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\begin{document}
%\title{Proposal}
%\author{Alcap}
%\maketitle
%\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%% TOC
%\tableofcontents
%\newpage
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\section{Scientific background and aim of the experiment}
\label{sec:motivation}
\subsection{Scientific background}
Charged lepton flavor violation (CLFV) has yet to be observed and is known to
be sensitive to new physics beyond the Standard Model (SM). The J-PARC E12
experiment, COMET~\cite{come07}, is a new experiment to search for a CLFV process of
neutrinoless muon-to-electron conversion in presence of a nucleus (\muec).
Utilising multi-kW pulsed 8$-$9 GeV proton beams, COMET can achieve a branching
ratio sensitivities lower than 10$^{-16}$, that is   10,000 better than current
best limit established by SINDRUM II~\cite{sindrumii}.  

Recently, COMET collaboration has adopted a staged approach, in which the COMET 
Phase--I~\cite{phaseI12}, with a partial muon transport solenoid, will
have physics runs in 2016. The tracking chamber for COMET Phase--I are designed
to measure charged particles of their momenta in the range from 70 MeV/$c$ to
105 MeV/$c$. 
In that momentum range, single hit
rate of the tracking chamber would be dominated by protons after nuclear muon
capture.  In order to limit the single hit rate to an
acceptable level, a proton absorber would be installed in
front of the tracking chambers to reduce proton hit rate. However, the proton
absorber would deteriorate the reconstructed momentum resolution of electrons
at birth. And similarly the rate of proton emission is important to determine
thickness of the muon stopping target made of aluminum. Therefore it is
important to know the rate so that the detector system can be optimized in
terms of both hit rate and momentum resolution.  
%Mu2e will be subject to significant backgrounds from the products of the
%nuclear capture
%process. Among them,  the background for protons is a particularly acute one.
%, and its detailed
%investigation is the subject of this proposal, which is a joint proposal on
%behalf of both the Mu2e and COMET collaborations.

%The tracking chambers of COMET Phase--I~\cite{phaseI12} and Mu2e are designed
%to be measure charged particles of their momenta greater than 70 MeV/$c$ and 53
%MeV/$c$ respectively. 

\subsection{Goal of the experiment}
The goal of the experiment is to measure the rate and energy spectra of the
protons emitted after a muon is captured on aluminum and silicon targets.
A precision of 5\% in the range from 3 to 6 MeV (momentum from 75 MeV/$c$ to
105 MeV/$c$) is required for both the rate and the energy spectra. 

\subsection{Urgency}
 The construction of 
COMET experimental hall has started in 2013, a prototype of the tracking
chamber is being designed, and chamber contruction should be finished by the
end of 2015.
The COMET collaboration needs to complete the final detector design as soon as
possible. Therefore, measurements of proton emission rates and spectrum that
can be done as early as possible become one of the critical path for the both
experiments.

% section motivation (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Present status of the research}
At present, the yield, energy spectrum and composition of the charged
particles emitted in muon capture on aluminum have not been measured in the
relevant energy range for COMET Phase--I.
Figure~\ref{fg:silicon-proton} shows the spectrum of charged particle emission
from muons being stopped and captured in a silicon detector \cite{sobo68}. The
peak below 1.4 MeV is from the recoiling heavy ions, mainly $^{27}$Al, when no
charged particles were emitted. Hungerford~\cite{hung34} fitted the silicon
spectrum in Fig.~\ref{fg:silicon-proton} with an empirical function given by
%
\begin{equation} p(T) = A(1-{T_{th} \over T})^{\alpha} e^{-(T/T_0)}
	\label{eq:protons} \end{equation}
%
	\begin{wrapfigure}{l}{0.5\textwidth}
		\vspace{-10pt}
		\centering
			\includegraphics[width=0.48\textwidth]{figs/si-proton.pdf} 
		\caption{Charged particle spectrum from muon capture on an active silicon
		target~\cite{sobo68}.} 
		\label{fg:silicon-proton} 
		\vspace{-10pt}
	\end{wrapfigure}
where $T$ is the kinetic energy and the fitted parameters are $A=0.105$
MeV$^{-1}$, $T_{th}$ = 1.4 MeV, $\alpha$=1.328 and $T_0$ = 3.1 MeV. The
spectrum is normalized to 0.1 per muon capture. Some other results in the past
experiments are summarized in a comprehensive review by D.F.
Measday~\cite{measday}.

