\chapter{The COMET experiment}
\label{cha:comet_overview}
\thispagestyle{empty}

This chapter describes the new experimental search for \mueconv, namely COMET -
(\textbf{CO}herent \textbf{M}uon to \textbf{E}lectron \textbf{T}ransition). The
experiment will be carried out at the Japan Proton Accelerator Research Complex
(J-PARC), aims at a sensitivity of \sn{6}{-17} i.e. 10,000 times better than the
current best limit.

%At the Japan Proton Accelerator Research Complex (J-PARC), an experiment to
%search for \muec~conversion, which is called 
 %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. 

%\begin{itemize}
  %\item present status of mueconv experiments
    %\begin{itemize}
      %\item SINDRUM-II description, results, short comings
      %\item new ideas: MECO, Mu2e, COMET
    %\end{itemize}
  %\item Concepts of COMET
    %\begin{itemize}
      %\item highly intense muon beam
      %\item pulsed proton beam
      %\item curved solenoids
    %\end{itemize}
  %\item COMET's beam lines and detectors
    %\begin{itemize}
      %\item proton beam: energy, time structure, planned operations
      %\item pion production: yields, target, capture solenoids
      %\item muon transportation: requirements, field
      %\item stopping target: material, geometry, field, energy loss
      %\item electron transportation:
      %\item detectors: electron tracker and calorimeter
      %\item DAQ
    %\end{itemize}
%\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Experimental status of \mueconv searches}
\label{sec:experimental_status_of_mueconv_searches}

\subsection{Experimental history}
\label{sub:experimental_history}

The searches for \mueconv has been ongoing for more than 50 years, started in
1952 with cosmic rays~\cite{LagarriguePeyrou.1952} and then moved to
accelerators. The list in the Table~\ref{tab:mueconv_history} is reproduced
from a recent review of Bernstein and Cooper~\cite{BernsteinCooper.2013}.
\begin{table}[htb]
  \begin{center}
    \begin{tabular}{l l l c}
      \toprule
      \textbf{Year} & \textbf{Limit} (90\% C.L.) & \textbf{Material}
      & \textbf{Reference}\\
      \midrule
      1952 & \sn{1.0}{-1}   & Sn, Sb  & \cite{LagarriguePeyrou.1952} \\
      1955 & \sn{5.0}{-4}   & Cu      & \cite{SteinbergerWolfe.1955} \\
      1961 & \sn{4.0}{-6}   & Cu      & \cite{SardCrowe.etal.1961}\\
      1961 & \sn{5.9}{-6}   & Cu      & \cite{ConversiLella.etal.1961}\\
      1962 & \sn{2.2}{-7}   & Cu      & \cite{ConfortoConversi.etal.1962}\\
      1964 & \sn{2.2}{-7}   & Cu      & \cite{ConversiLella.etal.1961}\\
      1972 & \sn{2.6}{-8}   & Cu      & \cite{ConversiLella.etal.1961}\\
      1977 & \sn{4.0}{-10}  & S       & \cite{ConversiLella.etal.1961}\\
      1982 & \sn{7.0}{-11}  & S       & \cite{ConversiLella.etal.1961}\\
      1988 & \sn{4.6}{-12}  & Ti      & \cite{ConversiLella.etal.1961}\\
      1993 & \sn{4.3}{-12}  & Ti      & \cite{ConversiLella.etal.1961}\\
      1995 & \sn{6.5}{-13}  & Ti      & \cite{ConversiLella.etal.1961}\\
      1996 & \sn{4.6}{-11}  & Pb      & \cite{ConversiLella.etal.1961}\\
      2006 & \sn{7.0}{-13}  & Au      & \cite{ConversiLella.etal.1961}\\
      \bottomrule
    \end{tabular}
  \end{center}
  \caption{History of \mueconv experiments, reproduced
  from~\cite{BernsteinCooper.2013}}
  \label{tab:mueconv_history}
\end{table}

The most recent experiments were the SINDRUM and SINDRUM-II at the Paul
Scherrer Institute (PSI), Switzerland. The SINDRUM-II measured the branching
ratio of \mueconv on a series of heavy targets: Ti, Pb and Au. The proton beam
at PSI is a continuous wave beam, with a time structure of 0.3 ns bursts every
19.75 \si{\nano\second}. An 8-\si{\milli\meter}-thick CH$_2$ degrader was used to reduce
the radiative pion capture and other prompt backgrounds. Cosmic backgrounds are
rejected using a combination of
passive shielding, veto counters  and reconstruction cuts. The momenta of muons
were 52 \si{\mega\electronvolt\per\cc} and 53 \si{\mega\electronvolt\per\cc}, and the
momentum spread was 2\%.  
\begin{figure}[htbp] \centering
  \includegraphics[width=0.85\textwidth]{figs/sindrumII_setup}
  \caption{SINDRUM-II set up}
  \label{fig:sindrumII_setup}
\end{figure}

