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thesis/Makefile
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@@ -5,7 +5,7 @@ TARGET= $(DOCNAME).pdf
default: $(TARGET)
$(TARGET): $(INPUT) Makefile chapters/*.tex custom_macro.tex mythesis.sty
$(TARGET): $(INPUT) Makefile chapters/*.tex custom_macro.tex mythesis.sty raw/*
@rm -f $(DOCNAME).{aux,toc,lof,lot}
pdflatex $< && bibtex $(DOCNAME) && pdflatex $< && pdflatex $<

15
thesis/chapters/chap1_intro.tex
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@@ -58,15 +58,18 @@ observation of CLFV would be a clear signal of new physics beyond the SM.
The COMET (\textbf{CO}herent \textbf{M}uon to \textbf{E}lectron
\textbf{T}ransition) Collaboration aims to probe the conversion of a muon to
an electron in a nucleus field at a sensitivity of $6\times10^{-17}$, pushing
for a four orders of magnitude improvement from the current limit set by the
an electron in a nucleus field at a single event sensitivity of \num{6E-17},
pushing for a four orders of magnitude improvement from the current limit set
by the
SINDRUM-II~\cite{Bertl.etal.2006}. A staging approach is adopted at the COMET
to achieve an intermediate physics result, as well as to gain operational
experience. The first stage, COMET Phase I, is scheduled to start in 2016 with
the goal sensitivity of $3\times 10^{-15}$ after a three-month-running period.
experience. The first stage, COMET Phase I, is scheduled to start data taking
in 2016 with the goal single event sensitivity of $3.1\times 10^{-15}$ after
a three-month running period.
A cylindrical drift chamber being developed by the Osaka University group
will be the main tracking detector in the COMET Phase I. It is anticipated that
together with the Kyushu University group and the Chinese groups
will be a main tracking detector in the COMET Phase I. It is anticipated that
the chamber will be heavily occupied by protons emitted after nuclear muon
capture in the stopping target, and thus an absorber will be installed to
reduce the proton hit rate to a tolerable level. A study of proton emission
@@ -83,6 +86,6 @@ sensitivities. Details of the study on proton emission are described in
Chapters~\ref{cha:alcap_phys},~\ref{cha:the_alcap_run_2013},~\ref{cha:data_analysis}:
physics, method, experimental set up, data analysis. The results and impacts of
the study on COMET Phase-I design is discussed in
Chapter~\ref{cha:discussions}.
Chapter~\ref{cha:discussions_on_the_impact_to_the_comet_phase_i}.
% chapter introduction (end)

127
thesis/chapters/chap2_mu_e_conv.tex
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@@ -1,7 +1,49 @@
\chapter{Lepton flavour and $\mu-e$ conversion}
\chapter{Overview}
\thispagestyle{empty}
\label{cha:clfv}
\section{Introduction}
\label{sec:introduction}
The COMET experiment~\cite{COMET.2007}, proposed at the Japan Proton
Accelerator Research Complex (J-PARC), is a next-generation-experiment that
searches for evidence of charged lepton flavour violation (CLFV) with muons.
The branching ratio of CLFV in the Standard Model, even with massive neutrinos,
is prohibitively small, at the order of $10^{-54}$. Therefore, any experimental
observation of CLFV would be a clear signal of new physics beyond the SM.
The COMET (\textbf{CO}herent \textbf{M}uon to \textbf{E}lectron
\textbf{T}ransition) Collaboration aims to probe the conversion of a muon to
an electron in a nucleus field at a single event sensitivity of \num{6E-17},
pushing for a four orders of magnitude improvement from the current limit set
by the
SINDRUM-II~\cite{Bertl.etal.2006}. A staging approach is adopted at the COMET
to achieve an intermediate physics result, as well as to gain operational
experience. The first stage, COMET Phase I, is scheduled to start data taking
in 2016 with the goal single event sensitivity of $3\times 10^{-15}$ after
a three-month running period.
A cylindrical drift chamber being developed by the Osaka University group
together with the Kyushu University group and the Chinese groups
will be a main tracking detector in the COMET Phase I. It is anticipated that
the chamber will be heavily occupied by protons emitted after nuclear muon
capture in the stopping target, and thus an absorber will be installed to
reduce the proton hit rate to a tolerable level. A study of proton emission
following nuclear muon capture for optimisation of the proton absorber is
presented in this thesis.
The thesis is structured as follows:
firstly,
the physics motivation of the COMET experiment, with muon's normal decays and
CLFV decays, is described in this later part of this chapter.
Chapter~\ref{cha:comet_overview} gives an overview of the
COMET experiment: beam lines, detectors and their requirements, and expected
sensitivities. Details of the study on proton emission are described in
Chapters~\ref{cha:alcap_phys},~\ref{cha:the_alcap_run_2013},~\ref{cha:data_analysis}:
physics, method, experimental set up, data analysis. The results and impacts of
the study on COMET Phase-I design is discussed in
Chapter~\ref{cha:discussions_on_the_impact_to_the_comet_phase_i}.
\section{Lepton flavour}
\label{sec:lepton_flavour}
According to the SM, all matter is built from a small set of fundamental
@@ -9,7 +51,7 @@ spin one-half particles, called fermions: six quarks and six leptons.
The six leptons form three generations (or flavours), namely:
\begin{equation*}
\binom{\nu_e}{e^-}, \quad \binom{\nu_\mu}{\mu^-} \quad \textrm{ and } \quad
\binom{\nu_\tau}{\tau^-}
\binom{\nu_\tau}{\tau^-}.
\end{equation*}
Each lepton is assigned a lepton flavour quantum number, $L_e$, $L_\mu$,
@@ -24,7 +66,7 @@ or, the interaction of an electron-type antineutrino with a proton (inverse
beta decay):
\begin{align*}
&\quad \overline{\nu}_e + p \rightarrow e^+ + n \\
L_e \quad &-1 \quad \textrm{ }0 \quad -1 \textrm{ } \quad 0
L_e \quad &-1 \quad \textrm{ }0 \quad -1 \textrm{ } \quad 0
\end{align*}
The decay of a muon to an electron and a photon, where lepton flavour numbers
@@ -40,15 +82,25 @@ are violated by one unit or more, is forbidden:
\end{aligned}
\label{eq:mueg}
\end{equation}
However, it is observed that neutrinos do change flavour in the so-called
neutrino oscillations where a neutrino of a certain lepton flavour
can be measured to have a different flavour as it travels in space-time. The
phenomenon has been confirmed in many experiments with solar neutrinos,
atmospheric neutrinos, reactor neutrinos and beam neutrinos. The observation
of neutrino oscillations means that the lepton flavour is not strictly
conserved and neutrinos are massive. The massive neutrinos allow lepton
flavour violation in the charged leptons, but at an unmeasurably small level
as described in \cref{sec:lepton_flavour_violation}.
%One more decay?
%\hl{TODO: Why massless neutrinos help lepton flavour conservation??}
%\hl{TODO: copied from KunoOkada}
%In the minimal version of the SM, where only one Higgs doublet is included and
%massless neutrinos are assumed, lepton flavor conservation is an automatic
%massless neutrinos are assumed, lepton conservation is an automatic
%consequence of gauge invariance and the renormalizability of the SM
%Lagrangian. It is the basis of a natural explanation for the smallness of
%lepton flavor violation (LFV) in charged lepton processes.
%lepton violation (LFV) in charged lepton processes.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Muon and its decays in the Standard Model}
@@ -111,15 +163,15 @@ or with an associated $e^+ e^-$ pair:
\label{eq:mu3e2nu}
\end{equation}
The dominant process, \micheldecay is commonly called Michel decay. It can be
described by the V-A interaction which is a special case of a local,
The dominant process, \micheldecay is commonly called the Michel decay. It can
be described by the V-A interaction which is a special case of a local,
derivative-free, lepton-number-conserving four-fermion interaction.
%using $V-A$
%inteaction, a special case of four-fermion interaction, by Louis
%Michel~\cite{Michel.1950}.
The model contains independent real parameters that can be determined from
measurements of muon life time, muon decay and inverse muon
decay. Experimental results from extensive measurements of Michel parameters
decay. Experimental results from extensive measurements of the Michel parameters
are consistent with the predictions of the V-A
theory~\cite{Michel.1950,FetscherGerber.etal.1986,BeringerArguin.etal.2012}.
@@ -127,9 +179,9 @@ The radiative decay~\eqref{eq:mue2nugamma} is treated as an internal
bremsstrahlung process~\cite{EcksteinPratt.1959}.
%It occurs at the rate of about 1\% of all muon decays.
Since it is not possible to clearly separated this mode
from Michel decay in the soft-photon limit, the radiative mode is regarded as
from the Michel decay in the soft-photon limit, the radiative mode is regarded as
a subset of the Michel decay. An additional parameter is included to describe
the electron and photon spectra in this decay channel. Like the case of
the electron and photon spectra in this decay channel. Like the case of the
Michel decay, experiments results on the branching ratio and the parameter are
in agreement with the SM's predictions~\cite{BeringerArguin.etal.2012}.
@@ -198,7 +250,7 @@ flavour was experimentally verified in the Nobel Prize-winning experiment of
Danby et al. at Brookhaven National Laboratory
(BNL)~\cite{DanbyGaillard.etal.1962}. Then the concepts of generations of
particles was developed~\cite{MakiNakagawa.etal.1962}, and integrated into the
SM, in which the lepton flavour conservation is guaranteed by and exact
SM, in which the lepton flavour conservation is guaranteed by an exact
symmetry, owing to massless neutrinos.
Following the above LFV searches with muons, searches with various particles,
@@ -215,14 +267,14 @@ must be modified to accommodate the massive neutrinos.
With the massive neutrinos charged lepton flavour violation (CLFV) must occur
through oscillations in loops. But, CLFV processes are highly suppressed in the
SM.
For example, Marciano and Mori ~\cite{MarcianoMori.etal.2008} calculated the
%\hl{TODO: Feynman diagram}
For example, Marciano and Mori~\cite{MarcianoMori.etal.2008} calculated the
branching ratio of the process \mueg to be \brmeg$<10^{-54}$. Other
CLFV processes with muons are also suppressed to similar practically
unmeasurable levels.%\hl{TODO: Feynman diagram}
Therefore, any experimental
unmeasurable levels. Therefore, any experimental
observation of CLFV would be an unambiguous signal of the physics beyond the
SM. Many models for physics beyond the SM, including supersymmetric (SUSY)
models, extra dimensional models, little Higgs models, predict
SM. Many theoretical models for physics beyond the SM, including supersymmetric
(SUSY) models, extra dimensional models, little Higgs models, predict
significantly larger CLFV
~\cite{MarcianoMori.etal.2008, MiharaMiller.etal.2013, BernsteinCooper.2013}.
