,FetscherGerber.etal.1986,BeringerArguin.etal.2012}.
@@ -127,9 +137,9 @@ The radiative decay~\eqref{eq:mue2nugamma} is treated as an internal
bremsstrahlung process~\cite{EcksteinPratt.1959}. bremsstrahlung process~\cite{EcksteinPratt.1959}.
%It occurs at the rate of about 1\% of all muon decays. %It occurs at the rate of about 1\% of all muon decays.
Since it is not possible to clearly separated this mode Since it is not possible to clearly separated this mode
from Michel decay in the soft-photon limit, the radiative mode is regarded as from the Michel decay in the soft-photon limit, the radiative mode is regarded as
a subset of the Michel decay. An additional parameter is included to describe a subset of the Michel decay. An additional parameter is included to describe
the electron and photon spectra in this decay channel. Like the case of the electron and photon spectra in this decay channel. Like the case of the
Michel decay, experiments results on the branching ratio and the parameter are Michel decay, experiments results on the branching ratio and the parameter are
in agreement with the SM's predictions~\cite{BeringerArguin.etal.2012}. in agreement with the SM's predictions~\cite{BeringerArguin.etal.2012}.
@@ -221,8 +231,8 @@ CLFV processes with muons are also suppressed to similar practically
unmeasurable levels.%\hl{TODO: Feynman diagram} unmeasurable levels.%\hl{TODO: Feynman diagram}
Therefore, any experimental Therefore, any experimental
observation of CLFV would be an unambiguous signal of the physics beyond the observation of CLFV would be an unambiguous signal of the physics beyond the
SM. Many models for physics beyond the SM, including supersymmetric (SUSY) SM. Many theoretical models for physics beyond the SM, including supersymmetric
models, extra dimensional models, little Higgs models, predict (SUSY) models, extra dimensional models, little Higgs models, predict
significantly larger CLFV significantly larger CLFV
~\cite{MarcianoMori.etal.2008, MiharaMiller.etal.2013, BernsteinCooper.2013}. ~\cite{MarcianoMori.etal.2008, MiharaMiller.etal.2013, BernsteinCooper.2013}.
%\hl{TODO: DNA of CLFV charts} %\hl{TODO: DNA of CLFV charts}
@@ -257,15 +267,15 @@ significantly larger CLFV
%occur at large rates by many new physics models, %occur at large rates by many new physics models,
Among the CLFV processes, the \mueg and Among the CLFV processes, the \mueg and
the \muec are expected to have large effect by many models. The current the \muec are expected to have large effect by many models. The current
experimental limits on these two decay modes are set by MEG experimental limits on these two decay modes are set respectively by the MEG
experiment~\cite{Adam.etal.2013} and SINDRUM-II experiment~\cite{Adam.etal.2013} and the SINDRUM-II
experiment~\cite{Bertl.etal.2006}: experiment~\cite{Bertl.etal.2006}:
\begin{equation} \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} \end{equation}
, and: and:
\begin{equation} \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} \end{equation}
%\hl{TODO: mueg and muec relations, Lagrangian \ldots} %\hl{TODO: mueg and muec relations, Lagrangian \ldots}
@@ -278,25 +288,26 @@ experiment~\cite{Bertl.etal.2006}:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Phenomenology of \mueconv} \section{Phenomenology of \mueconv}
\label{sec:phenomenoly_of_muec} \label{sec:phenomenoly_of_muec}
The conversion of a captured muon into an electron in the field of a nucleus The conversion of a captured negative muon in a muonic atom into an electron
has been one of the most powerful probe to search for CLFV. This section in the field of a nucleus has been one of the most powerful probe to search for
CLFV. This section
highlights phenomenology of the \muec. highlights phenomenology of the \muec.
\subsection{What is \mueconv} \subsection{What is \mueconv}
\label{sub:what_is_muec} \label{sub:what_is_muec}
When a muon is stopped in a material, it is quickly captured by atoms When a negatively charged muon is stopped in a material, it is quickly captured
into a high orbital momentum state, forming a muonic atom, then by an atom into a high orbital momentum state, forming a muonic atom, then
it rapidly cascades to the lowest state 1S. There, it undergoes either: it rapidly cascades to the lowest state 1S. There, it undergoes either:
\begin{itemize} \begin{itemize}
\item normal Michel decay: \micheldecay; or \item normal Michel decay: \micheldecay; or
\item weak capture by the nucleus: $\mu^- p \rightarrow \nu_\mu n$ \item weak capture by the nucleus: $\mu^- p \rightarrow \nu_\mu n$.
\end{itemize} \end{itemize}
In the context of physics beyond the SM, the exotic process of \mueconv where In the context of physics beyond the SM, the exotic process of \mueconv where
a muon decays to an electron without neutrinos is also a muon decays to an electron without neutrinos is also
expected, but it has never been observed. expected, but has never been observed:
\begin{equation} \begin{equation}
\mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z) \mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)\.
\end{equation} \end{equation}
The emitted electron in this decay The emitted electron in this decay
mode , the \mueconv electron, is mono-energetic at an energy far above the mode , the \mueconv electron, is mono-energetic at an energy far above the
@@ -322,8 +333,8 @@ The quantity measured in searches for \mueconv is the ratio between the rate of
\frac{\Gamma(\mu^-N \rightarrow e^-N)}{\Gamma(\textrm{capture})} \frac{\Gamma(\mu^-N \rightarrow e^-N)}{\Gamma(\textrm{capture})}
\label{eq:muerate_def} \label{eq:muerate_def}
\end{equation} \end{equation}
The normalisation to captures has advantages when one does calculation since %The normalisation to captures has advantages when one does calculation since
many details of the nuclear wavefunction cancel out in the ratio. %many details of the nuclear wavefunction cancel out in the ratio.
%Detailed %Detailed
%calculations have been performed by Kitano et al.~\cite{KitanoKoike.etal.2002a, %calculations have been performed by Kitano et al.~\cite{KitanoKoike.etal.2002a,
%KitanoKoike.etal.2007}, and Cirigliano et al.~\cite{Cirig} %KitanoKoike.etal.2007}, and Cirigliano et al.~\cite{Cirig}

2
thesis/chapters/frontmatter.tex
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@@ -10,7 +10,7 @@ Osaka University}
\begin{abstract} \begin{abstract}
%[\smaller \thetitle\\ \vspace*{1cm} \smaller {\theauthor}] %[\smaller \thetitle\\ \vspace*{1cm} \smaller {\theauthor}]
\thispagestyle{empty} \thispagestyle{empty}
COMET [1] is an experiment that aims to search for a charged lepton flavor COMET [1] is an experiment that aims to search for a charged lepton flavour
violation (CLFV) process, the muon-to-electron conversion in the presence of violation (CLFV) process, the muon-to-electron conversion in the presence of
a nucleus, a nucleus,
\muec. The process is forbidden in the Standard Model (SM), however is \muec. The process is forbidden in the Standard Model (SM), however is

16
thesis/thesis.tex
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@@ -21,7 +21,7 @@ following nuclear muon capture\\
\vspace{2mm} \vspace{2mm}
for the COMET experiment} for the COMET experiment}
\author{Nam Hoai Tran} \author{Nam Hoai Tran}
\date{September, 2014} \date{October, 2014}
\begin{document} \begin{document}
\begin{frontmatter} \begin{frontmatter}
@@ -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}