Electrons emitted from the target were tracked in a 0.33 T solenoid field.
Detector system consisted of a superconducting solenoid, two plastic
scintillation hodoscopes, a plexiglass Cerenkov hodoscope, and two drift
chambers. In the latest measurement, the SINDRUM-II collaboration have not
found any conversion electron from captured muons in a gold target, hence set
the upper limit for
the branching ratio of \mueconv in gold with 90 \% C.L. at \sn{7.0}{-13}.

The reconstructed momenta of electrons around the signal region from SINDRUM-II
is shown in the Figure~\ref{fig:sindrumII_result}. It can be seen that the muon
decay in orbit background falls steeply near the endpoint as expected, but, the
prompt background induced by pions still remains even after the cut in timing
and track angle. This indicates the problem of pion contamination is very
important in probing lower sensitivity.
\begin{figure}[htbp]
  \centering
  \includegraphics[width=0.55\textwidth]{figs/sindrumII_Au_result}
  \caption{SINDRUM-II result}
  \label{fig:sindrumII_result}
\end{figure}
% subsection experimental_history (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{New generation of \mueconv~experiments}
\label{sub:new_generation_of_mueconv_experiments}

A new generation of \mueconv experiments have been proposed with scenarios to
overcome pion induced background in the SINDRUM-II. Lobashev and collaborators
first suggested the basic idea for new \mueconv at the Moscow Muon Factory;
this idea was used to develop the MECO experiment at Brookhaven National
Laboratory. The MECO experiment was cancelled due to budget constraints. The two
modern experiments, COMET at J-PARC and Mu2e at Fermilab use the initial idea
with more upgrades and modifications.

The basic ideas of the modern experiments are:
\begin{enumerate}
  \item Highly intense muon source: the total number of muons needed is of the
    order of $10^{18}$ in order to achieve a sensitivity of $10^{-16}$. This
    can be done by producing more pions using a high power proton beam, and
    having a high efficiency pion collection system;
  \item Pulsed proton beam with an appropriate timing: the proton pulse should
    be short compares to the lifetime of muons in the stopping target material,
    and the period between pulses should be long enough for prompt backgrounds
    from pion to decay before beginning the measurement. It is also crucial
    that there is no proton leaks into the measuring interval;
  \item Curved solenoids for charge and momentum selection: at first, the curved
    solenoids remove the line of sight backgrounds. A charged particle travels
    through a curved solenoidal field will have the centre of the helical
    motion drifted up or down depends on the sign of the charge, and the
    magnitude of the drift is proportional to its momentum. By using this
    effect and placing suitable collimators, charge and momentum selection can
    be made.
\end{enumerate}
% subsection new_generation_of_mueconv_experiments (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% section experimental_status_of_mueconv_searches (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Concepts of the COMET experiment}
\label{sec:concepts_of_the_comet_experiment}
This section elaborates the design choices of the COMET to realise the basic
ideas mentioned above. Figures and numbers, other than noted, are taken from
the COMET's documentations: 
\begin{itemize}
    %TODO citations
  \item Conceptual design report for the COMET experiment~\cite{COMET.2009}
  \item Proposal Phase-I 2012
  \item TDR 2014
\end{itemize}


\subsection{Proton beam}
\label{sub:proton_beam}
A high power pulsed proton beam is of utmost importance to achieve the desired
sensitivity of the COMET experiment. A slow-extracted proton beam from
the J-PARC main ring (MR), which is designed to deliver \sn{3.6}{15} protons per
cycle at a frequency of 0.45 Hz, will be used for the COMET experiment. The
proton beam power of the current design is 8 GeV$\times$7 $\mu$A, or
\sn{4.4}{13} protons/s. The beam energy 8 \si{\giga\electronvolt} helps to minimise
the production of antiprotons. 