%\hl{TODO: DNA of CLFV charts}
@@ -256,16 +308,16 @@ significantly larger CLFV
%It is calculated that there are two CLFV processes that would
%occur at large rates by many new physics models,
Among the CLFV processes, the \mueg and
the \muec are expected to have large effect by many models. The current
experimental limits on these two decay modes are set by MEG
experiment~\cite{Adam.etal.2013} and SINDRUM-II
the \muec are expected to have large effect in many models. The current
experimental limits on these two decay modes are set respectively by the MEG
experiment~\cite{Adam.etal.2013} and the SINDRUM-II
experiment~\cite{Bertl.etal.2006}:
\begin{equation}
\mathcal{B}(\mu^+ \rightarrow e^+ \gamma) < 5.7 \times 10^{-13}
\mathcal{B}(\mu^+ \rightarrow e^+ \gamma) < 5.7 \times 10^{-13}\,,
\end{equation}
, and:
and:
\begin{equation}
\mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13}
\mathcal{B} (\mu^- + Au \rightarrow e^- +Au) < 7\times 10^{-13}\,.
\end{equation}
%\hl{TODO: mueg and muec relations, Lagrangian \ldots}
@@ -278,32 +330,32 @@ experiment~\cite{Bertl.etal.2006}:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Phenomenology of \mueconv}
\label{sec:phenomenoly_of_muec}
The conversion of a captured muon into an electron in the field of a nucleus
has been one of the most powerful probe to search for CLFV. This section
The conversion of a captured negative muon in a muonic atom into an electron
in the field of a nucleus has been one of the most powerful probe to search for
CLFV. This section
highlights phenomenology of the \muec.
\subsection{What is \mueconv}
\label{sub:what_is_muec}
When a muon is stopped in a material, it is quickly captured by atoms
into a high orbital momentum state, forming a muonic atom, then
When a negatively charged muon is stopped in a material, it is quickly captured
by an atom into a high orbital momentum state, forming a muonic atom, then
it rapidly cascades to the lowest state 1S. There, it undergoes either:
\begin{itemize}
\item normal Michel decay: \micheldecay; or
\item weak capture by the nucleus: $\mu^- p \rightarrow \nu_\mu n$
\item weak capture by the nucleus: $\mu^- p \rightarrow \nu_\mu n$.
\end{itemize}
In the context of physics beyond the SM, the exotic process of \mueconv where
a muon decays to an electron without neutrinos is also
expected, but it has never been observed.
expected, but has never been observed:
\begin{equation}
\mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)
\mu^{-} + N(A,Z) \rightarrow e^{-} + N(A,Z)\,.
\end{equation}
The emitted electron in this decay
mode , the \mueconv electron, is mono-energetic at an energy far above the
endpoint
The emitted electron in this decay mode, the \mueconv electron, is
mono-energetic at an energy far above the endpoint
of the Michel spectrum (52.8 MeV):
\begin{equation}
E_{\mu e} = m_\mu - E_b - \frac{E^2_\mu}{2m_N}
E_{\mu e} = m_\mu - E_b - \frac{E^2_\mu}{2m_N}\,.
\end{equation}
where $m_\mu$ is the muon mas; $E_b \simeq Z^2\alpha^2 m_\mu/2$ is the binding
energy of the muonic atom; and the last term is the nuclear recoil energy
@@ -322,8 +374,8 @@ The quantity measured in searches for \mueconv is the ratio between the rate of
\frac{\Gamma(\mu^-N \rightarrow e^-N)}{\Gamma(\textrm{capture})}
\label{eq:muerate_def}
\end{equation}
The normalisation to captures has advantages when one does calculation since
many details of the nuclear wavefunction cancel out in the ratio.
%The normalisation to captures has advantages when one does calculation since
%many details of the nuclear wavefunction cancel out in the ratio.
%Detailed
%calculations have been performed by Kitano et al.~\cite{KitanoKoike.etal.2002a,
%KitanoKoike.etal.2007}, and Cirigliano et al.~\cite{Cirig}
@@ -340,7 +392,10 @@ The mean lifetime $\tau = 1/\Gamma$, then:
\end{equation}
The mean lifetimes of free muons and muons in a material are well-known,
therefore the number of captures can be inferred from the number of stops. For
aluminium, $\frac{\Gamma_{\textrm{capture}}}{\Gamma_{\textrm{stop}}} = 0.609$
aluminium,
\begin{equation}
\frac{\Gamma_{\textrm{capture}}}{\Gamma_{\textrm{stop}}} = 0.609
\end{equation}
and the mean lifetime of stopped muons is 864
ns~\cite{SuzukiMeasday.etal.1987}.

320
thesis/chapters/chap3_comet.tex
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@@ -5,8 +5,8 @@
This chapter describes the new experimental search for \mueconv, namely COMET -
(\textbf{CO}herent \textbf{M}uon to \textbf{E}lectron \textbf{T}ransition). The
experiment will be carried out at the Japan Proton Accelerator Research Complex
(J-PARC), aims at a sensitivity of \sn{6}{-17} i.e. 10,000 times better than the
current best limit.
(J-PARC), aims at a single event sensitivity of \num{6E-17}, i.e. 10,000 times
better than the current best limit.
%At the Japan Proton Accelerator Research Complex (J-PARC), an experiment to
%search for \muec~conversion, which is called
@@ -48,8 +48,9 @@ current best limit.
The searches for \mueconv has been ongoing for more than 50 years, started in
1952 with cosmic rays~\cite{LagarriguePeyrou.1952} and then moved to
accelerators. The list in the Table~\ref{tab:mueconv_history} is reproduced
from a recent review of Bernstein and Cooper~\cite{BernsteinCooper.2013}.
accelerators. The list of upper limits for \mueconv in
\cref{tab:mueconv_history} is reproduced from a recent review of Bernstein
and Cooper~\cite{BernsteinCooper.2013}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l l l c}
@@ -62,57 +63,63 @@ from a recent review of Bernstein and Cooper~\cite{BernsteinCooper.2013}.
1961 & \sn{4.0}{-6} & Cu & \cite{SardCrowe.etal.1961}\\
1961 & \sn{5.9}{-6} & Cu & \cite{ConversiLella.etal.1961}\\
1962 & \sn{2.2}{-7} & Cu & \cite{ConfortoConversi.etal.1962}\\
1964 & \sn{2.2}{-7} & Cu & \cite{ConversiLella.etal.1961}\\
1972 & \sn{2.6}{-8} & Cu & \cite{ConversiLella.etal.1961}\\
1977 & \sn{4.0}{-10} & S & \cite{ConversiLella.etal.1961}\\
1982 & \sn{7.0}{-11} & S & \cite{ConversiLella.etal.1961}\\
1988 & \sn{4.6}{-12} & Ti & \cite{ConversiLella.etal.1961}\\
1993 & \sn{4.3}{-12} & Ti & \cite{ConversiLella.etal.1961}\\
1995 & \sn{6.5}{-13} & Ti & \cite{ConversiLella.etal.1961}\\
1996 & \sn{4.6}{-11} & Pb & \cite{ConversiLella.etal.1961}\\
2006 & \sn{7.0}{-13} & Au & \cite{ConversiLella.etal.1961}\\
1964 & \sn{2.2}{-7} & Cu & \cite{BartleyDavies.etal.1964}\\
1972 & \sn{2.6}{-8} & Cu & \cite{BrymanBlecher.etal.1972}\\
1977 & \sn{4.0}{-10} & S & \cite{BadertscherBorer.etal.1977}\\
1982 & \sn{7.0}{-11} & S & \cite{BadertscherBorer.etal.1982a}\\
1988 & \sn{4.6}{-12} & Ti & \cite{AhmadAzuelos.etal.1988a}\\
1993 & \sn{4.3}{-12} & Ti & \cite{DohmenGroth.etal.1993}\\
1996 & \sn{4.6}{-11} & Pb & \cite{HoneckerDohmen.etal.1996}\\
2006 & \sn{7.0}{-13} & Au & \cite{Bertl.etal.2006}\\
\bottomrule
%%TODO fix ref
\end{tabular}
\end{center}
\caption{History of \mueconv experiments, reproduced
from~\cite{BernsteinCooper.2013}}
\caption{History of \mueconv experiments with more and more stringent upper
limit.}
\label{tab:mueconv_history}
\end{table}
The most recent experiments were the SINDRUM and SINDRUM-II at the Paul
Scherrer Institute (PSI), Switzerland. The SINDRUM-II measured the branching
The latest experiments were the SINDRUM and SINDRUM-II at the Paul
Scherrer Institute (PSI), Switzerland. The SINDRUM-II
(\cref{fig:sindrumII_setup}) measured the branching
ratio of \mueconv on a series of heavy targets: Ti, Pb and Au. The proton beam
at PSI is a continuous wave beam, with a time structure of 0.3 ns bursts every
19.75 \si{\nano\second}. An 8-\si{\milli\meter}-thick CH$_2$ degrader was used to reduce
the radiative pion capture and other prompt backgrounds. Cosmic backgrounds are
at PSI is a continuous beam, with a time structure of 0.3 ns bursts every
19.75 \si{\nano\second}. An 8-\si{\milli\meter}-thick CH$_2$ degrader was used
to reduce the radiative pion capture and other prompt backgrounds. Cosmic
backgrounds are
rejected using a combination of
passive shielding, veto counters and reconstruction cuts. The momenta of muons
were 52 \si{\mega\electronvolt\per\cc} and 53 \si{\mega\electronvolt\per\cc}, and the
momentum spread was 2\%.
passive shielding, veto counters and reconstruction cuts. The momenta of beam
muons used in the experiment were \SI{52}{\MeV\per\cc} and
\SI{53}{\MeV\per\cc}, and the momentum spread was 2\%.
\begin{figure}[htbp] \centering
\includegraphics[width=0.85\textwidth]{figs/sindrumII_setup}
\caption{SINDRUM-II set up}
\caption{SINDRUM-II experimental set up, reprinted from
reference~\cite{Bertl.etal.2006} with permission from Springer.}
\label{fig:sindrumII_setup}
\end{figure}
Electrons emitted from the target were tracked in a 0.33 T solenoid field.
