\documentclass[12pt]{article}
\usepackage{latexsym,multicol,graphicx,rotating}
\usepackage{hyperref}
\usepackage{booktabs}
\usepackage{tabularx}
\usepackage{color}
\usepackage[affil-it]{authblk}

\hypersetup{
colorlinks = false,
linkcolor = red,
linktoc=page,
linkbordercolor={1 0 0}
%linkcolor=blue,
}
%%%%%%%%%%%%% user's command definitions
%\setlength{\textwidth}{16cm}
\newcommand{\ttbs}{\char'134}
\newcommand{\AmS}{{\protect\the\textfont2
  A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
\newcommand{\lagr}{\cal{L}}
\newcommand{\mueg}{$\mu^{+} \rightarrow e^{+}\gamma$~}
\newcommand{\meee}{$\mu \rightarrow eee$~}
\newcommand{\muenn}{$\mu \rightarrow e \nu \overline{\nu}$~}
\newcommand{\muenng}{$\mu \rightarrow e \nu \overline{\nu} \gamma$~}
\newcommand{\muec}{$\mu^{-} N \rightarrow e^{-} N$~}
\makeatletter
\def\@maketitle{%
  \newpage
  \null
  \vskip 2em%
  \begin{center}%
  \let \footnote \thanks
    {\Large\bfseries \@title \par}%
    \vskip 1.5em%
    {\normalsize
      \lineskip .5em%
      \begin{tabular}[t]{c}%
        \@author
      \end{tabular}\par}%
    \vskip 1em%
    {\normalsize \@date}%
  \end{center}%
  \par
  \vskip 1.5em}
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%% Begin
\begin{document}
\title{Proposal \\
Measurements of Muon Nuclear Capture 
\\on Aluminum to Study Background for \\
Muon to Electron Conversion Experiments}
\author[1]{Peter Kammel \thanks{pkammel@uw.edu}}
\author[2]{Yoshitaka Kuno \thanks{kuno@phys.sci.osaka-u.ac.jp}}
\affil[1]{University of Washington}
\affil[2]{Osaka University}
\maketitle
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{abstract}
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
would be a clear evidence of new physics beyond the SM.

Two new projects have been established to search for a CLFV process,
$\mu^-N\rightarrow e^-N$ conversion. They are Mu2e experiment at FNAL and the
COMET experiment 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 goal of the experiment is to measure the rates 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 rates and the energy spectra. Thin targets and a high quality, low
energy muon beam with a small momentum spread are essential for the experiment
so that a high rate of stopped muons can be achieved, and so that the charged
particles do not lose a significant amount of energy in the target - a main
difficulty that prevents any relevant measurements on these targets.
\end{abstract} 
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%% TOC
\tableofcontents
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Beam requirements and Beam request}
\label{sec:beamrequest}
Experimental area: $\pi$E1 beam line

\noindent Required beam properties:
\begin{itemize}
	\item Particle: $\mu^-$
	\item Momentum: 30 MeV/c
	\item Momentum width: 1.9 \% FWHM
	\item Beam spot: maximum 5 cm in diameter \textcolor{red}{(?)}
	\item Intensity: $5 \times 10^{4}$ s$^{-1}$
	\item Beam purity: \textcolor{red}{???}
\end{itemize}
\noindent Duration of the experiment: we are requesting three weeks of
measurements, with details: 
\begin{itemize}
	\item 2 days for setting up the equipments,
	\item 5 days for beam tuning and adjustment of data aquisition system,
	\item 7$\times$2 days for data taking with two different targets, this is
		based on the estimated rate of protons shown in Table~\ref{tb:rates} and we
		want to have at least $10^5$ events for each sample.
\end{itemize}
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Declaration of hazardous materials and equipments} % (fold)
\label{sec:safety}
%Declaration sheet of hazardous materials, still need detailed description in
%the full text ,though.
\begin{enumerate}
	\item Radiation: some calibration sources will be used, there is no dangerous
		radioactivity involved.
	\item High voltages: low current high voltages will be used, all HV cables
		are concealed within commercial HV supply units, cables and SHV connectors.
	\item Fire and explosion: no explosive material will be used in the
		experiment.
	\item Cryogenic apparatus: liquid nitrogen will be used for the Ge detector,
		standard precautions will be taken.
\end{enumerate}
\newpage
% section safety (end)

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Physics motivation} % (fold)
\label{sec:motivation}
\subsection{Introduction}

It is known that quarks and neutrinos are mixed and therefore their
flavors are not conserved in the Standard Model (SM). However, lepton
flavor violation for charged leptons has not yet been observed. In
the minimal version of the SM where massless neutrinos are assumed,
lepton flavor conservation is a natural consequence of the gauge
invariance. Therefore, it has been considered to naively explain why
charged lepton flavor violation (CLFV) is highly suppressed. More
recently, the observation of neutrino oscillations has demonstrated
that neutrinos are massive and mixed among different neutrino flavor
species. Therefore, lepton flavor for neutrinos is known to be
violated. 