The proton pulse width is chosen to be 100 ns, and the pulse period to be
$1 \sim 2 \textrm{ }\mu\textrm{s}$. This time structure is sufficient for the
search for \mueconv in an aluminium target where the lifetime of muons is 864
ns. A plan of accelerator operation to realise the scheme is shown in
the Figure~\ref{fig:comet_mr_4filled}, where  4 out of 9 MR buckets are filled.

As mentioned, it is very important that there is no stray proton arrives in the
measuring period between two proton bunches. An extinction factor is defined as
the ratio between number of protons in between two pulses and the number of
protons in the main pulse. In order to achieve the goal sensitivity of the
COMET, an extinction factor of \sn{}{-9} is required.

Requirements for the proton beam are summarised in the
Table~\ref{tab:comet_proton_beam}.

\begin{figure}[htb]
  \centering
    \includegraphics[width=0.8\textwidth]{figs/comet_mr_4filled}
    \caption{The COMET proton bunch structure in the RCS (rapid cycle
      synchrotron) and MR where 4 buckets
    are filled producing 100 \si{\nano\second} bunches separated by
    1.2~\si{\micro\second}.} 
  \label{fig:comet_mr_4filled}
\end{figure}

\begin{table}[htb]
  \begin{center}
    \begin{tabular}{l l}
      \toprule
      Beam power          & 56 \si{\kilo\watt}\\
      Energy              & 8 \si{\giga\electronvolt}\\
      Average current     & 7 \si{\micro\ampere}\\
      Beam emittance      & 10 $\pi\cdot$ mm$\cdot$ mrad\\
      Protons per bunch   & $<10^{11}$\\
      Extinction          & \sn{}{-9}\\
      Bunch separation    & $1 \sim 2$ \si{\micro\second}\\
      Bunch length        & 100 \si{\nano\second}\\
      \bottomrule
    \end{tabular}
  \end{center}
  \caption{Pulsed proton beam for the COMET experiment}
  \label{tab:comet_proton_beam}
\end{table}

% subsection proton_beam (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Pion production and capture solenoid}
\label{sub:pion_production_can_capture_solenoid}
Muons for the COMET experiment are produced by colliding the proton beam with
a pion production target, made of either platinum, gold or tungsten, collecting
pions and then letting them decay.  To collect as many pions (and cloud muons)
as possible, the pions are captured
using a high solenoidal magnetic field with a large solid angle. Since muons
will be stopped in a conversion target, low energy muons, and thus low energy
pions, are preferred. It is known from other measurements that backward
scattered pions (with respect to proton beam direction) of high energy are
suppressed, and the yield of low energy pions in the backward direction is not
too low compares to that of the forward direction (see
Figure~\ref{fig:pion_yield}). For these reasons, the COMET
decided to collect backward pions.
\begin{figure}[htb]
  \centering
    \includegraphics[width=0.95\textwidth]{figs/pion_yield}
    \caption{Comparison between backward and forward pions production in a gold
    target.}
  \label{fig:pion_yield}
\end{figure}

The pion capture system is composed of several superconducting solenoids:
capture solenoids and matching solenoids. The magnetic field distribution along
the beam axis of the COMET is shown in the Figure~\ref{fig:comet_Bfield}. The
peak field of 5 T is created by the capture solenoid, and the matching
solenoids provide a smooth transition from that peak field to the 3 T field in
the pions/muons transportation region.  The superconducting solenoids are
cooled by liquid helium, and a radiation shield composed of copper and tungsten
will be installed inside the cryostat to reduce radiation heat load. 
\begin{figure}[htb]
  \centering
    \includegraphics[width=0.85\textwidth]{figs/comet_Bfield}
  \caption{Magnetic field distribution along the COMET beam line.}
  \label{fig:comet_Bfield}
\end{figure}

% subsection pion_production_can_capture_solenoid (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Pions and muons transportation solenoids}
\label{sub:pion_and_muon_transportation}
Muons and pions are transported to the muon stopping target through a muon
beam line, which includes several curved and straight superconducting solenoid
magnets. A schematic layout of the muon beam line, include the capture and
detector sections, is shown in Figure~\ref{fig:comet_beamline_layout}.
\begin{figure}[htb]
  \centering
    \includegraphics[width=0.95\textwidth]{figs/comet_beamline_layout}
  \caption{Schematic layout of the COMET beam line.}
  \label{fig:comet_beamline_layout}
\end{figure}

