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\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