%\begin{figure}[tb] \centering
	%\includegraphics[width=0.7\textwidth]{figs/si-proton.pdf} \caption{charged
	%particle spectrum from muons stopping and being captured in a silicon
	%detector~\cite{sobo68}.} \label{fg:silicon-proton} \end{figure}
	%\begin{wrapfigure}{l}{0.5\textwidth}
		%\vspace{-25pt}
		%\begin{center} 
			%\includegraphics[width=0.48\textwidth]{figs/si-proton.pdf} 
		%\end{center}
		%\vspace{-20pt}
		%\caption{Charged particle spectrum from muon capture on an active silicon
		%target ~\cite{sobo68}.} 
		%\label{fg:silicon-proton} 
		%\vspace{-10pt}
	%\end{wrapfigure}

%\begin{table}[tb] 
	%\centering \caption{Probabilities in unites of $10^{-3}$ per
	%muon capture for inclusive proton emission calculated by Lifshitz and Singer.
	%The numbers in crescent parenthesis are estimates for the total inclusive
	%rate derived from the measured exclusive channels by the use of the
	%approximate regularity, such as $(\mu, \nu p):(\mu, \nu p n):(\mu, \nu p
	%2n):(\mu. \nu p 3n) = 1:6:4:4$.}\label{tb:proton} \vskip 3mm
	%\begin{tabularx}{\textwidth}{|c|c|c|c|X|}\hline Target nucleus & Calculation & Experiment
		%& Estimate & Comments \\ \hline $_{10}$Ne & & $200\pm 40$ & & \\
		%$^{27}_{13}$Al & 40 & $>28 \pm 4$ & (70) & 7.5 for $T>40$ MeV \\
		%$^{28}_{14}$Si & 144 & $150\pm30$ & & 3.1 and 0.34 $d$ for $T>18$ MeV \\
		%$^{31}_{15}$P & 35 & $>61\pm6$ & (91) & \\ $^{46}_{22}$Ti & & & & \\
		%$^{51}_{23}$V & 25 & $>20\pm1.8$ & (32) & \\ \hline \end{tabularx}
	%\end{table}

The limited information available makes it difficult to draw
quantitative conclusive detector design.  At this moment
the above analytical spectrum has been used to estimate proton
emission in COMET Phase--I detector designs.

For this measurement, a DC muon beam, such as at TRIUMF or PSI, is the best
choice. A test experiment has been conducted at PSI in 2009 by Mu2e, but
without a conclusive result. We have discussed with them to have a better
understanding of the instrumentations and possible backgrounds involved. An
experiment similar to the one in 2009 is scheduled at PSI in the end of
2013. This is a joint effort of the two collaborations, COMET and Mu2e.

The experiment in this proposal could serve two purposes: (a) cross check
for the PSI experiment, and (b) back up plan in case that the PSI experiment
could not be carried out.

\section{Experimental method} % (fold) \label{sec:expdescpription}
\begin{wrapfigure}{r}{0.4\textwidth}
	\centering
	\includegraphics[width=0.38\textwidth]{figs/setup_gr} 
	\caption{Schematic layout of the experimental setup}
	\label{fg:setup}
	\vspace{-10pt}
\end{wrapfigure}
A schematic layout of the experimental setup is shown in Fig.~\ref{fg:setup}.
Low energy negative muons (28 MeV/$c$) will enter a vacuum vessel
though a thin mylar window, and will be stopped in passive Al foils of 25
-- 200 $\mu m$
thickness, positioned under 45 degrees to the beam direction. 
As a cross check, an active silicon target of 140 $\mu m$ will also be used.
A long duct is prepared to avoid potential background from muons that are not
stopped in the target.