The requirements for the muon transportation beam line are:
\begin{itemize}
  \item being long enough for pions to decay, for instance, the survival rate
    of pions will be about \sn{2}{-3} after 20 m;
  \item being able to select low momentum negative muons with momentum of around
    40 MeV/$c$, and eliminate high momentum muons ($> 75\textrm{ MeV/}c$),
    since they can decay in flight and produce spurious signals of $\sim$ 105
    MeV electrons.
\end{itemize}
The selection of charge and momentum is done by the curved solenoids. It is
know that, in a curved solenoidal field, the centre of the helical trajectory
of a charged particle drifts perpendicularly to the curved plane. The magnitude
of the drift is given by:
\begin{align}
  D &= \frac{1}{qB} \frac{s}{R} \frac{p_L^2 + \frac{1}{2}p_T^2}{p_L}\\
    &= \frac{1}{qB} \frac{s}{R} \frac{p}{2} 
   \left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right)\\
    &= \frac{1}{qB} \theta_{bend} \frac{p}{2} 
   \left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right)
\end{align}
where $q$ is the electric charge of the particle; $B$ is the magnetic field at
the axis; $s$ and $R$ are the path length and the radius of the curvature; $p$,
$p_T$ and $p_L$ are total momentum, transversal momentum and longitudinal
momentum of the particles, respectively; $\theta = \textrm{atan}(p_T/p_L)$ is
the pitch angle of the helical trajectory; and $\theta_{bend} = s/R$ is called
the bending angle.
It is clear that $D$ is proportional to $\theta_{bend}$, to total momentum $p$.
Charged particles with opposite signs move in opposite directions. Therefore it
is possible to select muons around 40 MeV/$c$ by using suitable collimator
after the curved solenoid.

In order to keep the centre of the helical trajectories of the muons with
a reference momentum $p_0$ in the vertical plane, a compensating dipole field
parallel to the drift direction is needed. In the COMET, the dipole fields are
produced by additional coils winded around the solenoid coils. The magnitude of
the compensating field is:
\begin{equation}
  B_{\textrm{comp}} = \frac{1}{qR} \frac{p_0}{2} 
  \left( \textrm{cos}\theta_0 + \frac{1}{\textrm{cos}\theta_0} \right)
\end{equation}
where the trajectories of charged particles with momentum $p_0$ and pitch angle
$\theta_0$ are corrected to be on-axis. An average dipole field of 0.03 T is
needed to select 40 MeV/$c$ muons as required by the COMET design.
% subsection pion_and_muon_transportation (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Muon stopping target}
\label{sub:muon_stopping_target}
Muon stopping target is place at 180\si{\degree}~bending after the pion production
target (Figure~\ref{fig:comet_beamline_layout}) in its own solenoid. The target
is designed to maximise the muon stopping efficiency and minimise the energy
loss of signal electrons.

%\hl{TODO: Target choice: separation, product, lifetime, energy loss\ldots}
It is calculated that the branching ratio of \mueconv increases with atomic
number $Z$, and plateaus above $Z \simeq 30$, then decreases as $Z>60$. The
lifetime of muons inside a material decreases quickly as $Z$ increases.
Tracking wise, lower $Z$ material provides better reconstructed momentum
resolution. Therefore, light material is preferable as muon stopping target.

The first choice for the muon stopping target material in the COMET is
aluminium. A titanium target is also considered. Configuration of the target is
shown in the Table~\ref{tab:comet_al_target}. Monte Carlo studies with this
design showed that net stopping efficiency is 0.29, and average energy loss
of signal electrons is about 400 \si{\kilo\electronvolt}.
\begin{table}[htb]
  \begin{center}
    \begin{tabular}{l l}
      \toprule
      \textbf{Item} & \textbf{Specification}\\
      \midrule 
      Material    & Aluminium\\
      Shape       & Flat disks\\
      Disk radius & 100 \si{\milli\meter}\\
      Disk thickness & 200 \si{\micro\meter}\\
      Number of disks & 17\\
      Disk spacing    & 50 \si{\milli\meter}\\
      \bottomrule
    \end{tabular}
  \end{center}
  \caption{Configuration of the muon stopping target.}
  \label{tab:comet_al_target}
\end{table}

A graded magnetic field (reduces from 3 T to 1 T) is produced at the
location of the stopping target (see Figure~\ref{fig:comet_target_Bfield}) to
maximise the acceptance for \mueconv signals, since electrons emitted in the
backward
direction would be reflected due to magnetic mirroring. The graded field also
helps optimising the transmission efficiency to the subsequent electron
transport section.  
\begin{figure}[htb]
  \centering
    \includegraphics[width=0.85\textwidth]{figs/comet_target_Bfield}
  \caption{The graded magnetic field near the stopping target region.}
  \label{fig:comet_target_Bfield}
\end{figure}

