732 lines
35 KiB
TeX
732 lines
35 KiB
TeX
\chapter{The COMET experiment}
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\label{cha:comet_overview}
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\thispagestyle{empty}
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This chapter describes the new experimental search for \mueconv, namely COMET -
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(\textbf{CO}herent \textbf{M}uon to \textbf{E}lectron \textbf{T}ransition). The
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experiment will be carried out at the Japan Proton Accelerator Research Complex
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(J-PARC), aims at a sensitivity of \sn{6}{-17} i.e. 10,000 times better than the
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current best limit.
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%At the Japan Proton Accelerator Research Complex (J-PARC), an experiment to
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%search for \muec~conversion, which is called
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%has been proposed~\cite{comet07}. The experiment received Stage-1
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%approval in 2009. Utilising a proton beam of 56 kW (8 GeV $\times$ 7 $\mu$A)
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%from the J-PARC main ring, the COMET aims for a single event sensitivity of
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%$3 \times 10^{-17}$, which is 10000 times better than the current best limit.
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%\begin{itemize}
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%\item present status of mueconv experiments
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%\begin{itemize}
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%\item SINDRUM-II description, results, short comings
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%\item new ideas: MECO, Mu2e, COMET
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%\end{itemize}
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%\item Concepts of COMET
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%\begin{itemize}
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%\item highly intense muon beam
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%\item pulsed proton beam
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%\item curved solenoids
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%\end{itemize}
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%\item COMET's beam lines and detectors
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%\begin{itemize}
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%\item proton beam: energy, time structure, planned operations
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%\item pion production: yields, target, capture solenoids
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%\item muon transportation: requirements, field
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%\item stopping target: material, geometry, field, energy loss
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%\item electron transportation:
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%\item detectors: electron tracker and calorimeter
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%\item DAQ
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%\end{itemize}
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%\end{itemize}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Experimental status of \mueconv searches}
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\label{sec:experimental_status_of_mueconv_searches}
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\subsection{Experimental history}
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\label{sub:experimental_history}
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The searches for \mueconv has been ongoing for more than 50 years, started in
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1952 with cosmic rays~\cite{LagarriguePeyrou.1952} and then moved to
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accelerators. The list in the Table~\ref{tab:mueconv_history} is reproduced
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from a recent review of Bernstein and Cooper~\cite{BernsteinCooper.2013}.
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\begin{table}[htb]
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\begin{center}
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\begin{tabular}{l l l c}
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\toprule
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\textbf{Year} & \textbf{Limit} (90\% C.L.) & \textbf{Material}
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& \textbf{Reference}\\
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\midrule
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1952 & \sn{1.0}{-1} & Sn, Sb & \cite{LagarriguePeyrou.1952} \\
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1955 & \sn{5.0}{-4} & Cu & \cite{SteinbergerWolfe.1955} \\
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1961 & \sn{4.0}{-6} & Cu & \cite{SardCrowe.etal.1961}\\
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1961 & \sn{5.9}{-6} & Cu & \cite{ConversiLella.etal.1961}\\
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1962 & \sn{2.2}{-7} & Cu & \cite{ConfortoConversi.etal.1962}\\
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1964 & \sn{2.2}{-7} & Cu & \cite{ConversiLella.etal.1961}\\
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1972 & \sn{2.6}{-8} & Cu & \cite{ConversiLella.etal.1961}\\
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1977 & \sn{4.0}{-10} & S & \cite{ConversiLella.etal.1961}\\
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1982 & \sn{7.0}{-11} & S & \cite{ConversiLella.etal.1961}\\
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1988 & \sn{4.6}{-12} & Ti & \cite{ConversiLella.etal.1961}\\
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1993 & \sn{4.3}{-12} & Ti & \cite{ConversiLella.etal.1961}\\
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1995 & \sn{6.5}{-13} & Ti & \cite{ConversiLella.etal.1961}\\
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1996 & \sn{4.6}{-11} & Pb & \cite{ConversiLella.etal.1961}\\
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2006 & \sn{7.0}{-13} & Au & \cite{ConversiLella.etal.1961}\\
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\bottomrule
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\end{tabular}
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\end{center}
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\caption{History of \mueconv experiments, reproduced
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from~\cite{BernsteinCooper.2013}}
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\label{tab:mueconv_history}
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\end{table}
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The most recent experiments were the SINDRUM and SINDRUM-II at the Paul
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Scherrer Institute (PSI), Switzerland. The SINDRUM-II measured the branching
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ratio of \mueconv on a series of heavy targets: Ti, Pb and Au. The proton beam
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at PSI is a continuous wave beam, with a time structure of 0.3 ns bursts every
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19.75 \si{\nano\second}. An 8-\si{\milli\meter}-thick CH$_2$ degrader was used to reduce
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the radiative pion capture and other prompt backgrounds. Cosmic backgrounds are
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rejected using a combination of
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passive shielding, veto counters and reconstruction cuts. The momenta of muons
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were 52 \si{\mega\electronvolt\per\cc} and 53 \si{\mega\electronvolt\per\cc}, and the
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momentum spread was 2\%.
