writeup/AlCapTRIUMF/AlCap_DetailedStatement.tex

% eec_nrp_dspr.tex       written by M. Comyn       last updated 23-05-2012 by NM

% Use this LaTeX file to submit your TRIUMF EEC New Research Proposal
% Detailed Statement of Proposed Research

% NOTE:
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% \setcounter{expnum}{}
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  TRIUMF EEC New Research Proposal
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  Detailed Statement of Proposed Research for Experiment \#: \theexpnum}\\ \hline
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\begin{comment}
\footnotesize\sffamily


\noindent
\textbf{The EEC committees strongly recommend that you limit your
submissions, including figures and tables, to no more than 4 pages for the
MMSEEC or 10 pages for the SAPEEC. \ The following information should be
included:}%

\vspace*{-2mm}

\scriptsize\sffamily

\begin{Itemize}
\item[(a)]
\textbf{Scientific value of the experiment:}
Describe the importance of the experiment and its relation to previous
work and to theory.  All competitive measurements at other laboratories
should be mentioned.  Include examples of the best available theoretical
calculations with which the data will be compared.
\item[(b)]
\textbf{Description of the experiment:}
Techniques to be used, scale drawing of the apparatus, measurements to be
made, data rates and background expected, sources of systematic error,
results and precision anticipated.  Compare this precision with that
obtained in previous work and discuss its significance in regard to
constraining theory.  Give a precise list of targets to be used in order of
their priority.
\item[(c)]
\textbf{Experimental equipment:}
Describe the purpose of all major equipment to be used.
\item[(d)]
\textbf{Readiness:}
Provide a schedule for assembly, construction and testing of equipment.
Include equipment to be provided by TRIUMF. For secondary beam for ISAC, provide information on established yields of the isotope of interest as well as the established isobaric contaminants form the same target/ion-source combination.
\item[(e)]
\textbf{Beam time required:}
State in terms of number of 12-hour shifts.  Show details of the beam time
estimates, indicate whether prime-user or parasitic time is involved, and
distinguish time required for test and adjustment of apparatus.
\item[(f)]
\textbf{Data analysis:}
Give details and state what data processing facilities are to be provided
by TRIUMF.
\end{Itemize}

\footnotesize\sffamily


\noindent
\textbf{\boldmath For $\mu$SR experiments}, make sure that your detailed
information includes:

\vspace*{-2mm}

\scriptsize\sffamily

\begin{Itemize}
\item
a concise summary of the scientific problem under investigation, with
appropriate literature references;
\item
clear justification for the proposed experiments and, specifically, a
justification for using $\mu$SR/$\beta$-NMR techniques;
\item
a description of the experimental techniques to be used, naming the
$\mu$SR/$\beta$-NMR spectrometer(s) or ISAC facilities to be used;
\item
an analysis of beam time requirements, including a prioritized list of
samples;
\item
groups with multiple experiments should list all concurrent experiments and
proposals, including outside of TRIUMF, with an indication of how the
personnel effort is to be divided between these activities.
\end{Itemize}
\end{comment}

\normalsize\rmfamily

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\setcounter{expnum}{1371} %Enter your experiment number between the braces

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% Enter Detailed Statement of Proposed Research below:

\section{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}[b!]
\vspace{-40mm}
%\centering
\parbox{0.50\textwidth}{\hspace{-40mm}
\includegraphics[width=130mm,angle=270]{figs/YK-mu2e-gs.pdf}
}
\parbox{0.5\textwidth}{\vspace*{0cm}
	\includegraphics[width=80mm]{figs/YK-comet-gs.pdf}
}
\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-Detector.pdf}
\caption{Schematic layout of a cylindrical detector for COMET Phase-I.}
\label{fg:phase1}
%\vspace{-5mm}
\end{figure}

\section{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. 

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.

\begin{figure}[tb]
\centering
\includegraphics[width=0.5\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}

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{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{tabular}{|c|c|c|c|c|}\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{tabular}
\end{table}

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\%.

\begin{table}[tb]
	\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}{|l|c|c|c|} \hline
		proton degrader thickness & 0 mm & 5 mm& 7.5 mm\cr\hline\hline
%		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\hline
		hits per proton emission & 2.6 \% & 0.1 \% & 0.03 \% \cr\hline
		hits per muon capture$^{*}$ & $3.9\times10^{-3}$  & $1.5\times10^{-4}$ & $4.5\times10^{-5}$ \cr\hline
		\end{tabular}
	\end{center}
\end{table} 

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.
%


\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{Description of the experiment}

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.

\begin{figure}[tb]
	\begin{center}
	\includegraphics[width=0.5\textwidth]{figs/Tp.pdf}\includegraphics[width=0.5\textwidth]{figs/range1.png}
	\caption{Left: Momentum vs. energy for p, d, $\alpha$, right:
          proton range vs. energy in targets.}
        \label{basic.fig}
	\end{center}
\end{figure}

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}[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 10x10 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}[tp]
	\begin{center}
		\includegraphics[width=0.6\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}

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 TRIUMF 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. 
%
\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{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 TRIUMF
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 required}

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 TRIUMF.

\vspace{5mm}

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%
\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).
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%
\bibitem{hung34} E. Hungerford, ``Comment on Proton Emission after Muon Capture", MECO note 34.
%
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\end{document}