% subsection muon_stopping_target (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Electron transportation beam line}
\label{sub:electron_transportation_beam_line}
The 180\si{\degree}~bending electron transport solenoids help remove line-of-sight
between the target and the detector system. It works similarly to the muon
transportation section, but is tuned differently to accept electrons of about
105~\si{\mega\electronvolt\per\cc}. A compensation field of 0.17 T along the
vertical direction will be applied. Electrons with momentum less than 80
\si{\mega\electronvolt\per\cc} are blocked at the exit of this section by
a collimator to reduce DIO electrons rate. The net acceptance of signals of
\mueconv is about 0.32, and the detector hit rate will be in the order of
1~\si{\kilo\hertz}~for \sn{}{11} stopped muons\si{\per\second}.
% subsection electron_transportation_beam_line (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Electron detectors}
\label{sub:electron_detectors}
The \mueconv signal electrons is measured by an electron detector system, which
consists of straw-tube trackers and an electromagnetic calorimeter - shown in
Figure~\ref{fig:comet_detector_system}. The
requirements for the detector system is to distinguish electrons from other
particles, and measure their momenta, energy and timings. The whole detector
system is in a uniform solenoidal magnetic field under vacuum. Passive and
active shielding against cosmic rays is considered.

The tracking detector has to provide a momentum resolution less than
350~\si{\kilo\electronvolt\per\cc} in order to achieve a sensitivity of
\sn{3}{-17}.  There are five stations of straw-tube gas chambers, each provides
two
dimensional information. Each straw tube is 5~\si{\milli\meter} in diameter and has
a 25~\si{\micro\meter}-thick wall. According to a GEANT4 Monte Carlo simulation,
a position resolution of 250~\si{\micro\meter} can be obtained, which is enough for
350~\si{\kilo\electronvolt\per\cc} momentum resolution. The DIO background of 0.15
events is estimated.

The electromagnetic calorimeter serves three purposes: a) to measure electrons
energy with high energy resolution; b) to provide timing information and
trigger timing for the detector system; and c) to provide additional data on
hit positions. Two candidate crystals, GSO and LYSO, are under consideration.
\begin{figure}[htb]
  \centering
    \includegraphics[width=0.75\textwidth]{figs/comet_detector_system}
  \caption{Layout of the electron detectors.}
  \label{fig:comet_detector_system}
\end{figure}

The requirements for \mueconv signals are:
\begin{itemize}
  \item from the 350~\si{\kilo\electronvolt\per\cc}~momentum resolution, the signal
    region is determined to be 103.5~\si{\mega\electronvolt\per\cc}~to
    105.2~\si{\mega\electronvolt\per\cc}; 
  \item transversal momentum of signal electrons is required to be greater than
    52~\si{\mega\electronvolt\per\cc} to remove backgrounds from beam electrons and
    muons decay in flight;
  \item timing wise, conversion electrons should arrive in the time window of
    detection which is about 700~\si{\nano\second}~after each proton pulses
    (Figure~\ref{fig:comet_meas_timing}). The acceptance in this detection
    window is about 0.39 for aluminium.
\end{itemize}

\begin{figure}[htb]
  \centering
    \includegraphics[width=0.7\textwidth]{figs/comet_meas_timing}
  \caption{Timing window of detection.}
  \label{fig:comet_meas_timing}
\end{figure}
% subsection electron_detectors (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Signal sensitivity and background estimation}
\label{sub:signal_sensitivity_and_background_estimation}
The single event sensitivity (SES) of the \mueconv search is defined as:
\begin{equation}
  \mathcal{B}(\mu^-Al\rightarrow e^- Al) = 
  \frac{1}{N^{\textrm{stop}}_{\mu}\cdot f_{\textrm{cap}} \cdot A_e}
  \label{eq:mue_sensitivity}
\end{equation}
where $N^{\textrm{stop}}_{\mu}$ is the number of muons stopping in the muon
target; $f_{\textrm{cap}}$ is the fraction of captured muons; and $A_e$ is the
detector acceptance. The total number of stopped muons is projected as
$N^{\textrm{stop}}_{\mu} = 2\times 10^{18}$ for a \sn{2}{7}\si{\second}~run time;
$f_{\textrm{cap}} = 0.61$ for aluminium; and the total acceptance for the COMET
detector system is $A_e =0.031$. Using these
numbers, the SES of the COMET is calculated to be
\sn{2.6}{-17}. The 90\% CL upper limit is given by $2.3\times\mathcal{B}$:
\begin{equation}
  \mathcal{B}(\mu^-Al\rightarrow e^- Al) < 6 \times 10^{-17} \quad
  \textrm{(90\% C.L.)}
\end{equation}