In the framework of the Standard Model (SM) with massive neutrinos and their
mixing, the branching ratio of $\mu\rightarrow e\gamma$ decay can be estimated.
This process is suppressed by the GIM mechanism and the estimated branching
ratio is tiny, about $O(10^{-54})$ As a result, the observation of CLFV would
indicate a clear signal of new physics beyond the SM.  The discovery of CLFV is
considered to be one of the important subjects in elementary particle
physics~\cite{Kuno:1999jp}.

CLFV is known to be sensitive to various extension of new physics beyond the
SM. Among them, a well-motivated physics model is a supersymmetric (SUSY)
model.  In SUSY models, the slepton mixing (given by off-diagonal elements of
the slepton mass matrix) would introduce CLFV. In the minimum SUSY scenario,
the slepton mass matrix is assumed to be diagonal at the Planck scale. At a low
energy scale, new physics phenomena such as grand-unification (GUT) or neutrino
seesaw would introduce off-diagonal matrix elements such as $\Delta
m_{\tilde{\mu}\tilde{e}}$ through quantum corrections (renormalization).
Therefore, the slepon mixing is sensitive to GUT (at $10^{16}$ GeV) or neutrino
seesaw mechanism (at $10^{13-14}$ GeV). As a result,  CLFV has potential to
study physics at very high energy scale.

A prominent muon CLFV processes is coherent neutrino-less conversion of a
negative muon to an electron (\muec conversion) in a muonic atom.  When a
negative muon is stopped in material, it is trapped by an atom, and a muonic
atom is formed. After it cascades down energy levels in the muonic atom, the
muon is bound in its 1{\em s} ground state. The fate of the muon is then either
decay in orbit (DIO) ($\mu^{-} \rightarrow e^{-}\nu_{\mu} \overline{\nu}_{e}$)
or nuclear muon capture by a nucleus $N(A,Z)$ of mass number $A$ and atomic
number $Z$, namely, $\mu^{-} + N(A,Z) \rightarrow \nu_{\mu} + N(A,Z-1)$.
However, in the context of lepton flavor violation in physics beyond the
Standard Model, the exotic process of neutrino-less muon capture, such as
%
\begin{equation} \mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z), \end{equation}
%
is also expected. This process is called \muec conversion in a muonic atom.
This process violates the conservation of lepton flavor numbers, $L_{e}$ and
$L_{\mu}$, by one unit, but the total lepton number, $L$, is conserved. 

The event signature of coherent \muec conversion in a muonic atom is a
mono-energetic single electron emitted from the conversion with an energy
($E_{\mu e}$) of $E_{\mu e} = m_{\mu} - B_{\mu} - E_{recoil}$, where $m_{\mu}$
is the muon mass, and $B_{\mu}$ is the binding energy of the 1$s$ muonic atom.
$E_{recoil}$ is the nuclear recoil energy which is small and can be ignored.
Since $B_{\mu}$ varies for various nuclei, $E_{\mu e}$ could be different. For
instance, $E_{\mu e} = 104.9$ MeV for aluminum (Al) and $E_{\mu e}$ = 104.3 MeV
for titanium (Ti).

From an experimental point of view, \muec conversion is a very attractive
process: Firstly, the energy of the signal electron of about 105 MeV is far
above the end-point energy of the normal muon decay spectrum ($\sim$ 52.8 MeV).
Secondly, since the event signature is a mono-energetic electron, no
coincidence measurement is required. The search for this process has the
potential to improve sensitivity by using a high muon rate without suffering
from accidental background events, which would be serious for other processes,
such as $\mu\rightarrow e\gamma$ and $\mu\rightarrow eee$ decays.