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\begin{figure}[htbp] \centering
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\includegraphics[width=0.85\textwidth]{figs/sindrumII_setup}
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\caption{SINDRUM-II set up}
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\label{fig:sindrumII_setup}
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\end{figure}
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Electrons emitted from the target were tracked in a 0.33 T solenoid field.
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Detector system consisted of a superconducting solenoid, two plastic
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scintillation hodoscopes, a plexiglass Cerenkov hodoscope, and two drift
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chambers. In the latest measurement, the SINDRUM-II collaboration have not
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found any conversion electron from captured muons in a gold target, hence set
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the upper limit for
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the branching ratio of \mueconv in gold with 90 \% C.L. at \sn{7.0}{-13}.
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The reconstructed momenta of electrons around the signal region from SINDRUM-II
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is shown in the Figure~\ref{fig:sindrumII_result}. It can be seen that the muon
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decay in orbit background falls steeply near the endpoint as expected, but, the
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prompt background induced by pions still remains even after the cut in timing
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and track angle. This indicates the problem of pion contamination is very
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important in probing lower sensitivity.
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=0.55\textwidth]{figs/sindrumII_Au_result}
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\caption{SINDRUM-II result}
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\label{fig:sindrumII_result}
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\end{figure}
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% subsection experimental_history (end)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{New generation of \mueconv~experiments}
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\label{sub:new_generation_of_mueconv_experiments}
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A new generation of \mueconv experiments have been proposed with scenarios to
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overcome pion induced background in the SINDRUM-II. Lobashev and collaborators
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first suggested the basic idea for new \mueconv at the Moscow Muon Factory;
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this idea was used to develop the MECO experiment at Brookhaven National
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Laboratory. The MECO experiment was cancelled due to budget constraints. The two
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modern experiments, COMET at J-PARC and Mu2e at Fermilab use the initial idea
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with more upgrades and modifications.
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The basic ideas of the modern experiments are:
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\begin{enumerate}
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\item Highly intense muon source: the total number of muons needed is of the
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order of $10^{18}$ in order to achieve a sensitivity of $10^{-16}$. This
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can be done by producing more pions using a high power proton beam, and
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having a high efficiency pion collection system;
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\item Pulsed proton beam with an appropriate timing: the proton pulse should
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be short compares to the lifetime of muons in the stopping target material,
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and the period between pulses should be long enough for prompt backgrounds
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from pion to decay before beginning the measurement. It is also crucial
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that there is no proton leaks into the measuring interval;
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\item Curved solenoids for charge and momentum selection: at first, the curved
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solenoids remove the line of sight backgrounds. A charged particle travels
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through a curved solenoidal field will have the centre of the helical
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motion drifted up or down depends on the sign of the charge, and the
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magnitude of the drift is proportional to its momentum. By using this
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effect and placing suitable collimators, charge and momentum selection can
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be made.