Potential backgrounds for the COMET are:
\begin{enumerate}
  \item Intrinsic physics backgrounds: originates from muons stopped in the
    stopping target, including muon decays in orbit, radiative muon capture and
    particles such as protons and neutrons emitted after muon capture;
  \item Beam related backgrounds: caused by particles (electrons, pions, muons
    and antiprotons) in the beam. They are either prompt or late-arriving.
    A beam pulsing with high proton extinction factor is required to reject
    this type of backgrounds;
  \item Accidental background from cosmic rays
\end{enumerate}
The expected background rates for the COMET at an SES of
\sn{3}{-17} is summarised in Table~\ref{tab:comet_background_estimation}.
\begin{table}[htb]
  \begin{center}
    %\begin{tabular}{l l}
    \begin{tabular}{l r@{.}l}
      \toprule
      \textbf{Background} & \multicolumn{2}{l}{\textbf{Events}}\\
      \midrule 
    %\end{tabular}{l l}
    %\begin{tabular}{l r@{.}l}
      Radiative pion capture        &    0&05\\
      Beam electrons                & $<$0&1\\
      Muon decay in flight          & $<$0&0002\\
      Pion decay in flight          & $<$0&0001\\
      Neutron induced               &    0&024\\
      Delayed pion radiative capture &   0&002\\
      Antiproton induced            &    0&007\\
      Muon decay in orbit           &    0&15\\
      Radiative muon capture        & $<$0&001\\
      Muon capture with neutron emission & $<$0&001\\
      Muon capture with proton emission  & $<$0&001\\
      Cosmic ray muons              & 0&002\\
      Electron cosmic ray muons     & 0&002\\
      \midrule
      \textbf{Total}                &0&34\\
      \bottomrule
    \end{tabular}
  \end{center}
  \caption{Backgrounds of the COMET experiment.}
  \label{tab:comet_background_estimation}
\end{table}

% subsection signal_sensitivity_and_background_estimation (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% section concepts_of_the_comet_experiment (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{The COMET Phase-I}
\label{sec:the_comet_phase_i}
The techniques of beam pulsing and curved solenoids that the COMET will utilise
are believed to greatly reduce potential backgrounds, by several orders of
magnitude, for the \mueconv search. That also means that backgrounds are being
extrapolated over four orders of magnitude from existing data. In order to
obtain data-driven estimates of backgrounds, and inform the detailed design for
the ultimate COMET experiment, and initial phase is desirable. Also, the 5-year
mid-term plan from 2013 of J-PARC includes the construction of the COMET beam
line. For these reasons, the COMET collaboration considers a staged approach
with the first stage, so called COMET Phase-I, with a shorter muon
transportation solenoid, up to the first 90\si{\degree}.

%\begin{wrapfigure}{r}{0.5\textwidth}
  %\centering
  %\includegraphics[width=0.49\textwidth]{figs/comet_phase1_layout}
  %\caption{Lay out of the COMET Phase-I, the target and detector solenoid are
  %placed after the first 90\degree~bend.}
  %\label{fig:comet_phase1_layout}
%\end{wrapfigure}
\begin{SCfigure}
  \centering
  \caption{Lay out of the COMET Phase-I, the target and detector solenoid are
  placed after the first 90\si{\degree}~bend.}
  \includegraphics[width=0.4\textwidth]{figs/comet_phase1_layout}
  \label{fig:comet_phase1_layout}
\end{SCfigure}