The previous search for \muec conversion was performed by the SINDRUM II
collaboration at PSI.  The SINDRUM II spectrometer consisted of a set of
concentric cylindrical drift chambers inside a superconducting solenoid magnet
of 1.2 Tesla. They set an upper limit of \muec in Au of $B(\mu^{-} + Au
\rightarrow e^{-} + Au) < 7 \times 10^{-13}$. 

\begin{figure}[htb]
%\vspace{-40mm}
\centering
\includegraphics[width=\textwidth]{figs/comet-mu2e}
\caption{Schematic layouts of the Mu2e (left) and the COMET (right).}
\label{fg:mu2ecomet}
%\vspace{-5mm}
\end{figure}

New experimental projects to search for \muec conversion with a higher
sensitivity are being pursued in the USA and Japan. The proposal in
the USA is the Mu2e experiment at FNAL~\cite{mu2e08}. It is aiming to
search for \muec conversion at a sensitivity of better than
$10^{-16}$. Figure~\ref{fg:mu2ecomet}(left) shows its proposed layout.
 It consists of the production solenoid system, the transport solenoid system
 and the detector solenoid system. The Mu2e experiment is planned to combat
 beam-related background events with the help of a 8 GeV/$c$ bunched proton
 beam of about 8 kW in beam power at FNAL. The detector solenoid is a straight
 solenoid and therefore both positive and negative charged particles from the
 target enter the detector. The Mu2e experiment was approved at FNAL PAC in
 2009 and obtained the DOE CD-0 approval. Right now the Mu2e collaboration is
 working on CD-1.

The other experimental proposal to search for \muec conversion, which is called
COMET (COherent Muon to Electron Transition), is being prepared at the Japan
Proton Accelerator Research Complex (J-PARC), Tokai, Japan~\cite{come07}. The
aimed sensitivity at COMET is similar to Mu2e, namely better than $10^{-16}$. A
schematic layout of the COMET experiment is presented in
Figure~\ref{fg:mu2ecomet}(right). The major differences of the designs between
Mu2e and COMET exist in the adoption of C-shape curved solenoid magnets for
electron transport. It is useful to eliminate oppositely-charged particles
(like protons) from nuclear muon capture, before going into the detector,
resulting in lower single counting rates in the detectors.  

Recently, the COMET collaboration has taken a two-staged approach, in which
COMET Phase-I starts early and COMET Phase-II (the full COMET) will
follow~\cite{phaseI12}. KEK and J-PARC have endorsed the staged approach.
Because of the Phase-I budgetary constraints, a detector to search for \muec
conversion in COMET Phase-I would be a cylindrical drift chamber placed in a
solenoidal magnetic field, as shown in Fig.~\ref{fg:phase1}. In this
configuration, both positive and negative particles (including protons) could
enter the drift chamber. Right now, KEK is keen to start construction of COMET
Phase-I in 2013 as the earliest, if the budget is available. 
%
\begin{figure}[htb!]
\centering
\includegraphics[width=.5\textwidth]{figs/comet_phase1_tracker}
\caption{Schematic layout of a cylindrical detector for COMET Phase-I.}
\label{fg:phase1}
%\vspace{-5mm}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Scientific value of the experiment}

We, as a jointed force between Mu2e and COMET, would like to measure rates and
energy spectrum of charged particle emission after nuclear muon capture on
aluminum. The rates and spectra of charged particle emission, in particular
protons, is very important to optimize the detector configuration both for the
Mu2e and COMET Phase-I experiments. 

\noindent The tracking chambers of COMET Phase-I 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.
The second source of the hit rate will be electrons from muon decays in orbit
(DIO). 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.

\noindent Unfortunately 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}
%
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 Table~\ref{tb:proton}. 

\begin{figure}[htb] 
	\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{table}[htb] 
	\centering \caption{Probabilities in unites of $10^{-3}$ per
	muon capture for inclusive proton emission calculated by Lifshitz and
	Singer~\cite{lifshitz80}.
	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}{ccccX}
		\toprule
		Target nucleus & Calculation & Experiment & Estimate & Comments \\ 
		\midrule
		%$_{10}$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) 	& \\ 
		\bottomrule
	\end{tabularx}
\end{table}

\noindent The limited information available at present makes it difficult to
draw quantitative conclusive detector design. From Table~\ref{tb:proton}, the
yield for Al can be taken from experiment to be $>$3\% for $T>40$ MeV, or from
theory to be 4\%, or estimated based on the ratio of exclusive channels from
other nuclei to be 7\%, or speculated to be as high as Si 
%or Ne
, namely 15-20\%. The
energy spectrum can only be inferred from the Si data or from
Ref.~\cite{bala67}. At this moment, for both COMET Phase-I and Mu2e, this
analytical spectrum has been used to estimate proton emission. And also the $p,
d, \alpha$ composition is not known. The Ti proton yield can only be estimated
from V to be around 3\%.