Detector system consisted of a superconducting solenoid, two plastic
Electrons emitted from the target were tracked in a 0.33 T solenoidal magnetic
field. Detector system consisted of a superconducting solenoid, two plastic
scintillation hodoscopes, a plexiglass Cerenkov hodoscope, and two drift
chambers. In the latest measurement, the SINDRUM-II collaboration have not
found any conversion electron from captured muons in a gold target, hence set
the upper limit for
the branching ratio of \mueconv in gold with 90 \% C.L. at \sn{7.0}{-13}.
the branching ratio of \mueconv in gold with 90 \% C.L. at \num{7.0E-13}.
The reconstructed momenta of electrons around the signal region from SINDRUM-II
is shown in the Figure~\ref{fig:sindrumII_result}. It can be seen that the muon
is shown in \cref{fig:sindrumII_result}. It can be seen that the muon
decay in orbit background falls steeply near the endpoint as expected, but, the
prompt background induced by pions still remains even after the cut in timing
and track angle. This indicates the problem of pion contamination is very
important in probing lower sensitivity.
important in probing better sensitivity.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.55\textwidth]{figs/sindrumII_Au_result}
\caption{SINDRUM-II result}
\caption{SINDRUM-II results showing background events reaching into the
signal region. Reprinted from reference~\cite{Bertl.etal.2006} with
permission from Springer.}
%TODO: explain top and bottom figure
\label{fig:sindrumII_result}
\end{figure}
% subsection experimental_history (end)
@@ -124,28 +131,30 @@ A new generation of \mueconv experiments have been proposed with scenarios to
overcome pion induced background in the SINDRUM-II. Lobashev and collaborators
first suggested the basic idea for new \mueconv at the Moscow Muon Factory;
this idea was used to develop the MECO experiment at Brookhaven National
Laboratory. The MECO experiment was cancelled due to budget constraints. The two
modern experiments, COMET at J-PARC and Mu2e at Fermilab use the initial idea
Laboratory. The MECO experiment was cancelled due to budget constraints. Two
recent experiments, COMET at J-PARC and Mu2e at Fermilab, use the initial idea
with more upgrades and modifications.
The basic ideas of the modern experiments are:
The basic ideas of the two experiments are:
\begin{enumerate}
\item Highly intense muon source: the total number of muons needed is of the
order of $10^{18}$ in order to achieve a sensitivity of $10^{-16}$. This
can be done by producing more pions using a high power proton beam, and
having a high efficiency pion collection system;
\item Pulsed proton beam with an appropriate timing: the proton pulse should
\item Pulsed proton beam: the proton pulse should
be short compares to the lifetime of muons in the stopping target material,
and the period between pulses should be long enough for prompt backgrounds
from pion to decay before beginning the measurement. It is also crucial
that there is no proton leaks into the measuring interval;
\item Curved solenoids for charge and momentum selection: at first, the curved
solenoids remove the line of sight backgrounds. A charged particle travels
through a curved solenoidal field will have the centre of the helical
motion drifted up or down depends on the sign of the charge, and the
magnitude of the drift is proportional to its momentum. By using this
effect and placing suitable collimators, charge and momentum selection can
be made.
through a curved solenoidal magnetic field has the centre of the helical
motion drifted up or down with respect to the bending plane depends on the
sign of the charge, and the magnitude of the drift is proportional to its
momentum. By using this effect and placing suitable collimators, charge and
momentum selection can be made. Details of the magnet system are described
in \cref{sub:pion_production_can_capture_solenoid} and
\cref{sub:pion_and_muon_transportation}.
\end{enumerate}
% subsection new_generation_of_mueconv_experiments (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -156,13 +165,14 @@ The basic ideas of the modern experiments are:
\section{Concepts of the COMET experiment}
\label{sec:concepts_of_the_comet_experiment}
This section elaborates the design choices of the COMET to realise the basic
ideas mentioned above. Figures and numbers, other than noted, are taken from
the COMET's documentations:
ideas mentioned previously. Figures and numbers, other than noted, are taken
from the COMET's documentations:
\begin{itemize}
%TODO citations
\item Conceptual design report for the COMET experiment~\cite{COMET.2009}
\item Proposal Phase-I 2012
\item TDR 2014
\item Conceptual design report for the COMET experiment~\cite{COMET.2009},
\item Experimental Proposal for Phase-I of the COMET Experiment at
J-PARC~\cite{COMET.2012},
\item and COMET Phase-I Technical Design Report~\cite{COMET.2014}.
\end{itemize}
@@ -172,30 +182,30 @@ A high power pulsed proton beam is of utmost importance to achieve the desired
sensitivity of the COMET experiment. A slow-extracted proton beam from
the J-PARC main ring (MR), which is designed to deliver \sn{3.6}{15} protons per
cycle at a frequency of 0.45 Hz, will be used for the COMET experiment. The
proton beam power of the current design is 8 GeV$\times$7 $\mu$A, or
\sn{4.4}{13} protons/s. The beam energy 8 \si{\giga\electronvolt} helps to minimise
the production of antiprotons.
proton beam power of the current design is $\SI{8}{\GeV}\times \SI{7}{\uA}$, or
\num{4.4E13} protons/s at \SI{8}{\GeV}. The beam energy was chosen to minimise
the production of antiprotons which may introduce background events.
The proton pulse width is chosen to be 100 ns, and the pulse period to be
$1 \sim 2 \textrm{ }\mu\textrm{s}$. This time structure is sufficient for the
search for \mueconv in an aluminium target where the lifetime of muons is 864
ns. A plan of accelerator operation to realise the scheme is shown in
the Figure~\ref{fig:comet_mr_4filled}, where 4 out of 9 MR buckets are filled.
from \SIrange{1}{2}{\us}. This time structure is sufficient for the
search for \mueconv in an aluminium target where the mean lifetime of negative
muons in muonic atoms is \SI{864}{\ns}. One possible plan of accelerator
operation to realise the beam pulsing is shown in \cref{fig:comet_mr_4filled},
where 4 out of 9 MR buckets are filled.
As mentioned, it is very important that there is no stray proton arrives in the
measuring period between two proton bunches. An extinction factor is defined as
the ratio between number of protons in between two pulses and the number of
protons in the main pulse. In order to achieve the goal sensitivity of the
COMET, an extinction factor of \sn{}{-9} is required.
COMET, an extinction factor less than \num{E-9} is required.
Requirements for the proton beam are summarised in the
Table~\ref{tab:comet_proton_beam}.
Requirements for the proton beam are summarised in \cref{tab:comet_proton_beam}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.8\textwidth]{figs/comet_mr_4filled}
\caption{The COMET proton bunch structure in the RCS (rapid cycle
synchrotron) and MR where 4 buckets
\caption{The COMET proton bunch structure in the RCS (Rapid Cycling
Synchrotron) and MR where 4 buckets
are filled producing 100 \si{\nano\second} bunches separated by
1.2~\si{\micro\second}.}
\label{fig:comet_mr_4filled}
@@ -234,7 +244,7 @@ pions, are preferred. It is known from other measurements that backward
scattered pions (with respect to proton beam direction) of high energy are
suppressed, and the yield of low energy pions in the backward direction is not
too low compares to that of the forward direction (see
Figure~\ref{fig:pion_yield}). For these reasons, the COMET
\cref{fig:pion_yield}). For these reasons, the COMET
decided to collect backward pions.
\begin{figure}[htb]
\centering
@@ -243,10 +253,9 @@ decided to collect backward pions.
target.}
\label{fig:pion_yield}
\end{figure}
The pion capture system is composed of several superconducting solenoids:
capture solenoids and matching solenoids. The magnetic field distribution along
the beam axis of the COMET is shown in the Figure~\ref{fig:comet_Bfield}. The
the beam axis of the COMET is shown in \cref{fig:comet_Bfield}. The
peak field of 5 T is created by the capture solenoid, and the matching
solenoids provide a smooth transition from that peak field to the 3 T field in
the pions/muons transportation region. The superconducting solenoids are
@@ -258,6 +267,7 @@ will be installed inside the cryostat to reduce radiation heat load.
\caption{Magnetic field distribution along the COMET beam line.}
\label{fig:comet_Bfield}
\end{figure}
%TODO full comet field
% subsection pion_production_can_capture_solenoid (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -266,7 +276,7 @@ will be installed inside the cryostat to reduce radiation heat load.
Muons and pions are transported to the muon stopping target through a muon
beam line, which includes several curved and straight superconducting solenoid
magnets. A schematic layout of the muon beam line, include the capture and
detector sections, is shown in Figure~\ref{fig:comet_beamline_layout}.
detector sections, is shown in \cref{fig:comet_beamline_layout}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.95\textwidth]{figs/comet_beamline_layout}
@@ -292,7 +302,7 @@ of the drift is given by:
&= \frac{1}{qB} \frac{s}{R} \frac{p}{2}
\left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right)\\
&= \frac{1}{qB} \theta_{bend} \frac{p}{2}
\left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right)
\left( \textrm{cos}\theta + \frac{1}{\textrm{cos}\theta} \right)\,,
\end{align}
where $q$ is the electric charge of the particle; $B$ is the magnetic field at
the axis; $s$ and $R$ are the path length and the radius of the curvature; $p$,
@@ -312,7 +322,7 @@ produced by additional coils winded around the solenoid coils. The magnitude of
the compensating field is:
\begin{equation}
B_{\textrm{comp}} = \frac{1}{qR} \frac{p_0}{2}
\left( \textrm{cos}\theta_0 + \frac{1}{\textrm{cos}\theta_0} \right)
\left( \textrm{cos}\theta_0 + \frac{1}{\textrm{cos}\theta_0} \right)\,,
\end{equation}
where the trajectories of charged particles with momentum $p_0$ and pitch angle
$\theta_0$ are corrected to be on-axis. An average dipole field of 0.03 T is
@@ -321,23 +331,44 @@ needed to select 40 MeV/$c$ muons as required by the COMET design.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Muon stopping target}
\label{sub:muon_stopping_target}
Muon stopping target is place at 180\si{\degree}~bending after the pion production
target (Figure~\ref{fig:comet_beamline_layout}) in its own solenoid. The target
Muon stopping target is place at 180\si{\degree}~bending after the pion
production target (\cref{fig:comet_beamline_layout}) in its own solenoid. The
target
is designed to maximise the muon stopping efficiency and minimise the energy
loss of signal electrons.