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\end{enumerate}
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% subsection new_generation_of_mueconv_experiments (end)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% section experimental_status_of_mueconv_searches (end)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Concepts of the COMET experiment}
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\label{sec:concepts_of_the_comet_experiment}
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This section elaborates the design choices of the COMET to realise the basic
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ideas mentioned above. Figures and numbers, other than noted, are taken from
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the COMET's documentations:
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\begin{itemize}
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%TODO citations
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\item Conceptual design report for the COMET experiment~\cite{COMET.2009}
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\item Proposal Phase-I 2012
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\item TDR 2014
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\end{itemize}
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\subsection{Proton beam}
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\label{sub:proton_beam}
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A high power pulsed proton beam is of utmost importance to achieve the desired
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sensitivity of the COMET experiment. A slow-extracted proton beam from
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the J-PARC main ring (MR), which is designed to deliver \sn{3.6}{15} protons per
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cycle at a frequency of 0.45 Hz, will be used for the COMET experiment. The
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proton beam power of the current design is 8 GeV$\times$7 $\mu$A, or
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\sn{4.4}{13} protons/s. The beam energy 8 \si{\giga\electronvolt} helps to minimise
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the production of antiprotons.
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The proton pulse width is chosen to be 100 ns, and the pulse period to be
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$1 \sim 2 \textrm{ }\mu\textrm{s}$. This time structure is sufficient for the
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search for \mueconv in an aluminium target where the lifetime of muons is 864
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ns. A plan of accelerator operation to realise the scheme is shown in
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the Figure~\ref{fig:comet_mr_4filled}, where 4 out of 9 MR buckets are filled.
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As mentioned, it is very important that there is no stray proton arrives in the
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measuring period between two proton bunches. An extinction factor is defined as
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the ratio between number of protons in between two pulses and the number of
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protons in the main pulse. In order to achieve the goal sensitivity of the
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COMET, an extinction factor of \sn{}{-9} is required.
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Requirements for the proton beam are summarised in the
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Table~\ref{tab:comet_proton_beam}.
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\begin{figure}[htb]
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\centering
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\includegraphics[width=0.8\textwidth]{figs/comet_mr_4filled}
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\caption{The COMET proton bunch structure in the RCS (rapid cycle
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synchrotron) and MR where 4 buckets
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are filled producing 100 \si{\nano\second} bunches separated by
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1.2~\si{\micro\second}.}
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\label{fig:comet_mr_4filled}
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\end{figure}
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\begin{table}[htb]
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\begin{center}
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\begin{tabular}{l l}
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\toprule
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Beam power & 56 \si{\kilo\watt}\\
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Energy & 8 \si{\giga\electronvolt}\\
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Average current & 7 \si{\micro\ampere}\\
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Beam emittance & 10 $\pi\cdot$ mm$\cdot$ mrad\\
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Protons per bunch & $<10^{11}$\\
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Extinction & \sn{}{-9}\\
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Bunch separation & $1 \sim 2$ \si{\micro\second}\\
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Bunch length & 100 \si{\nano\second}\\
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\bottomrule
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\end{tabular}
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\end{center}
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\caption{Pulsed proton beam for the COMET experiment}
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\label{tab:comet_proton_beam}
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\end{table}
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% subsection proton_beam (end)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Pion production and capture solenoid}
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\label{sub:pion_production_can_capture_solenoid}
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Muons for the COMET experiment are produced by colliding the proton beam with
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a pion production target, made of either platinum, gold or tungsten, collecting
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pions and then letting them decay. To collect as many pions (and cloud muons)
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as possible, the pions are captured
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using a high solenoidal magnetic field with a large solid angle. Since muons
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will be stopped in a conversion target, low energy muons, and thus low energy
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pions, are preferred. It is known from other measurements that backward
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scattered pions (with respect to proton beam direction) of high energy are
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suppressed, and the yield of low energy pions in the backward direction is not
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too low compares to that of the forward direction (see
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Figure~\ref{fig:pion_yield}). For these reasons, the COMET
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decided to collect backward pions.