The COMET Phase-I has two major goals:
\begin{enumerate}
  \item Direct measurements of the proton extinction factor, and other potential
    backgrounds for the full COMET experiment. These include backgrounds due to
    beam particles such as pions, neutrons, antiprotons, photons and electrons;
    and physics background from muon DIO. Straw tube trackers and crystal
    calorimeter with the same technology in the full COMET will be used, thus
    these detectors can be regarded as the final prototype.
  \item Search for \mueconv with an intermediate sensitivity of \sn{3.1}{-15},
    a two orders of magnitude improvement from the SINDRUM-II limit. To realise
    this goal, two options for detectors are being considered, either a reused
    of the detectors for background measurements, or a dedicated detector.
    The latter will be described in detail later.
\end{enumerate}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Proton beam for the COMET Phase-I}
\label{sub:proton_beam_for_the_comet_phase_i}
Proton beam for the Phase-I differs only in beam power compares to that of the
full COMET. It is estimated that a beam power of
3.2~\si{\kilo\watt}~$=$~8~\si{\giga\electronvolt}~$\times$~0.4~\si{\micro\ampere}~(or
\sn{2.5}{12} protons\si{\per\second}) will be enough for beam properties
study and achieving the physics goal of this stage.
Starting from a lower intensity is also suitable for performing accelerator
studies that are needed to realise 8~\si{\giga\electronvolt} beam extraction from
the J-PARC main ring.
% subsection proton_beam_for_the_comet_phase_i (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Pion production and transportation solenoids}
\label{sub:pion_production_and_transportation_solenoids}

Since the beam power will be lower, it is proposed to use a graphite target in
the Phase-I. This will minimise the activation of the target station and heat
shield which will be easier for necessary upgrading for Phase-II operation.
A target length of 600~\si{\milli\meter}~(1.5 radiation length) and target radius of
20~\si{\milli\meter}~are chosen. The target is located at the centre of the pion
capture solenoid where the peak magnetic field of 5 T is achieved.
A correction dipole filed of 0.05 T is also applied to improve the pion yield.

The pion/muon beam line for COMET Phase-I consists of the pion capture solenoid
section (CS), muon transport solenoid section (TS) up to the first
90\si{\degree}~bending, and a set of matching solenoids (see
Figure~\ref{fig:comet_phase1_magnets}). At the end of the muon beam line, the
detectors and the detector solenoid (DS) are installed. To reduce beam
backgrounds, a beam collimator is placed upstream of the detector solenoid.
\begin{figure}[htb]
  \centering
    \includegraphics[width=0.85\textwidth]{figs/comet_phase1_magnets}
  \caption{A schematic view of the superconducting solenoid magnet system for
  the COMET Phase-I. Prefix CS is for capture solenoids, MS is for matching
  solenoids, and TS is for transport solenoids. BS and DS are beam collimation
  system and detector solenoid, respectively.} 
\label{fig:comet_phase1_magnets}
\end{figure}
% subsection pion_production_and_transportation_solenoids (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Detectors for \mueconv search in the Phase-I}
\label{sub:detectors_for_mueconv_search_in_the_phase_i}

As mentioned, two types of detectors are considered for physics measurements in
the Phase-I. The dedicated detector system consists of a cylindrical drift
chamber (CDC), a trigger hodoscope, a proton absorber and a detector solenoid
(Figure~\ref{fig:comet_phase1_cydet}).
The whole system is referred as cylindrical detector system (CyDet) in the
COMET's documentation. The CyDet has advantages that low momentum particles for
the stopping target will not reach the detector, thus the hit rates are kept 
manageable even at high beam currents. Furthermore, the majority of beam
particles, except those scattering at large angles, will not directly hit the
CyDet.

\begin{figure}[htb]
  \centering
    \includegraphics[width=0.85\textwidth]{figs/comet_phase1_cydet}
  \caption{Schematic layout of the CyDet.}
  \label{fig:comet_phase1_cydet}
\end{figure}

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
Table~\ref{tab:comet_phase1_cdc_params}.  
Trigger hodoscopes are placed at both upstream and downstream ends of the CDC.
An absorber is placed concentrically with respect to the CDC axis to
reduce potential high rates caused by protons emitted after nuclear muon
capture in the stopping target.

The CDC covers the region
from \SIrange{500}{831}{\milli\meter}~in the radial direction. The length
of the CDC is 1500~\si{\milli\meter}. The inner wall is made of
a 100~\si{\micro\meter}-thick aluminised Mylar. The end-plates will be conical
in shape and about 10~\si{\milli\meter}-thick to support the feedthroughs. The outer
wall is
made of 5~\si{\milli\meter}~carbon fibre reinforced plastic (CFRP). 