%\hl{TODO: Target choice: separation, product, lifetime, energy loss\ldots}
It is calculated that the branching ratio of \mueconv increases with atomic
number $Z$, and plateaus above $Z \simeq 30$, then decreases as $Z>60$. The
lifetime of muons inside a material decreases quickly as $Z$ increases.
Tracking wise, lower $Z$ material provides better reconstructed momentum
resolution. Therefore, light material is preferable as muon stopping target.
number $Z$, and plateaus above $Z \simeq 30$, then decreases as $Z>60$ (see
\cref{fig:comet_mueconv_RateVsZ}). Although the sensitivity is better for
higher $Z$ material, the acceptance of the measurement time window decreases
quickly because the average lifetime of negative muons inside a material
decreases as $Z^{-4}$.
%Tracking wise, lower $Z$ material provides better
%reconstructed momentum
%resolution.
Therefore, light material is preferable as muon stopping target.
\begin{figure}[hbp]
\centering
\includegraphics[width=0.60\textwidth]{figs/comet_mueconv_RateVsZ}
\caption{Target dependence of the \mueconv rate in different models
calculated by Cirigliano and colleagues~\cite{CiriglianoKitano.etal.2009}.
The conversion rates are normalised to the rate in aluminium. Four models
were considered and noted with letters: D for dipole-interaction-dominated
model, V for vector and S for scalar interactions. The three vertical lines
from left to right correspond to $Z=13$(Al), $Z=22$(Ti), and $Z=82$(Pb)
respectively. Reprinted figure from
reference~\cite{CiriglianoKitano.etal.2009}. Copyright 2009 by the
American Physical Society.}
\label{fig:comet_mueconv_RateVsZ}
\end{figure}
The first choice for the muon stopping target material in the COMET is
aluminium. A titanium target is also considered. Configuration of the target is
shown in the Table~\ref{tab:comet_al_target}. Monte Carlo studies with this
aluminium. A titanium target is also considered in the future. Configuration of
the target is shown in \cref{tab:comet_al_target}. Monte Carlo studies with
this
design showed that net stopping efficiency is 0.29, and average energy loss
of signal electrons is about 400 \si{\kilo\electronvolt}.
of signal electrons is about \SI{400}{\keV}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l l}
@@ -358,7 +389,7 @@ of signal electrons is about 400 \si{\kilo\electronvolt}.
\end{table}
A graded magnetic field (reduces from 3 T to 1 T) is produced at the
location of the stopping target (see Figure~\ref{fig:comet_target_Bfield}) to
location of the stopping target (see \cref{fig:comet_target_Bfield}) to
maximise the acceptance for \mueconv signals, since electrons emitted in the
backward
direction would be reflected due to magnetic mirroring. The graded field also
@@ -375,36 +406,36 @@ transport section.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Electron transportation beam line}
\label{sub:electron_transportation_beam_line}
The 180\si{\degree}~bending electron transport solenoids help remove line-of-sight
The \ang{180} bending electron transport solenoids help remove line-of-sight
between the target and the detector system. It works similarly to the muon
transportation section, but is tuned differently to accept electrons of about
105~\si{\mega\electronvolt\per\cc}. A compensation field of 0.17 T along the
vertical direction will be applied. Electrons with momentum less than 80
\si{\mega\electronvolt\per\cc} are blocked at the exit of this section by
\SI{105}{\MeV\per\cc}. A compensation field of \SI{0.17}{\tesla} along the
vertical direction will be applied. Electrons with momentum less than
\SI{80}{\MeV\per\cc} are blocked at the exit of this section by
a collimator to reduce DIO electrons rate. The net acceptance of signals of
\mueconv is about 0.32, and the detector hit rate will be in the order of
1~\si{\kilo\hertz}~for \sn{}{11} stopped muons\si{\per\second}.
\SI{1}{\kHz} for a muon stopping rate of \SI{E11}{\Hz}.
% subsection electron_transportation_beam_line (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Electron detectors}
\label{sub:electron_detectors}
The \mueconv signal electrons is measured by an electron detector system, which
consists of straw-tube trackers and an electromagnetic calorimeter - shown in
Figure~\ref{fig:comet_detector_system}. The
\cref{fig:comet_detector_system}. The
requirements for the detector system is to distinguish electrons from other
particles, and measure their momenta, energy and timings. The whole detector
system is in a uniform solenoidal magnetic field under vacuum. Passive and
active shielding against cosmic rays is considered.
The tracking detector has to provide a momentum resolution less than
%%TODO 350 or 150?
350~\si{\kilo\electronvolt\per\cc} in order to achieve a sensitivity of
\sn{3}{-17}. There are five stations of straw-tube gas chambers, each provides
two
dimensional information. Each straw tube is 5~\si{\milli\meter} in diameter and has
a 25~\si{\micro\meter}-thick wall. According to a GEANT4 Monte Carlo simulation,
a position resolution of 250~\si{\micro\meter} can be obtained, which is enough for
350~\si{\kilo\electronvolt\per\cc} momentum resolution. The DIO background of 0.15
events is estimated.
two dimensional information. Each straw tube is 5~\si{\milli\meter} in diameter
and has a 25-\si{\micro\meter}-thick wall. According to a GEANT4 Monte Carlo
simulation, a position resolution of 250~\si{\micro\meter} can be obtained,
which is enough for 350~\si{\kilo\electronvolt\per\cc} momentum resolution. The
DIO background of 0.15 events is expected.
The electromagnetic calorimeter serves three purposes: a) to measure electrons
energy with high energy resolution; b) to provide timing information and
@@ -427,7 +458,7 @@ The requirements for \mueconv signals are:
muons decay in flight;
\item timing wise, conversion electrons should arrive in the time window of
detection which is about 700~\si{\nano\second}~after each proton pulses
(Figure~\ref{fig:comet_meas_timing}). The acceptance in this detection
(\cref{fig:comet_meas_timing}). The acceptance in this detection
window is about 0.39 for aluminium.
\end{itemize}
@@ -472,7 +503,7 @@ Potential backgrounds for the COMET are:
\item Accidental background from cosmic rays
\end{enumerate}
The expected background rates for the COMET at an SES of
\sn{3}{-17} is summarised in Table~\ref{tab:comet_background_estimation}.
\sn{3}{-17} is summarised in \cref{tab:comet_background_estimation}.
\begin{table}[htb]
\begin{center}
%\begin{tabular}{l l}
@@ -516,11 +547,12 @@ are believed to greatly reduce potential backgrounds, by several orders of
magnitude, for the \mueconv search. That also means that backgrounds are being
extrapolated over four orders of magnitude from existing data. In order to
obtain data-driven estimates of backgrounds, and inform the detailed design for
the ultimate COMET experiment, and initial phase is desirable. Also, the 5-year
mid-term plan from 2013 of J-PARC includes the construction of the COMET beam
line. For these reasons, the COMET collaboration considers a staged approach
with the first stage, so called COMET Phase-I, with a shorter muon
transportation solenoid, up to the first 90\si{\degree}.
the ultimate COMET experiment, a staged approach is desirable. Also, the
KEK/J-PARC 5-year mid-term plan from 2013 includes the construction
of the COMET beam line. For these reasons, the COMET collaboration considers
to carry out the experiment in two stages. The first stage, so called COMET
Phase-I, with a shorter muon transportation solenoid, up to the first
90\si{\degree}.
%\begin{wrapfigure}{r}{0.5\textwidth}
%\centering
@@ -531,8 +563,8 @@ transportation solenoid, up to the first 90\si{\degree}.
%\end{wrapfigure}
\begin{SCfigure}
\centering
\caption{Lay out of the COMET Phase-I, the target and detector solenoid are
placed after the first 90\si{\degree}~bend.}
\caption{Layout of the COMET Phase-I, the target and detector solenoid are
placed after the end of the first \ang{90} bend.}
\includegraphics[width=0.4\textwidth]{figs/comet_phase1_layout}
\label{fig:comet_phase1_layout}
\end{SCfigure}
@@ -545,11 +577,11 @@ The COMET Phase-I has two major goals:
and physics background from muon DIO. Straw tube trackers and crystal
calorimeter with the same technology in the full COMET will be used, thus
these detectors can be regarded as the final prototype.
\item Search for \mueconv with an intermediate sensitivity of \sn{3.1}{-15},
a two orders of magnitude improvement from the SINDRUM-II limit. To realise
this goal, two options for detectors are being considered, either a reused
of the detectors for background measurements, or a dedicated detector.
The latter will be described in detail later.
\item Search for \mueconv with an intermediate single event sensitivity of
\num{3.1E-15}, a two orders of magnitude improvement from the SINDRUM-II
limit. Another dedicated detector system (described in
\cref{sub:detectors_for_mueconv_search_in_the_phase_i}) is considered for
this physics measurement.
\end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -558,11 +590,11 @@ The COMET Phase-I has two major goals:
Proton beam for the Phase-I differs only in beam power compares to that of the
full COMET. It is estimated that a beam power of
3.2~\si{\kilo\watt}~$=$~8~\si{\giga\electronvolt}~$\times$~0.4~\si{\micro\ampere}~(or
\sn{2.5}{12} protons\si{\per\second}) will be enough for beam properties
\sn{2.5}{12} protons per second) will be enough for beam properties
study and achieving the physics goal of this stage.
Starting from a lower intensity is also suitable for performing accelerator
studies that are needed to realise 8~\si{\giga\electronvolt} beam extraction from
the J-PARC main ring.
studies that are needed to realise 8~\si{\giga\electronvolt} beam extraction
from the J-PARC main ring.
% subsection proton_beam_for_the_comet_phase_i (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Pion production and transportation solenoids}
@@ -579,7 +611,7 @@ A correction dipole filed of 0.05 T is also applied to improve the pion yield.
The pion/muon beam line for COMET Phase-I consists of the pion capture solenoid
section (CS), muon transport solenoid section (TS) up to the first
90\si{\degree}~bending, and a set of matching solenoids (see
Figure~\ref{fig:comet_phase1_magnets}). At the end of the muon beam line, the
\cref{fig:comet_phase1_magnets}). At the end of the muon beam line, the
detectors and the detector solenoid (DS) are installed. To reduce beam
backgrounds, a beam collimator is placed upstream of the detector solenoid.
\begin{figure}[htb]
@@ -599,7 +631,7 @@ backgrounds, a beam collimator is placed upstream of the detector solenoid.