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\begin{figure}[htb]
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\centering
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\includegraphics[width=0.95\textwidth]{figs/pion_yield}
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\caption{Comparison between backward and forward pions production in a gold
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target.}
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\label{fig:pion_yield}
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\end{figure}
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The pion capture system is composed of several superconducting solenoids:
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capture solenoids and matching solenoids. The magnetic field distribution along
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the beam axis of the COMET is shown in the Figure~\ref{fig:comet_Bfield}. The
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peak field of 5 T is created by the capture solenoid, and the matching
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solenoids provide a smooth transition from that peak field to the 3 T field in
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the pions/muons transportation region. The superconducting solenoids are
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cooled by liquid helium, and a radiation shield composed of copper and tungsten
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will be installed inside the cryostat to reduce radiation heat load.
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\begin{figure}[htb]
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\centering
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\includegraphics[width=0.85\textwidth]{figs/comet_Bfield}
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\caption{Magnetic field distribution along the COMET beam line.}
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\label{fig:comet_Bfield}
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\end{figure}
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% subsection pion_production_can_capture_solenoid (end)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Pions and muons transportation solenoids}
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\label{sub:pion_and_muon_transportation}
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Muons and pions are transported to the muon stopping target through a muon
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beam line, which includes several curved and straight superconducting solenoid
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magnets. A schematic layout of the muon beam line, include the capture and
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detector sections, is shown in Figure~\ref{fig:comet_beamline_layout}.
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\begin{figure}[htb]
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\centering
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\includegraphics[width=0.95\textwidth]{figs/comet_beamline_layout}
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\caption{Schematic layout of the COMET beam line.}
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\label{fig:comet_beamline_layout}
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\end{figure}
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The requirements for the muon transportation beam line are:
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\begin{itemize}
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\item being long enough for pions to decay, for instance, the survival rate
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of pions will be about \sn{2}{-3} after 20 m;
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\item being able to select low momentum negative muons with momentum of around
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40 MeV/$c$, and eliminate high momentum muons ($> 75\textrm{ MeV/}c$),
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since they can decay in flight and produce spurious signals of $\sim$ 105
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MeV electrons.
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\end{itemize}
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The selection of charge and momentum is done by the curved solenoids. It is
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know that, in a curved solenoidal field, the centre of the helical trajectory
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of a charged particle drifts perpendicularly to the curved plane. The magnitude
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of the drift is given by:
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\begin{align}
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D &= \frac{1}{qB} \frac{s}{R} \frac{p_L^2 + \frac{1}{2}p_T^2}{p_L}\\
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&= \frac{1}{qB} \frac{s}{R} \frac{p}{2}
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\left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right)\\
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&= \frac{1}{qB} \theta_{bend} \frac{p}{2}
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\left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right)
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\end{align}
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where $q$ is the electric charge of the particle; $B$ is the magnetic field at
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the axis; $s$ and $R$ are the path length and the radius of the curvature; $p$,
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$p_T$ and $p_L$ are total momentum, transversal momentum and longitudinal
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momentum of the particles, respectively; $\theta = \textrm{atan}(p_T/p_L)$ is
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the pitch angle of the helical trajectory; and $\theta_{bend} = s/R$ is called
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the bending angle.
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It is clear that $D$ is proportional to $\theta_{bend}$, to total momentum $p$.
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Charged particles with opposite signs move in opposite directions. Therefore it
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is possible to select muons around 40 MeV/$c$ by using suitable collimator
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after the curved solenoid.
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In order to keep the centre of the helical trajectories of the muons with
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a reference momentum $p_0$ in the vertical plane, a compensating dipole field
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parallel to the drift direction is needed. In the COMET, the dipole fields are
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produced by additional coils winded around the solenoid coils. The magnitude of
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the compensating field is:
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\begin{equation}
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B_{\textrm{comp}} = \frac{1}{qR} \frac{p_0}{2}
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\left( \textrm{cos}\theta_0 + \frac{1}{\textrm{cos}\theta_0} \right)
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\end{equation}
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where the trajectories of charged particles with momentum $p_0$ and pitch angle
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$\theta_0$ are corrected to be on-axis. An average dipole field of 0.03 T is
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needed to select 40 MeV/$c$ muons as required by the COMET design.