\noindent It might be worth to present how proton emission affects a single
rate of the tracking chambers.  As an example for COMET Phase-I, single rates
of the tracking chamber (cylindrical drift chamber) have been simulated based
on the spectrum given in Eq.(\ref{eq:protons}). To reduce protons entering the
tracking chamber, in addition to the inner wall of the drift chamber (of 400
$\mu$m) a cylindrical proton absorber of different thickness is located in
front of the tracking chamber. Monte Carlo simulations were done with three
different thickness of proton degrader, namely 0~mm, 5~mm, and 7.5~mm.
%Figure~\ref{fig:protongenerated} shows a proton momentum spectrum generated
(larger than 50 MeV/$c$) in the simulation study, and regions in red show
protons reaching the first layer.  The results are summarized in
Table~\ref{tb:protonhits}, where the proton emission rate of 0.15 per muon
capture is assumed. If we assume the number of muons stopped in the
muon-stopping target is $5.8 \times 10^{9}$/s, the number of muon capture on
aluminum is about $3.5 \times 10^{9}$/s since the fraction of muon capture in
aluminum is $f_{cap}=0.61$. Therefore the total number of hits in all the cells
in the first layer is estimated to be 530 kHz (1.3 MHz) for the case of a
proton degrader of 5 mm (0 mm) thickness. This example present the importance
to understand the proton emission, rate and spectrum, from nuclear muon capture
on aluminum for COMET Phase-I and Mu2e.
%
\begin{table}[htb] 
	\begin{center} 
		\caption{Total numbers of hits in the first
	layer by protons emitted from muon capture for different trigger counter
	thickness. 100 k proton events were generated for COMET Phase-I. 15 \%
	protons per muon capture is assumed.} 
	\label{tb:protonhits} 
	\vspace{5mm}
	\begin{tabular}{lccc} 
		\toprule
		Proton degrader thickness & 0 mm & 5 mm& 7.5 mm\\
		\midrule
%		number of 1 hit events & 2467 & 87 & 28 \cr\hline number of 2 hit events &
%		73 & 8 & 1 \cr\hline number of 3 hit events & 9 & 0 & 0 \cr\hline\hline
%		number of 4 hit events & 1 & 0 & 0 \cr\hline\hline
		Hits & 2644 & 103 & 30 \cr
		Hits per proton emission & 2.6 \% & 0.1 \% & 0.03 \% \cr
		Hits per muon capture & $3.9\times10^{-3}$  & $1.5\times10^{-4}$ & $4.5\times10^{-5}$ \cr
		\bottomrule
	\end{tabular}
	\end{center} 
\end{table} 



\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{Description of the experiment} % (fold) \label{sec:expdescpription}
%\begin{itemize} 
	%\item principle of the measurement, technique and apparatus
	%\item proposed measurements, expected performance and rates 
	%\item estimation of beam time needed 
	%\item Involvement of the contributing partners: manpower and finances 
	%\item Requests to PSI 
%\end{itemize}

The goal of the experiment is a measurement of the rate and energy spectrum of
charged particle emission after muon capture in the favored conversion target
Al, as well as Si (as normalization and cross check) and Ti (as an alternative
conversion target material). Both rate and energy spectrum should be measured
to 5\% precision down to an energy of 2.5 MeV.

The basic requirements are summarized is Fig.~\ref{basic.fig}. As the emitted
charged particles deposit a significant amount of energy during their passage
through the target material, thin targets and thus excellent momentum
resolution of the low energy muon beam are critical for this experiment. This
is exactly the reason, why the older experiments in the literature, performed
with thick targets and less sophisticated beams, are unsuitable for providing
the required yield and spectral information for low energy protons. In detail,
the observed energy spectrum $g(T_f)$ of protons emitted from the stopping
target is a convolution of the initial capture spectrum $f(T_i)$ with a
response function $k(T_f,T_i)$: 
\begin{equation} 
	g(T_f) = \int_0^\infty k(T_f,T_i) f(T_i) dT_i 
\end{equation} 
The response function can be readily calculated for a uniform muon stopping
distribution within the target depth.  The resulting distortion of the original
energy distribution taken from Equ.~\ref{eq:protons} is illustrated in
Fig.~\ref{response.fig}  for different target thickness.  