As mentioned, two types of detectors are considered for physics measurements in
the Phase-I. The dedicated detector system consists of a cylindrical drift
chamber (CDC), a trigger hodoscope, a proton absorber and a detector solenoid
(Figure~\ref{fig:comet_phase1_cydet}).
(\cref{fig:comet_phase1_cydet}).
The whole system is referred as cylindrical detector system (CyDet) in the
COMET's documentation. The CyDet has advantages that low momentum particles for
the stopping target will not reach the detector, thus the hit rates are kept
@@ -614,26 +646,28 @@ CyDet.
\label{fig:comet_phase1_cydet}
\end{figure}
\subsubsection{CDC configuration}
\label{ssub:CDC_configuration}
The CDC is the main tracking detector that provides information for
reconstruction of charged particle tracks and measuring their momenta. The key
parameters for the CDC are listed in the
Table~\ref{tab:comet_phase1_cdc_params}.
\cref{tab:comet_phase1_cdc_params}.
Trigger hodoscopes are placed at both upstream and downstream ends of the CDC.
An absorber is placed concentrically with respect to the CDC axis to
A proton absorber is placed concentrically with respect to the CDC axis to
reduce potential high rates caused by protons emitted after nuclear muon
capture in the stopping target.
The CDC covers the region
from \SIrange{500}{831}{\milli\meter}~in the radial direction. The length
of the CDC is 1500~\si{\milli\meter}. The inner wall is made of
a 100~\si{\micro\meter}-thick aluminised Mylar. The end-plates will be conical
in shape and about 10~\si{\milli\meter}-thick to support the feedthroughs. The outer
wall is
made of 5~\si{\milli\meter}~carbon fibre reinforced plastic (CFRP).
a 500-\si{um}-thick carbon fibre reinforced plastic (CFRP, density
\SI{1.57}{\gram\per\cubic\m}). The end-plates will
be conical in shape and about 10-\si{\mm}-thick to support the
feedthroughs. The outer wall is made of 5-\si{\mm} CFRP.
The CDC is arranged in 20 concentric sense layers with alternating positive and
negative stereo angles. The sense wires are made of gold-plated tungsten,
30~\si{\micro\meter} in diameter, tensioned to 50~\si{\gram}. The field wires
\SI{25}{\um} in diameter, tensioned to \SI{50}{\gram}. The field wires
are uncoated aluminium wires with a diameter of 80~\si{\micro\meter}, at the same
tension of \SI{50}{\gram}. A high voltage of $1700\sim1900$~\si{\volt} will be
applied to the sense wires with the field wires at ground potential, giving an
@@ -674,37 +708,72 @@ these configurations, an intrinsic momentum resolution of
\label{tab:comet_phase1_cdc_params}
\end{table}
The maximum usable muon beam intensity will be limited by the detector hit
\subsubsection{Hit rate on the CDC}
\label{ssub:hit_rate_on_the_cdc}
The maximal usable muon beam intensity will be limited by the detector hit
occupancy. Charge particles with transversal momentum greater than 70
\si{\mega\electronvolt\per\cc} are expected to reach the CDC. Those particles are:
\si{\mega\electronvolt\per\cc} are expected to reach the CDC. Those include:
protons emitted from nuclear muon capture, and electrons from muon decay in
orbit. It is calculated that the hit rate due to proton emission dominates,
where the highest rate is 11~\si{\kilo\hertz\per}cell compares to
5~\si{\kilo\hertz\per}
cell contributing from DIO electrons. Another potential issue caused by protons
is the ageing effect on the CDC as they leave about a 100 times larger
orbit (DIO). It is calculated that the hit rate due to proton emission dominates,
where the highest rate is \SI{11}{\kHz\per}cell compares to
\SI{5}{\kHz\per}cell contributing from DIO electrons. Another potential issue
%%TODO check the hit rates against TDR
caused by protons is the ageing effect on the CDC as they leave about a 100
times larger
energy deposit than the minimum ionisation particles.
%%TODO integration charge ...
For those reasons, we plan to install an absorber to reduce the rate of protons
reaching the CDC. However, there is no experimental data available for the rate
For those reasons, we plan to install a proton absorber to reduce the rate of
protons reaching the CDC. However, there is no experimental data available for
the rate
of protons emitted after muon capture in aluminium. In the design of the COMET
Phase-I, we use a conservative estimation of the rate of protons from energy
spectrum of charged particles emitted from muon capture in
$^{28}$Si~\cite{SobottkaWills.1968}. The baseline design for the proton
absorber is 1.0~\si{\milli\meter}-thick CFRP, which contributes
195~\si{\kilo\electronvolt\per\cc} to the momentum resolution of reconstructed
track.
absorber is 0.5~\si{\milli\meter}-thick CFRP, making the total thickness
of material before the sensitive region is \SI{1.0}{\mm} in CFRP. In this
configuration, the inner wall and the proton absorber contribute a spread of
\SI{167}{\keV\per\cc} to the momentum of a \mueconv signal electron. This
figure is a little below the spread cause by multiple scatterings on the
chamber gas at \SI{197}{\keV\per\cc}.
The impact of the proton absorber on the CDC's hit rate and momentum
resolution is summarised in \cref{tab:comet_absorber_impact}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{@{}cccc@{}}
\toprule
\textbf{Absorber }& \textbf{Total CFRP }&\textbf{Proton }&
\textbf{$\Delta p$}\\
\textbf{thickness }& \textbf{thickness }&\textbf{hit rate }& \\
(\si{\mm}) &(\si{\mm}) & (\si{\kHz}) & (\si{\keV\per\cc}) \\
\midrule
0 & 0.5 & 130 & 131 \\
0.5 & 1.0 & 34 & 167 \\
1.0 & 1.5 & 11 & 195 \\
1.5 & 2.0 & 6 & 252 \\
\bottomrule
\end{tabular}
\end{center}
\caption{Hit rates and contributions to momentum spread of the proton
absorber and inner wall of the CDC. The resolutions are calculated for
mono-energetic electrons of \SI{104.96}{\MeV\per\cc}.}
\label{tab:comet_absorber_impact}
\end{table}
In order to obtain a better understanding of the protons emission, and then
further optimisation of the CDC, a dedicated experiment to measure proton
emission rate and energy spectrum is being carried out at PSI. This experiment
is described in detail in next chapters.
It should be noted that the proton hit rate is not a problem for the COMET
Phase-II where the additional electron transport solenoid would removed all
protons emitted.
% subsection detectors_for_mueconv_search_in_the_phase_i (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Sensitivity of the \mueconv search in the Phase-I}
\label{sub:sensitivity_of_the_mueconv_search_in_the_phase_i}
The SES for the Phase-I is given by
the Equation~\ref{eq:mue_sensitivity}. Using $N_{\mu} = 1.3\times 10^{16}$,
the \eqref{eq:mue_sensitivity}. Using $N_{\mu} = 1.3\times 10^{16}$,
$f_{\textrm{cap}} = 0.61$, and $A_e = 0.043$ from MC study for the Phase-I, the
SES becomes:
\begin{equation}
@@ -715,10 +784,11 @@ SES becomes:
\subsection{Time line of the COMET Phase-I and Phase-II}
\label{sub:time_line_of_the_phase_i}
We are now in the construction stage of the COMET Phase-I, which is planned to
be finished by the end of 2016. We will carry out engineering run in 2016,
be finished in the middle of 2016. We will carry out engineering run in the
second half of 2016,
and subsequently, physics run in 2017. A beam time of 90 days is expected to
achieve the goal sensitivity of the Phase-I. An anticipated schedule for the
COMET, both Phase-I and Phase-II, is shown in Figure~\ref{fig:sched}.
COMET, both Phase-I and Phase-II, is shown in \cref{fig:sched}.
\begin{figure}[tbh]
\centering
\includegraphics[width=0.8\textwidth]{figs/sched}

617
thesis/chapters/chap4_alcap_phys.tex
View File

@@ -5,19 +5,19 @@
\thispagestyle{empty}
As mentioned earlier, the emission rate of protons
following nuclear muon capture on aluminium is of interest to the COMET Phase-I
since protons can cause a very high hit rate on the proposed cylindrical drift
since protons could cause a very high hit rate on the proposed cylindrical drift
chamber. Another \mueconv experiment, namely Mu2e at Fermilab, which aims at
a similar goal sensitivity as that of the COMET, also shares the same interest
on proton emission. Therefore, a joint COMET-Mu2e project was formed to carry
out the measurement of proton, and other charged particles, emission. The
experiment, so-called AlCap, has been proposed and approved to be carried out
at PSI in 2013~\cite{AlCap.2013}. In addition to proton, the AlCap
at PSI in 2013~\cite{AlCap.2013}. In addition to proton emission, the AlCap
experiment will also measure:
\begin{itemize}
\item neutrons, because they can cause backgrounds on other detectors and
damage the front-end electronics; and
\item photons, since they provide ways to normalise number of stopped muons
in the stopping target.
\item neutron emission, because neutrons could cause backgrounds on the other
detectors and damage the front-end electronics; and
\item photon emission to validate the normalisation number of stopped
muons in the stopping target.
\end{itemize}
The emission of particles following muon capture in nuclei
@@ -27,7 +27,7 @@ energy nuclear physics'' where it is postulated that the weak interaction is
well understood and muons are used as an additional probe to investigate the
nuclear structure~\cite{Singer.1974, Measday.2001}.
Unfortunately, the proton emission rate for aluminium in the energy range of
interest is not available. This chapter reviews the current knowledge on
interest has not been measured. This chapter reviews the current knowledge on
emission of particles with emphasis on proton.
%theoretically and experimentally, hence serves as the motivation for the AlCap
%experiment.
@@ -66,21 +66,20 @@ emission of particles with emphasis on proton.
Theoretically, the capturing process can be described in the following
stages~\cite{FermiTeller.1947, WuWilets.1969}:
\begin{enumerate}
\item High to low (a few \si{\kilo\electronvolt}) energy: the muon velocity are
greater than the velocity of the valence electrons of the atom. Slowing
\item High to low (a few \si{\kilo\electronvolt}) energy: the muon velocity
are greater than the velocity of the valence electrons of the atom. Slowing
down process is similar to that of fast heavy charged particles. It takes
about \sn{}{-9} to \sn{}{-10} \si{\second}~to slow down from a relativistic
\sn{}{8}~\si{\electronvolt}~energy to 2000~\si{\electronvolt}~in condensed matter,
about \SIrange{E-10}{E-9}{\s} to slow down from a relativistic
\SI{E8}{\eV} energy to \SI{2000}{\eV} in condensed matter,
and about 1000 times as long in air.
