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%%%%%%%%%%%%%%%%%%%%%%%%%%% Begin
\begin{document}
%\title{Proposal}
%\author{Alcap}
%\maketitle
%\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%% TOC
%\tableofcontents
%\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Scientific background and aim of the experiment}
\label{sec:motivation}
\subsection{Scientific background}
The recent observation that neutrinos oscillate and change flavour and so have
mass requires an extension to the SM and demonstrates that lepton flavour is
not an absolutely conserved quantity. However, even in this minimal extension
to the SM, accommodating neutrino masses, the rate of charged lepton flavour
violating (CLFV) interactions is predicted to be $O(10^{-54})$, and is far too
small to be observed. As such, any experimental observation of CLFV
ould be a clear evidence of new physics beyond the SM.

Two new projects have ben established to search for a CLFV process,
$\mu^-N\rightarrow e^-N$ conversion. They are Mu2e experiment~\cite{mu2e08} 
at FNAL and the COMET experiment~\cite{come07} at J-PARC. The two experiments
will both utilise multi-kW pulsed 8$-$9 GeV proton beams to achieve a branching
ratio sensitivities lower than 10$^{-16}$, that is   10,000 better than current
best limit established by SINDRUM II.  Both COMET Phase--I and 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. In that momentum ranges, it turns out that single hit
rates of the tracking chambers would be dominated by protons after nuclear muon
capture.  In order to limit the single hit rate of the tracking chamber to an
acceptable level, both experiments are considering to place proton absorbers in
front of the tracking chambers to reduce proton hit rates. 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.  

\subsection{Goal of the experiment}
The goal of the experiment is to measure the rate and energy spectra of the
charged particles emitted after a muon is captured on aluminum, silicon and
titanium targets. A precision of 5\% down to an energy of 2.5 MeV is required
for both the rate and the energy spectra. 

\subsection{Urgency}
The Mu2e experiment is now under the DOE Critical Decision Review process. The
COMET Phase--I construction, at least the beam line, might start next year in
2013. The COMET collaboration needs to complete the 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 Al and Ti have not been measured in the
relevant energy range for COMET Phase--I and Mu2e.
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, for both COMET
Phase--I and Mu2e, the above analytical spectrum has been used to estimate proton
emission. And also the $p, d, \alpha$ composition is not known. 

A test experiment has been conducted at PSI in 2009 and we have had a better
understanding of the intrumentations and possible backgrounds involved.

\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}.
It will be an improved version of a test experiment performed by part of this
collaboration at PSI in 2009.

Low energy negative muons (less than 30 MeV/c) will be detected by external beam
counters  and then enter a vacuum vessel though a thin mylar
window. They will be stopped in passive Al and Ti foils of 25 to 200 $\mu m$
thickness, positioned under 45 degrees to the beam direction. As a cross check
they will also be stopped in active Si detectors used as 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. 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.  

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. 

The main systematic issues are as follows. 

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

\item Deconvolute the orginal proton spectrum $f(T_i)$: firstly, an optimal
	cloud muon beam is requested for the experiment. Second, 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 with an active target.
\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: electron background will be determined with $\mu^+$, neutron
	recoils by absorbing the proton component before the Si detectors. A
	dangerous background are muons stops in walls and scattered into the Si
	detector. 
\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 10--day beamtime for the test measurement.  This is based on
the estimation as follows. 
\begin{itemize}
		\setlength{\itemsep}{1pt}
		\setlength{\parskip}{0pt}
		\setlength{\parsep}{0pt}
	\item 2 days setup time including the installation of the equipment, 
	\item 1 days of beam tuning and adjustment of electronics, 
	\item 1 week for data taking with 2 different thick targets of 3.5 day data
		taking for each.
		Data taking of 7 days is based on the estimated rate of protons using
		Geant4 simulation: the proton yield is  $5\times 10^{-4}$ per stopped
		muons, about 50\% of muons will be stopped in the 200 $\mu m$ target, and
		we will use the double pulse to have 50 bunches of muons in one second.
		We want to accumulate 3000 events for each sample in this test experiment.
\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{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}