Two packages
of charged particle detectors are positioned on opposite sides, parallel
to the target surface. The thin Si detectors (65 $\mu m$) will provide dE/dx
information. The thick Si detectors (1500 $\mu m$) stop protons up to about 12
MeV. According to a simple Geant4 simulation, we can use dE/dx method to do
PID (Fig.~\ref{fg:dedx}).

%Plastic scintillators positioned
%behind these Si detector observe potential higher energy protons and veto
%through--going electrons.  
The symmetry
between the left and right Si stations allows for a powerful monitor of
systematic effects. Differences between the detectors would indicate background
due to different stopping material, non--uniform stopping distribution or
differences due to muon scattering. 

Muon bunch signal will be used as the trigger for the DAQ system. The DAQ
system collects data in a fixed period of time after this trigger.
Timing and energy information from silicon detectors will be read out by
flash ADCs (FADC).

Particle identification can also be done using TOF method. In this case,
extended pipes need to be connected to the chamber, and distance between dE and
E detectors would be increased to about 15 cm.

Careful shielding of direct or scattered
muons is required, as the stopping fraction is small and proton emission is a
rare capture branch. As shown, we are considering a geometry, where there is no
direct line of sight between any low Z material exposed to muons, with all
shielding done with lead. 

In order to normalize a  number of muons stopping in the aluminum target, a
germanium detector to measure muonic X-rays from muons stopping in the aluminum
target is installed. 

\begin{wrapfigure}{r}{0.4\textwidth}
	\centering
	\includegraphics[width=0.38\textwidth]{figs/dEdx-mlf} 
	\caption{PID using two silicon detectors: 65 $\mu m$ and 1500 $\mu m$ thick}
	\label{fg:dedx}
	\vspace{-10pt}
\end{wrapfigure}
The main systematic issues are as follows. 

\begin{itemize}
		\setlength{\itemsep}{1pt}
		\setlength{\parskip}{0pt}
		\setlength{\parsep}{0pt}

\item Deconvolute the orginal proton spectrum $f(T_i)$: the use of an active
	Si target allow the experimental calibration of the response function,
	because both initial energy $T_i$ and final energy $T_f$ of protons are
	accessible.
\item Absolute calibration: the number of
	muon stops will be determined with
	the Ge detector. Again, the use of an active Si target allows for a cross
	calibration. The proton detection efficiency will be simulated by Geant4 and
	calibrated with the active Si target.
\item The PID of emitted charged particles will be determined by dE/dx.
\item Background: a dangerous background comes from muons stop in walls and
	scatter into the Si detectors. 
\end{itemize}

%A realistic Geant4 simulation is being developed. It will serve as an important
%tool to optimize the geometry, in particular regarding background and response
%function. Currently the geometry of the PSI test run is being implemented for a
%realistic check of the simulation.

%We have a vacuum chamber and Si detectors, which were used for a
%similar measurement done at PSI in 2009. For a coming beam test, the
%vacuum chamber is being tested now at University of Washington
%(UW). The two exiting Si detectors are also being tested at UW. A
%possibility to prepare another set of Si detectors is being
%sought. Amplifiers for the existing Si detects are available. The
%Osaka University (OU) group is preparing DAQ system based on a PSI
%standard data acquisition system (MIDAS). The OU group is making
%arrangement of getting a Ge detector for muonic X-ray measurement,
%either borrowing from someone or purchasing a new one. Monte Carlo
%simulations necessary to optimize detector configuration is undergoing
%at OU and University College London (UCL). 
%Some test beam run to examine a number of muons of low momentum is
%being requested in September, 2012 and
%will be performed with a simplified set-up. The full set-up will be
%ready beginning December 2012.
%\begin{figure}[htb] 
	%\begin{center}
	%\includegraphics[width=0.9\textwidth]{figs/dedx.png} 
	%\caption{2-dim. plots of
	%S1 (vertical) vs S2 (horizontal) counters. The plot in top left is for all
	%charged particles. The ones in top right, bottom left and bottom right are
	%for only protons, proton+deuteron, proton+deuteron+muons.}
	%\label{fg:dedx}
%\end{center} 
%\end{figure}

%Figure~\ref{fg:dedx} shows Monte Carlo simulation studies of two-dimensional
%plots of energy of the S1 counter (dE/dX) vs. energy of the S2 counter. From
%Fig.~\ref{fg:dedx}, it is clearly seen that we can discriminate protons,
%deuterons and scattered muons and electrons by this particle identification
%method. And the range of proton energy from 2.5 MeV to 20 MeV can be detected. 