\item Low energy to rest: in this phase, the muon velocity is less than that
of the valence electrons, the muon is considered to be moving inside
a degenerate electron gas. The muon rapidly comes to a stop either in
condensed matters ($\sim$\sn{}{-13}~\si{\second}) or in gases ($\sim$\sn{}{-9}
\si{\second}).
\item Atomic capture: the muon has no kinetic energy, it is captured by the
host atom into one of high orbital states, forming a muonic atom. The
condensed matters ($\simeq\SI{E-13}{\s}$) or in gases ($\simeq\SI{E-9}{\s}$).
\item Atomic capture: when the muon has no kinetic energy, it is captured by
a host atom into one of high orbital states, forming a muonic atom. The
distribution of initial states is not well known. The details depend on
whether the material is a solid or gas, insulator or material
whether the material is a solid or gas, insulator or metal.
\item Electromagnetic cascade: since all muonic states are unoccupied, the
muon cascades down to states of low energy. The transition is accompanied
by the emission of Auger electrons or characteristic X-rays, or excitation
@@ -88,10 +87,12 @@ stages~\cite{FermiTeller.1947, WuWilets.1969}:
state, 1S, from the instant of its atomic capture is
$\sim$\sn{}{-14}\si{\second}.
\item Muon disappearance: after reaching the 1S state, the muons either
decays with a half-life of \sn{2.2}{-6}~\si{\second}~or gets captured by the
nucleus. In hydrogen, the capture to decay probability ratio is about
\sn{4}{-4}. Around $Z=11$, the capture probability is roughly equal to the
decay probability. In heavy nuclei ($Z\sim50$), the ratio of capture to
decays or gets captured by the nucleus. The possibility to be captured
effectively shortens the mean lifetime of negative muons stopped in
a material. In hydrogen, the capture to decay
probability ratio is about \sn{4}{-4}. Around $Z=11$, the capture
probability is roughly equal to the
decay probability. In heavy nuclei ($Z\geq$), the ratio of capture to
decay probabilities is about 25.
The K-shell muon will be $m_\mu/m_e \simeq 207$ times nearer the nucleus
@@ -108,24 +109,25 @@ stages~\cite{FermiTeller.1947, WuWilets.1969}:
\label{sec:nuclear_muon_capture}
The nuclear capture process is written as:
\begin{equation}
\mu^- + A(N, Z) \rightarrow A(N, Z-1) + \nu_\mu
\mu^- + A(N, Z) \rightarrow A(N, Z-1) + \nu_\mu \,.
\label{eq:mucap_general}
\end{equation}
The resulting nucleus can be either in its ground state or in an excited state.
The reaction is manifestation of the elementary ordinary muon capture on the
proton:
\begin{equation}
\mu^- + p \rightarrow n + \nu_\mu
\mu^- + p \rightarrow n + \nu_\mu \,.
\label{eq:mucap_proton}
\end{equation}
If the resulting nucleus at is in an excited state, it could cascade to lower
states by emitting light particles and leaving a residual heavy nucleus. The
light particles are mostly neutrons and (or) photons. Neutrons can also be
If the resulting nucleus at is in an excited state, it could cascade down to
lower states by emitting light particles and gamma rays, leaving a residual
heavy nucleus. The light particles are mostly neutrons and (or) photons.
Neutrons can also be
directly knocked out of the nucleus via the reaction~\eqref{eq:mucap_proton}.
Charged particles are emitted with probabilities of a few percent, and are
mainly protons, deuterons and alphas have been observed in still smaller
probabilities. Because of the central interest on proton emission, it is covered
in a separated section.
probabilities. Because of the central interest on proton emission, it is
discussed in a separated section.
\subsection{Muon capture on the proton}
\label{sub:muon_capture_on_proton}
@@ -138,10 +140,10 @@ in a separated section.
%$\mu p$ atom is quite active, so it is likely to form muonic molecules like
%$p\mu p$, $p\mu d$ and $p\mu t$, which complicate the study of weak
%interaction.
The underlying interaction in proton capture in Equation~\eqref{eq:mucap_proton}
The underlying interaction in proton capture in~\eqref{eq:mucap_proton}
at nucleon level and quark level
are depicted in the Figure~\ref{fig:feyn_protoncap}. The flow of time is from
the left to the right hand side, as an incoming muon and an up quark
are depicted in \cref{fig:feyn_protoncap}. The direction of time is
from the left to the right hand side, as an incoming muon and an up quark
exchange a virtual $W$ boson to produce a muon neutrino and a down quark, hence
a proton transforms to a neutron.
@@ -156,7 +158,10 @@ a proton transforms to a neutron.
\end{figure}
The four-momentum transfer in the interaction is fixed at
$q^2 = (q_n - q_p)^2 = -0.88m_\mu^2 \ll m_W^2$. The smallness of the momentum
\begin{equation}
q^2 = (q_n - q_p)^2 = -0.88m_\mu^2 \ll m_W^2\,.
\end{equation}
The smallness of the momentum
transfer in comparison to the $W$ boson's mass makes it possible to treat the
interaction as a four-fermion interaction with Lorentz-invariant transition
amplitude:
@@ -181,14 +186,14 @@ is factored out in Eq.~\eqref{eq:4fermion_trans_amp}):
\label{eq:weakcurrent_ud}
\end{equation}
If the nucleon were point-like, the nucleon current would have the same form as
in Eq.~\eqref{eq:weakcurrent_ud} with suitable wavefunctions of the proton and
in \eqref{eq:weakcurrent_ud} with suitable wavefunctions of the proton and
neutron. But that is not the case, in order to account for the complication of
the nucleon, the current must be modified by six real form factors
$g_i(q^2), i = V, M, S, A, T, P$:
\begin{align}
J_\alpha &= i\bar{\psi}_n(V^\alpha - A^\alpha)\psi_p,\\
J_\alpha &= i\bar{\psi}_n(V^\alpha - A^\alpha)\psi_p\,,\\
V^\alpha &= g_V (q^2) \gamma^\alpha + i \frac{g_M(q^2)}{2m_N}
\sigma^{\alpha\beta} q_\beta + g_S(q^2)q^\alpha,\\
\sigma^{\alpha\beta} q_\beta + g_S(q^2)q^\alpha\,, \textrm{ and}\\
A^\alpha &= g_A(q^2)\gamma^\alpha \gamma_5 + ig_T(q^2)
\sigma^{\alpha\beta} q_\beta\gamma_5 + \frac{g_P(q^2)}{m_\mu}\gamma_5
q^\alpha,
@@ -223,7 +228,7 @@ muonic molecules $p\mu p$, $d\mu p$ and $t\mu p$, $g_P$ is the least
well-defined form factor. Only recently, it is measured with a reasonable
precision~\cite{AndreevBanks.etal.2013a}.
The values of the six form factors at $q^2 = -0.88m^2_\mu$ are listed in
Table~\ref{tab:formfactors}.
\cref{tab:formfactors}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l l l}
@@ -259,35 +264,8 @@ $\Lambda_t$ is given by:
where $\Lambda_c$ and $\Lambda_d$ are partial capture rate and decay rate,
respectively, and $Q$ is the Huff factor, which is corrects for the fact that
muon decay rate in a bound state is reduced because of the binding energy
reduces the available energy.
%The total capture rates for several selected
%elements are compiled by Measday~\cite{Measday.2001},
%and reproduced in
%Table~\ref{tab:total_capture_rate}.
%\begin{table}[htb]
%\begin{center}
%\begin{tabular}{l l r@{.}l r@{.}l@{$\pm$}l l}
%\toprule
%\textbf{$Z$ ($Z_{\textrm{eff}}$)} &
%\textbf{Element} &
%\multicolumn{2}{l}{\textbf{Mean lifetime}} &
%\multicolumn{3}{l}{\textbf{Capture rate}} &
%\textbf{Huff factor}\\
%& &
%\multicolumn{2}{c}{\textbf{(\nano\second)}} &
%\multicolumn{3}{l}{\textbf{$\times 10^3$ (\reciprocal\second)}} &\\
%\midrule
%1 (1.00) & $^1$H & 2194&90 $\pm$0.07 & 0&450 &0.020 & 1.00\\
%& $^2$H & 2194&53 $\pm$0.11 & 0&470 &0.029 & \\
%2 (1.98) & $^3$He & 2186&70 $\pm$0.10 & 2&15 &0.020 & 1.00\\
%& $^4$He & 2195&31 $\pm$0.05 & 0&470&0.029 & \\
%\bottomrule
%\end{tabular}
%\end{center}
%\caption{Total capture rate of the muon in nuclei for several selected
%elements, compiled by Measday~\cite{Measday.2001}}
%\label{tab:total_capture_rate}
%\end{table}
reduces the available energy. The correction begins to be significant for
$Z\geq 40$ as shown in \cref{tab:total_capture_rate}.
Theoretically, it is assumed that the muon capture rate on a proton of the
nucleus depends only on the overlap of the muon with the nucleus. For light
@@ -312,13 +290,56 @@ reduced because a smaller phase-space in the nuclear muon capture compares to
that of a nucleon; and $X_2 = 3.125$ takes into account the fact that it is
harder for protons to transforms into neutrons due to the Pauli exclusion
principle in heavy nuclei where there are more neutrons than protons.