\begin{figure}[htb] 
	\begin{center}
		\includegraphics[width=\textwidth]{figs/protonrange.png}
		\caption{Left: Momentum vs. energy for p, d, $\alpha$, right: proton range
		vs. energy in targets.} 
		\label{basic.fig} 
	\end{center} 
\end{figure}
%\vskip-5ex
\begin{figure}[tb] 
	\begin{center} 
		\includegraphics[width=0.6\textwidth]{figs/Si_emitted.pdf}
		\caption{Calculated proton emission spectrum as function of target
		thickness (red: 0 $\mu m$, green: 50 $\mu m$, blue: 100 $\mu m$, black:
		1000 $\mu m$,  .} 
		\label{response.fig} 
	\end{center} 
\end{figure}

\begin{figure}[tb] 
	\begin{center}
		\includegraphics[width=0.405\textwidth]{figs/expcad.png}\includegraphics[width=0.6\textwidth]{figs/exp.png}
		\caption{Left: CAD of layout, right: picture of vacuum vessel with
		detectors.} 
		\label{setup.fig} 
	\end{center} 
\end{figure}

A schematic layout of the experimental setup is shown in Fig.~\ref{setup.fig}.
It will be an improved version of a test experiment performed by part of this
collaboration at PSI in 2009.

Low energy muons will be detected by external beam counters (scintillator and
wire chamber, not shown) and then enter a vacuum vessel though a thin mylar
window. They will be stopped in passive Al and Ti foils of 25 to 100 $\mu m$
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, perpenticular
to the target surface. The geometry is chosen so as to minimize the pathlength
of the emitted protons, and limit their direction to be nearly perpendicular to
the detectors, improving the PID resolution by dE/dx separation. The main
detector of the package is a 5$\times$5 cm$^2$ Si detector of 1500 $\mu m$
thickness (MSX), stopping protons up to about 12 MeV. Plastic scintillators
positioned
behind this Si detector observe potential higher energy protons and veto
through--going electrons. To provide dE/dx information some data will be taken
with two 10x10 cm$^2$ thin Si detectors (65 $\mu m$, MSQ). These detectors are
4-fold segmented. Still, their large capacitance deteriorates the overal
resolution, so measurement with and without them are foreseen. The symmetry
between the left and right Si station 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. We also will have telescopes to detect electrons from
muons for additional normalization of a number of muons stopped. 

The main systematic issues are as follows. 

\begin{itemize}
\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 $T_i$ and $T_f$ 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 Geant and
	calibrated with the active Si target.

\item PID. The PID of emitted charged particles will be determined by dE/dx,
	also the use of time of flight will be investigated.

\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.

\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}

\begin{table}[htb]
	\begin{center}
		\caption{Estimated event rates for various targets of different
		thickness. Incoming $10^{4}$ muons/sec and proton emission rate of
		0.15 per muon capture are assumed. The efficiency of Si detector of
		100 \% is also assumed. } 
		\vskip1ex
		%\scalebox{0.75}{
		\begin{tabular}{cccc}
			\toprule
			Target 		& \% Stopping & Event rate (Hz) & Event rate (Hz) \\ 
			thickness ($\mu$m)& in target & All particles & Protons \\ 
			\midrule
			50  & 2  & 8.1 	& 1.0   \\ 
			100 & 16 & 21.3 & 1.5  \\ 
			150 & 38 & 39.9 & 2.1  \\ 
			200 & 53 & 51.1 & 2.4  \\ 
			\bottomrule
		\end{tabular}
		%}
		\end{center}
		\label{tb:rates} 
	\end{table}

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 10 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 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. 
%
%\begin{table}[htb!] 
	%\caption{Estimated event rates for various targets of
	%different thickness. Incoming $10^{5}$ muons/sec and proton emission rate of
	%0.15 per muon capture are assumed. The efficiency of Si detector of 100 \% is
	%also assumed. }
	%\label{tb:rates} \begin{center} \begin{tabular}{|c|c|c|c|c|c|}
		%\hline target & stopping & geometry & hit rate & hit rate & hit rate \\
		%thickness & in target  & acceptance  & all particles & protons & protons \\
		%($\mu$m) & (\%) & ($\%$) & (Hz) & (Hz) & (Hz) ($T>$2.5 MeV) \\ \hline 50 &
		%28 & 1.1 & 250 & 6 & 4 \\ \hline 100 & 58 & 1.1 & 800 & 25 & 18 \\ \hline
		%150 & 77 & 1.0 & 1200 & 33 & 25 \\ \hline \end{tabular} \end{center}
	%\end{table}