%The event rates are estimated based on Monte Carlo simulation.  Preliminary
%results are summarized in Table~\ref{tb:rates}. They will be updated once we
%have full information about the PSI beam properties. As seen in
%Table~\ref{tb:rates}, proton rates of $T>2.5$ MeV are not large. A muon beam
%whose momentum is low and momentum width is narrow is of critical importance.
%And also a ratio of signal to background is 1:50. Therefore, a good particle
%identification is important. From Monte Carlo simulation, a combination of
%dE/dX and E counters has a sufficient capability of discriminating protons from
%the other charged particles. 
% section expdescpription (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Beam time estimation}

We are requesting a 6--day beam time (two consecutive blocks).  This is based on
the estimation as follows: 
\begin{itemize}
	\setlength{\itemsep}{1pt}
	\setlength{\parskip}{0pt}
	\setlength{\parsep}{0pt}
	\item 1 days of beam tuning and adjustment of electronics, 
	\item 5 days of data taking: the proton hit rate on the detectors estimated
		by the Geant4 simulation is $2 \times 10^{-3}$ per muon bunch. We want to
		accumulate 5000 events in 20 bins from 3 MeV to 6 MeV, that means 10000
	proton events in total. So, we will need $5 \times 10^{6}$ bunches, or $2
	\times 10^5$ seconds = 2.3 days ( at 25 Hz beam frequency) for one sample. We
	intend to have two measurements with two targets: active silicon, and
	aluminum 200 $\mu m$.
\end{itemize}

\begin{thebibliography}{9}

%\bibitem{Kuno:1999jp}
  %Y.~Kuno and Y.~Okada,
	%``Muon decay and physics beyond the standard model,''
  %{\it Rev.\ Mod.\ Phys.\  }{\bf 73}, 151 (2001)     
%\bibitem{masi06} L.~Calibbi, A.~Faccia, A.~Masierro, and S.K. Vempati, Phys.
%Rev. {\bf D74} 116002 (2006).
%
%\bibitem{mu2e08} R.M.~Carry {\it et al.} (Mu2e collaboration), ``Proposal to
	%Search for \muec with a Single Event Sensitivity Below $10^{-16}$, FNAL
	%proposal, 2008.
%
\bibitem{come07} Y.~Kuno {\it et al.} (COMET collaboration),  ``A Experimental
	Search for Lepton Flavor Violating \muec Conversion at Sensitivity of
	$10^{-16}$ with A Slow-Extracted Bunched Proton Beam'', J-PARC Proposal, 2007
	and J-PARC Conceptual Design Report, 2009.

\bibitem{sindrumii} W.~Bertl {\it et al.} (SINDRUM-II collaboration),  ``A
	search for $\mu - e$ conversion in muonic gold'', The European Physical
	Journal C 47 (2006).
337-346.\\
%
\bibitem{phaseI12} Y.~Kuno {\it et al.} (COMET collaboration), ``Letter of
	Intent of Phase--I for the COMET Experiment at J-PARC'', March
	2012. 
%
\bibitem{sobo68} S.E. Sobotka and E.L. Willis, Phys. Rev. Lett. {\bf 20}
	596-598, (1968).
%
%\bibitem{bala67} V. Balashov and R. Eramzhyan. Atomic Energy Reviews 5, 1967.
%
\bibitem{hung34} E. Hungerford, ``Comment on Proton Emission after Muon
	Capture'', MECO note 34.

\bibitem{measday} D.F. Measday, {\it Phys.  Rep. }{\bf 354} (2001) 
\end{thebibliography}
\end{document}