The total capture rates for several selected elements are compiled by
Measday~\cite{Measday.2001}, and reproduced in \cref{tab:total_capture_rate}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{r c S S S}
\toprule
$Z (Z_{eff})$ & \textbf{Element} & \textbf{Mean lifetime (\si{\ns})}
& \textbf{Capture rate ($\times 10^{-3}$ \si{\ns})} & \textbf{Huff factor}\\
%& & \textbf{(\si{\ns})} & \textbf{($\times 10^{-3} \si{\Hz}$)} &\\
\midrule
1 (1.00)& $^{1}$H & 2194.90 (7)& 0.450 (20)& 1.00 \\
& $^{2}$H & 2194.53 (11)& 0.470 (29)& \\
2 (1.98)& $^{3}$He & 2186.70 (10)& 2.15 (2)& 1.00\\
& $^{4}$He & 2195.31 (5)& 0.356 (26)&\\
3 (2.94)& $^{6}$Li & 2175.3 (4)& 4.68 (12)& 1.00 \\
& $^{7}$Li & 2186.8 (4)& 2.26 (12)& \\
4 (3.89)& $^{9}$Be & 2168 (3)& 6.1 (6)& 1.00 \\
5 (4.81)& $^{10}$B & 2072 (3)& 27.5 (7)& 1.00 \\
& $^{11}$B & 2089 (3)& 23.5 (7)& 1.00 \\
6 (5.72)& $^{12}$C & 2028 (2)& 37.9 (5)& 1.00 \\
& $^{13}$C & 2037 (8)& 35.0 (20)& \\
7 (6.61)& $^{14}$N & 1919 (15)& 66 (4)& 1.00 \\
8 (7.49)& $^{16}$O & 1796 (3)& 102.5 (10)& 0.998 \\
& $^{18}$O & 1844 (5)& 88.0 (14)& \\
9 (8.32)& $^{19}$F & 1463 (5)& 229 (1)& 0.998 \\
13 (11.48)& $^{27}$Al& 864 (2)& 705 (3)& 0.993 \\
14 (12.22)& $^{28}$Si& 758 (2)& 868 (3)& 0.992 \\
20 (16.15)& Ca & 334 (2)& 2546 (20)& 0.985 \\
40 (25.61)& Zr & 110.4 (10)& 8630 (80)& 0.940 \\
82 (34.18)& Pb & 74.8 (4)& 12985 (70)& 0.844 \\
83 (34.00)& Bi & 73.4 (4)& 13240 (70)& 0.840 \\
90 (34.73)& Th & 77.3 (3)& 12560 (50)& 0.824 \\
92 (34.94)& U & 77.0 (4)& 12610 (70)& 0.820 \\
\bottomrule
\end{tabular}
\end{center}
\caption{Total nuclear capture rate for negative muon in several elements,
compiled by Measday~\cite{Measday.2001}}
\label{tab:total_capture_rate}
\end{table}
% subsection total_capture_rate (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Neutron emission}
\label{sub:neutron_emission}
The average number of neutrons emitted per muon capture generally increases
with $Z$, but there are large deviations from the trend due to particular
nuclear structure effects. The trend is shown in Table~\ref{tab:avg_neutron}
nuclear structure effects. The trend is shown in \cref{tab:avg_neutron}
and can be expressed by a simple empirical function
$n_{avg} = (0.3 \pm 0.02)A^{1/3}$~\cite{Singer.1974}.
\begin{table}[htb]
@@ -347,18 +368,18 @@ $n_{avg} = (0.3 \pm 0.02)A^{1/3}$~\cite{Singer.1974}.
The neutron emission can be explained by several mechanisms:
\begin{enumerate}
\item Direct emission follows reaction~\eqref{eq:mucap_proton}: these neutrons
have fairly high energy, from a few \si{\mega\electronvolt}~to as high as 40--50
\si{\mega\electronvolt}.
have fairly high energy, from a few \si{\si{\MeV}}~to as high as 40--50
\si{\si{\MeV}}.
\item Indirect emission through an intermediate compound nucleus: the energy
transferred to the neutron in the process~\eqref{eq:mucap_proton} is 5.2
\si{\mega\electronvolt} if the initial proton is at rest, in nuclear
\si{\si{\MeV}} if the initial proton is at rest, in nuclear
environment, protons have a finite momentum distribution, therefore the
mean excitation energy of the daughter nucleus is around 15 to 20
\si{\mega\electronvolt}~\cite{Mukhopadhyay.1977}. This is above the nucleon
\si{\si{\MeV}}~\cite{Mukhopadhyay.1977}. This is above the nucleon
emission threshold in all complex nuclei, thus the daughter nucleus can
de-excite by emitting one or more neutrons. In some actinide nuclei, that
excitation energy might trigger fission reactions. The energy of indirect
neutrons are mainly in the lower range $E_n \le 10$ \si{\mega\electronvolt}
neutrons are mainly in the lower range $E_n \le 10$ \si{\si{\MeV}}
with characteristically exponential shape of evaporation process. On top of
that are prominent lines might appear where giant resonances occur.
\end{enumerate}
@@ -382,39 +403,43 @@ data. There are two reasons for that:
neutron emission. The rate is about 15\% for light nuclei and
reduces to a few percent for medium and heavy nuclei.
\item The charged particles are short ranged: the emitted protons,
deuterons and alphas are typically low energy (2--20~\mega\electronvolt).
deuterons and alphas are typically low energy ( \SIrange{2}{20}{\MeV}).
But a relatively thick target is normally needed in order to achieve
a reasonable muon stopping rate and charged particle statistics. Therefore,
emulsion technique is particularly powerful.
\end{enumerate}
The first study was done by Morigana and Fry~\cite{MorinagaFry.1953} where
24,000 muon tracks were stopped in their nuclear emulsion which contains silver,
bromine, and other light elements, mainly nitrogen, carbon, hydrogen and
bromine AgBr, and other light elements, mainly nitrogen, carbon, hydrogen and
oxygen. The authors identified a capture on a light element as it would leave
a recoil
track of the nucleus. They found that for silver bromide AgBr, $(2.2 \pm
track of the nucleus. They found that for silver bromide, $(2.2 \pm
0.2)\%$ of the captures produced protons and $(0.5 \pm 0.1)\%$ produced alphas.
For light elements, the emission rate for proton and alpha are respectively
$(9.5 \pm 1.1)\%$ and $(3.4 \pm 0.7)\%$. Subsequently, Kotelchuk and
Tyler~\cite{KotelchuckTyler.1968} had a result which was about 3 times more
statistics and in fair agreement with Morigana and Fry
(Figure~\ref{fig:kotelchuk_proton_spectrum})
(\cref{fig:kotelchuk_proton_spectrum})
\begin{figure}[htb]
\centering
\includegraphics[width=0.65\textwidth]{figs/kotelchuk_proton_spectrum}
\caption{Early proton spectrum after muon capture in silver bromide AgBr
recorded using nuclear emulsion. Image is taken from
Ref.~\cite{KotelchuckTyler.1968}}
\caption{Proton spectrum after muon capture in silver bromide AgBr in
early experiments recorded using nuclear emulsion. The closed circles
are data points from Morigana and Fry~\cite{MorinagaFry.1953}, the
histogram is measurement result of Kotelchuk and
Tyler~\cite{KotelchuckTyler.1968}. Reprinted figure from
reference~\cite{KotelchuckTyler.1968}. Copyright 1968 by the American
Physical Society.}
\label{fig:kotelchuk_proton_spectrum}
\end{figure}
Protons with higher energy are technically easier to measure, but because of
the much lower rate, they can only be studied at meson facilities. Krane and
colleagues~\cite{KraneSharma.etal.1979} measured proton emission from
aluminium, copper and lead in the energy range above 40 \mega\electronvolt~and
aluminium, copper and lead in the energy range above \SI{40}{\MeV} and
found a consistent exponential shape in all targets. The integrated yields
above 40 \mega\electronvolt~are in the \sn{}{-4}--\sn{}{-3} range (see
Table~\ref{tab:krane_proton_rate}), a minor contribution to total proton
above \SI{40}{\MeV} are in the \sn{}{-4}--\sn{}{-3} range (see
\cref{tab:krane_proton_rate}), a minor contribution to total proton
emission rate.
\begin{table}[htb]
\begin{center}
@@ -438,7 +463,7 @@ emission rate.
\end{table}
Their result on aluminium, the only experimental data existing for this target,
is shown in Figure~\ref{fig:krane_proton_spec} in comparison with spectra from
is shown in \cref{fig:krane_proton_spec} in comparison with spectra from
neighbouring elements, namely silicon measured by Budyashov et
al.~\cite{BudyashovZinov.etal.1971} and magnesium measured Balandin et
al.~\cite{BalandinGrebenyuk.etal.1978}. The authors noted aluminium data and
@@ -454,24 +479,26 @@ might be at work in this mass range.
target (closed circle) in the energy range above 40 MeV and an exponential
fit. The open squares are silicon data from Budyashov et
al.~\cite{BudyashovZinov.etal.1971}, the open triangles are magnesium data
from Balandin et al.~\cite{BalandinGrebenyuk.etal.1978}.}
from Balandin et al.~\cite{BalandinGrebenyuk.etal.1978}. Reprinted
figure from reference~\cite{KraneSharma.etal.1979}. Copyright 1979 by
the American Physical Society.}
\label{fig:krane_proton_spec}
\end{figure}
The aforementioned difficulties in charged particle measurements could be
solved using an active target, just like nuclear emulsion. Sobottka and
Wills~\cite{SobottkaWills.1968} took this approach when using a Si(Li) detector
to stop muons. They obtained a spectrum of charged particles up to 26
\mega\electronvolt~in Figure~\ref{fig:sobottka_spec}. The peak below 1.4
\mega\electronvolt~is due to the recoiling $^{27}$Al. The higher energy events
to stop muons. They obtained a spectrum of charged particles up to \SI{26}{\MeV}
in \cref{fig:sobottka_spec}. The peak below \SI{1.4}{\MeV}
is due to the recoiling $^{27}$Al. The higher energy events
including protons, deuterons and alphas constitute $(15\pm 2)\%$ of capture
events, which is consistent with a rate of $(12.9\pm1.4)\%$ from gelatine
observed by Morigana and Fry. This part has an exponential
decay shape with a decay constant of 4.6 \mega\electronvolt. Measday
decay shape with a decay constant of 4.6 \si{\MeV}. Measday
noted~\cite{Measday.2001} the fractions of events in
the 26--32 \mega\electronvolt~range being 0.3\%, and above 32
\mega\electronvolt~range being 0.15\%. This figure is in agreement with the
integrated yield above 40 \mega\electronvolt~from Krane et al.
the 26--32 \si{\MeV}~range being 0.3\%, and above 32
\si{\MeV}~range being 0.15\%. This figure is in agreement with the
integrated yield above 40 \si{\MeV}~from Krane et al.