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% subsection pion_and_muon_transportation (end)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Muon stopping target}
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\label{sub:muon_stopping_target}
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Muon stopping target is place at 180\si{\degree}~bending after the pion production
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target (Figure~\ref{fig:comet_beamline_layout}) in its own solenoid. The target
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is designed to maximise the muon stopping efficiency and minimise the energy
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loss of signal electrons.
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%\hl{TODO: Target choice: separation, product, lifetime, energy loss\ldots}
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It is calculated that the branching ratio of \mueconv increases with atomic
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number $Z$, and plateaus above $Z \simeq 30$, then decreases as $Z>60$. The
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lifetime of muons inside a material decreases quickly as $Z$ increases.
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Tracking wise, lower $Z$ material provides better reconstructed momentum
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resolution. Therefore, light material is preferable as muon stopping target.
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The first choice for the muon stopping target material in the COMET is
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aluminium. A titanium target is also considered. Configuration of the target is
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shown in the Table~\ref{tab:comet_al_target}. Monte Carlo studies with this
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design showed that net stopping efficiency is 0.29, and average energy loss
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of signal electrons is about 400 \si{\kilo\electronvolt}.
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\begin{table}[htb]
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\begin{center}
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\begin{tabular}{l l}
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\toprule
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\textbf{Item} & \textbf{Specification}\\
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\midrule
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Material & Aluminium\\
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Shape & Flat disks\\
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Disk radius & 100 \si{\milli\meter}\\
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Disk thickness & 200 \si{\micro\meter}\\
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Number of disks & 17\\
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Disk spacing & 50 \si{\milli\meter}\\
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\bottomrule
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\end{tabular}
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\end{center}
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\caption{Configuration of the muon stopping target.}
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\label{tab:comet_al_target}
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\end{table}
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A graded magnetic field (reduces from 3 T to 1 T) is produced at the
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location of the stopping target (see Figure~\ref{fig:comet_target_Bfield}) to
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maximise the acceptance for \mueconv signals, since electrons emitted in the
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backward
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direction would be reflected due to magnetic mirroring. The graded field also
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helps optimising the transmission efficiency to the subsequent electron
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transport section.
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\begin{figure}[htb]
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\centering
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\includegraphics[width=0.85\textwidth]{figs/comet_target_Bfield}
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\caption{The graded magnetic field near the stopping target region.}
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\label{fig:comet_target_Bfield}
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\end{figure}
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% subsection muon_stopping_target (end)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Electron transportation beam line}
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\label{sub:electron_transportation_beam_line}
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The 180\si{\degree}~bending electron transport solenoids help remove line-of-sight
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between the target and the detector system. It works similarly to the muon
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transportation section, but is tuned differently to accept electrons of about
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105~\si{\mega\electronvolt\per\cc}. A compensation field of 0.17 T along the
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vertical direction will be applied. Electrons with momentum less than 80
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\si{\mega\electronvolt\per\cc} are blocked at the exit of this section by
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a collimator to reduce DIO electrons rate. The net acceptance of signals of
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\mueconv is about 0.32, and the detector hit rate will be in the order of
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1~\si{\kilo\hertz}~for \sn{}{11} stopped muons\si{\per\second}.
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% subsection electron_transportation_beam_line (end)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Electron detectors}
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\label{sub:electron_detectors}
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The \mueconv signal electrons is measured by an electron detector system, which
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consists of straw-tube trackers and an electromagnetic calorimeter - shown in
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Figure~\ref{fig:comet_detector_system}. The
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requirements for the detector system is to distinguish electrons from other
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particles, and measure their momenta, energy and timings. The whole detector
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system is in a uniform solenoidal magnetic field under vacuum. Passive and
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active shielding against cosmic rays is considered.
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The tracking detector has to provide a momentum resolution less than
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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)
|