The CDC is arranged in 20 concentric sense layers with alternating positive and
negative stereo angles. The sense wires are made of gold-plated tungsten,
30~\si{\micro\meter} in diameter, tensioned to 50~\si{\gram}. The field wires
are uncoated aluminium wires with a diameter of 80~\si{\micro\meter}, at the same
tension of \SI{50}{\gram}. A high voltage of $1700\sim1900$~\si{\volt} will be
applied to the sense wires with the field wires at ground potential, giving an
avalanche gain of
approximately \sn{4}{4}. A gas mixture of helium:isobutane(90:10) is preferred
since the CDC momentum resolution is dominated by multiple scattering. With
these configurations, an intrinsic momentum resolution of
197~\si{\kilo\electronvolt\per\cc} is achievable according to our tracking study.

\begin{table}[htb]
  \begin{center}
    \begin{tabular}{l l l}
      \toprule
      \textbf{Inner wall} & Length & 1500 \si{\milli\meter}\\
                          & Radius & 500  \si{\milli\meter}\\
      \midrule 
      \textbf{Outer wall} & Length & 1740.9 \si{\milli\meter}\\
                          & Radius & 831 \si{\milli\meter}\\
      \midrule 
      \textbf{Sense wire} & Number of layers  & 20\\
                          & Material  & Gold-plated tungsten\\
                          & Diameter  & 30 \si{\micro\meter}\\
                          & Number of wires & 4986\\
                          & Tension   & 50 \si{\gram}\\
                          %& Radius of the innermost wire at the EP & 530 mm\\
                          %& Radius of the outermost wire at the EP & 802 mm\\
      \midrule
      \textbf{Field wire} & Material  & Aluminium\\
                          & Diameter  & 80 \si{\micro\meter}\\
                          & Number of wires & 14562\\
                          & Tension   & 50 \si{\gram}\\
      \midrule
      \textbf{Gas}        & & Helium:Isobutane (90:10)\\
      \bottomrule
    \end{tabular}
  \end{center}
  \caption{Main parameters of the CDC for the COMET Phase-I.}
  \label{tab:comet_phase1_cdc_params}
\end{table}

The maximum usable muon beam intensity will be limited by the detector hit
occupancy. Charge particles with transversal momentum greater than 70
\si{\mega\electronvolt\per\cc} are expected to reach the CDC. Those particles are:
protons emitted from nuclear muon capture, and electrons from muon decay in
orbit. It is calculated that the hit rate due to proton emission dominates,
where the highest rate is 11~\si{\kilo\hertz\per}cell compares to
5~\si{\kilo\hertz\per}
cell contributing from DIO electrons. Another potential issue caused by protons
is the ageing effect on the CDC as they leave about a 100 times larger
energy deposit than the minimum ionisation particles.

For those reasons, we plan to install an absorber to reduce the rate of protons
reaching the CDC. However, there is no experimental data available for the rate
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, which contributes
195~\si{\kilo\electronvolt\per\cc} to the momentum resolution of reconstructed
track.

In order to obtain a better understanding of the protons emission, and then
further optimisation of the CDC, a dedicated experiment to measure proton
emission rate and energy spectrum is being carried out at PSI. This experiment
is described in detail in next chapters.
% subsection detectors_for_mueconv_search_in_the_phase_i (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Sensitivity of the \mueconv search in the Phase-I}
\label{sub:sensitivity_of_the_mueconv_search_in_the_phase_i}
The SES for the Phase-I is given by
the Equation~\ref{eq:mue_sensitivity}. Using $N_{\mu} = 1.3\times 10^{16}$,
$f_{\textrm{cap}} = 0.61$, and $A_e = 0.043$ from MC study for the Phase-I, the
SES becomes: 
\begin{equation}
  \mathcal{B}(\mu^-Al\rightarrow e^- Al) = 3.1\times 10^{-15}
\end{equation}
% subsection sensitivity_of_the_mueconv_search_in_the_phase_i (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Time line of the COMET Phase-I and Phase-II}
\label{sub:time_line_of_the_phase_i}
We are now in the construction stage of the COMET Phase-I, which is planned to
be finished by the end of 2016. We will carry out engineering run in 2016,
and subsequently, physics run in 2017. A beam time of 90 days is expected to
achieve the goal sensitivity of the Phase-I. An anticipated schedule for the
COMET, both Phase-I and Phase-II, is shown in Figure~\ref{fig:sched}.
\begin{figure}[tbh]
	\centering
\includegraphics[width=0.8\textwidth]{figs/sched}
\caption{The anticipated schedule of the COMET experiment.}
\label{fig:sched}
\end{figure}

% subsection time_line_of_the_phase_i (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% section the_comet_phase_i (end)