%\begin{comment} A schematic layout of the experimental setup is shown in
%Fig.~\ref{fg:setup}. The setup has silicon detectors to measure energy of
%charged particles emitted from nuclear muon capture on aluminum. We set an
%aluminum target in a vacuum chamber at the end of M9B muon channel. Negative
%muons of momentum of less than 40 MeV/$c$ are used. The use of lower momentum
%muons (cloud $\mu^{-}$ beam) would increase muons stopping in a thin aluminum
%target, thus reducing backgrounds. Or, we can use a degrader to maximize a
%number of muons in the aluminum target.  Figure~\ref{fg:muonstop} shows muon
%stopping distribution in a 50 $\mu$m thick muon stopping target with various
%thick upstream plastic scintillator, and in this case the muon momentum is 30
%MeV/$c$. From Fig.~\ref{fg:muonstop}, the thickness of 13mm is found to be
%optimum. 

%Two plastic scintillation counters to identify muons stopping in the aluminum
%target will be installed. The muons pass the beam counter and stops at the
%aluminum target, The muons that do not stop pass the downstream counter so that
%we can identify the muons stopped.


%\begin{figure}[t!] \parbox{0.5\textwidth}{ \begin{center}
	%\includegraphics[width=0.48\textwidth]{figs/setup.pdf} \caption{schematic
	%layout of the setup.}\label{fg:setup} \end{center} }
	%\parbox{0.5\textwidth}{\vspace*{0cm} \begin{center}
		%\includegraphics[width=0.48\textwidth]{figs/muonstop.pdf} \caption{Monte
		%Carlo simulation on muon stopping distribution in a 50 $\mu$m target for
		%various degrader thickness, in top from left to right, thickness of a
		%upstream plastic scintillator is 10mm, 11mm, 12mm, in bottom from left to
		%right, 13mm, 14 mm, and 15mm.}\label{fg:muonstop} \end{center} }
	%\end{figure}

%Charged particles emitted from nuclear muon capture on aluminum are detected by
%a pair of two silicon detectors, one of which is a thin silicon detector to
%measure dE/dX of charged particles (``S1 counter"), and the other is a thick
%silicon detector to measure their total energies, (``S2 counter"). The S1 and
%S2 Si detectors are 65 $\mu$m and 1500 $\mu$m thickness respectively. Behind
%the $E$ counter, a veto counter to ensure charged particles stopping in the S2
%counter is set. In front of the silicon counters, collimators are installed to
%determine the fiducial. 

%\begin{figure}[htb!] \begin{center}
	%\includegraphics[width=\textwidth]{figs/dedx.pdf} \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}

%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 (not shown in Fig.~\ref{fg:setup}). It is also currently
%being considered to have a telescope to detect electrons from muons for
%additional normalization of a number of muons stopped. 

%Aluminum targets with various thickness (from 50 $\mu$m to 200 $\mu$m) will be
%used. It can be tilted with an angle of $30-45^{\circ}$ with respect to the
%muon beam axis.  It is important to have a thin target to measure the spectrum
%precisely, otherwise some deconvolution process to correct for energy loss of
%protons in the target should be involved. It is noted, however that a 200
%$\mu$m thick aluminum disk will be used in both COMET Phase-I and Mu2e
%experiment.


%\end{comment}
% section expdescpription (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Readiness}

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.

%\section{Beam time estimation}

%We are requesting a 36 shifts (three weeks) for measurement.  This is based on
%the estimation as follows. We will need a 2 days setup time including the
%installation of the equipment, and 5 days of beam tuning to maximize a number
%of muons stopping in the target, adjustment of data taking electronics, and
%2 different thick targets of 7 day data taking for each. Each sample must be
%installed in the chamber, evacuated (we need good vacuum). Data taking of
%7 days is based on the estimated rate of protons 
%%whose kinetic energy $T>$ 2,6 MeV
 %shown in Table~\ref{tb:rates}. We will accommodate at least 100 k events
%for each sample.

\section{Data analysis}

Data will be analyzed independently at Osaka University, University of
Washington, and University College London, using standard analysis libraries
and our own analysis routines. There is no special requirement on data analysis
support to PSI.

\vspace{5mm}





\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'', unpublished, March
	2012. 
%
\bibitem{sobo68} S.E. Sobotka and E.L. Willis, Phys. Rev. Lett. {\bf 20}
	596-598, 1968.

\bibitem{lifshitz80} M. Lifshitz and P. Singer, Phys. Rev. C {\bf 22}
	2135-2150, 1980.
%
\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.
%
\end{thebibliography}
\end{document}