In principle, the active target technique could be applied to other material
such as germanium, sodium iodine, caesium iodine, and other scintillation
@@ -480,13 +507,14 @@ identification like in nuclear emulsion, the best one can achieve after all
corrections is a sum of all charged particles. It should be noted here
deuterons can contribute significantly, Budyashov et
al.~\cite{BudyashovZinov.etal.1971} found deuteron components to be
$(34\pm2)\%$ of the charged particle yield above 18 \mega\electronvolt~in
$(34\pm2)\%$ of the charged particle yield above 18 \si{\MeV}~in
silicon, and $(17\pm4)\%$ in copper.
\begin{figure}[htb]
\centering
\includegraphics[width=0.75\textwidth]{figs/sobottka_spec}
\caption{Charged particle spectrum from muon capture in a silicon detector,
image taken from Sobottka and Wills~\cite{SobottkaWills.1968}.}
measured by Sobottka and Wills~\cite{SobottkaWills.1968}. The plot is
reproduced from the original figure in reference~\cite{SobottkaWills.1968}.}
\label{fig:sobottka_spec}
\end{figure}
@@ -513,42 +541,48 @@ active target measurement and found that the reaction
$^{28}\textrm{Si}(\mu^-,\nu pn)^{26}\textrm{Mg}$ could occur at a similar rate
to that of the $^{28}\textrm{Si}(\mu^-,\nu p)^{27}\textrm{Mg}$. That also
indicates that the deuterons and alphas might constitute a fair amount in the
spectrum in Figure~\ref{fig:sobottka_spec}.
spectrum in \cref{fig:sobottka_spec}.
Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978} studied $(\mu^-,\nu p)$,
$(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$, $(\mu^-,\nu p3n)$ and $(\mu^-,\nu\alpha)$
in a wide range of 18 elements from sodium to bismuth.Their results plotted
against the Coulomb barrier for the outgoing protons are given in
Figure~\ref{fig:wyttenbach_rate_1p}, ~\ref{fig:wyttenbach_rate_23p}. The
classical Coulomb barrier $V$ they used are given by:
\cref{fig:wyttenbach_rate_1p}.
%and \cref{fig:wyttenbach_rate_23p}.
The classical Coulomb barrier $V$ they used are given by:
\begin{equation}
V = \frac{zZe^2}{r_0A^{\frac{1}{3}} + \rho},
V = \frac{zZe^2}{r_0A^{\frac{1}{3}} + \rho}\,,
\label{eqn:classical_coulomb_barrier}
\end{equation}
where $z$ and $Z$ are the charges of the outgoing particle and of the residual
nucleus, values $r_0 = 1.35 \textrm{ fm}$, and $\rho = 0 \textrm{ fm}$ for
protons were taken.
nucleus respectively, $e^2 = 1.44 \si{\MeV}\cdot\textrm{fm}$, $r_0 = 1.35
\textrm{ fm}$, and $\rho = 0 \textrm{ fm}$ for protons were taken.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/wyttenbach_rate_1p}
\caption{Activation results from Wyttenbach et
al.~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p)$ and
$(\mu^-,\nu pn)$ reactions.}
\includegraphics[width=0.48\textwidth]{figs/wyttenbach_rate_1p}
\includegraphics[width=0.505\textwidth]{figs/wyttenbach_rate_23p}
\caption{Activation results from Wyttenbach and
colleagues~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p)$,
$(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$ and $(\mu^-,\nu p3n)$ reactions. The
cross section of each individual channels decreases exponentially as the
Coulomb barrier for proton emission increases.
Reprinted figure from reference~\cite{WyttenbachBaertschi.etal.1978} with
permission from Elsevier.}
\label{fig:wyttenbach_rate_1p}
\end{figure}
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/wyttenbach_rate_23p}
\caption{Activation results from Wyttenbach et
al.~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p2n)$ and
$(\mu^-,\nu p3n)$ reactions.}
\label{fig:wyttenbach_rate_23p}
\end{figure}
%\begin{figure}[htb]
%\centering
%\includegraphics[width=0.85\textwidth]{figs/wyttenbach_rate_23p}
%\caption{Activation results from Wyttenbach et
%al.~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p2n)$ and
%$(\mu^-,\nu p3n)$ reactions.}
%\label{fig:wyttenbach_rate_23p}
%\end{figure}
Wyttenbach et al.\ saw that the cross section of each reaction decreases
Wyttenbach and colleagues saw that the cross section of each reaction decreases
exponentially with increasing Coulomb barrier. The decay constant for all
$(\mu^-,\nu pxn)$ is about 1.5 per \mega\electronvolt~of Coulomb barrier. They
also commented a ratio for different de-excitation channels:
$(\mu^-,\nu pxn)$ is about 1.5 per \si{\MeV}~of Coulomb barrier. They
also observed a ratio for different de-excitation channels:
\begin{equation}
(\mu^-,\nu p):(\mu^-,\nu pn):(\mu^-,\nu p2n):(\mu^-,\nu p3n) = 1:6:4:4,
\label{eqn:wyttenbach_ratio}
@@ -558,7 +592,7 @@ the results from Vil'gel'mova et al.~\cite{VilgelmovaEvseev.etal.1971} as being
too high, but Measday~\cite{Measday.2001} noted it it is not
necessarily true since there has been suggestion from other experiments that
$(\mu^-, \nu p)$ reactions might become more important for light nuclei.
Measday also commented that the ratio~\eqref{eqn:wyttenbach_ratio} holds over
Measday noted that the ratio~\eqref{eqn:wyttenbach_ratio} holds over
a broad range of mass, but below $A=40$ the $(\mu^-,\nu p)$ reaction can vary
significantly from nucleus to nucleus.
% subsection experimental_status (end)
@@ -572,33 +606,34 @@ nucleus is formed, and then it releases energy by statistical emission of
various particles. Three models for momentum distribution of protons in the
nucleus were used: (I) the Chew-Goldberger distribution
$\rho(p) \sim A/(B^2 + p^2)^2$; (II) Fermi gas at zero temperature; and (III)
Fermi gas at a finite temperature ($kT = 9$ \mega\electronvolt).
Fermi gas at a finite temperature ($kT = 9$ \si{\MeV}).
A very good agreement with the experimental result for the alpha emission was
obtained with distribution (III), both in the absolute percentage and the energy
distribution (curve (III) in the left hand side of
Figure~\ref{fig:ishii_cal_result}). However, the calculated emission of protons
at the same temperature falls short by about 10
times compares to the data. The author also found that the distribution
(I) is unlikely to be suitable for proton emission, and using that distribution
for alpha emission resulted in a rate 15 times larger than observed.
obtained with distribution (III).
%, both in the absolute percentage and the energy
%distribution (curve (III) in the left hand side of
%\cref{fig:ishii_cal_result}).
However, the calculated emission rate of protons at the same temperature was 10
times smaller the experimental results from Morigana and Fry. The author
found the distribution (I) is unlikely to be suitable for proton emission,
and using that distribution
for alpha emission resulted in a rate 15 times larger than the observed rate.
\begin{figure}[htb]
\centering
\includegraphics[width=.49\textwidth]{figs/ishii_cal_alpha}
%\hspace{10mm}
\includegraphics[width=.49\textwidth]{figs/ishii_cal_proton}
\caption{Alpha spectrum (left) and proton spectrum (right) from Ishii's
calculation~\cite{Ishii.1959} in comparison with experimental data from
Morigana and Fry. Image is taken from Ishii's paper.}
\label{fig:ishii_cal_result}
\end{figure}
%\begin{figure}[htb]
%\centering
%\includegraphics[width=.49\textwidth]{figs/ishii_cal_alpha}
%\includegraphics[width=.49\textwidth]{figs/ishii_cal_proton}
%\caption{Alpha spectrum (left) and proton spectrum (right) from Ishii's
%calculation~\cite{Ishii.1959} in comparison with experimental data from
%Morigana and Fry. Image is taken from Ishii's paper.}
%\label{fig:ishii_cal_result}
%\end{figure}
Singer~\cite{Singer.1974} noted that by assuming a reduced effective mass for
the nucleon, the average excitation energy will increase, but the proton
emission rate does not significantly improve and still could not explain the
the nucleon, the average excitation energy increases, but the proton
emission rate is not significantly improved and still could not explain the
large discrepancy. He concluded that the evaporation mechanism can account
for only a small fraction of emitted protons. Moreover, the high energy protons
of 25--50 \mega\electronvolt~cannot be explained by the evaporation mechanism.
of 25--50 \si{\MeV}~cannot be explained by the evaporation mechanism.
He and Lifshitz~\cite{LifshitzSinger.1978, LifshitzSinger.1980} proposed two
major corrections to Ishii's model:
\begin{enumerate}
@@ -611,23 +646,25 @@ major corrections to Ishii's model:
is possibility for particles to escape from the nucleus.
\end{enumerate}
With these improvements, the calculated proton spectrum agreed reasonably with
data from Morigana and Fry in the energy range $E_p \le 30$ \mega\electronvolt.
data from Morigana and Fry in the energy range $E_p \le 30$ \si{\MeV}.
Lifshitz and Singer noted the pre-equilibrium emission is more important for
heavy nuclei. Its contribution in light nuclei is about a few percent,
increasing to several tens of percent for $100<A<180$, then completely
dominating in very heavy nuclei. This trend is also seen in other nuclear
reactions at similar excitation energies. The pre-equilibrium emission also
dominates the higher-energy part, although it falls short at energies higher
than 30 \mega\electronvolt. The comparison between the calculated proton
than 30 \si{\MeV}. The comparison between the calculated proton
spectrum and experimental data is shown in
Fig.~\ref{fig:lifshitzsinger_cal_proton}.
\cref{fig:lifshitzsinger_cal_proton}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/lifshitzsinger_cal_proton}
\caption{Proton energy spectrum from muon capture in AgBr, the data in
histogram is from Morigana and Fry, calculation by Lifshitz and
Singer~\cite{LifshitzSinger.1978} showed contributions from the
pre-equilibrium emission and the equilibrium emission.}
pre-equilibrium emission and the equilibrium emission. Reprinted figure
from reference~\cite{LifshitzSinger.1978}. Copyright 1978 by the American
Physical Society.}
\label{fig:lifshitzsinger_cal_proton}
\end{figure}
@@ -641,36 +678,62 @@ proton emission rate $(\mu^-, \nu p)$ and the inclusive emission rate:
The deuteron emission channels are included to comparisons with activation
data where there is no distinguish between $(\mu^-, \nu pn)$ and $(\mu^-,d)$,
\ldots Their calculated emission rates together with available experimental
data is reproduced in Table~\ref{tab:lifshitzsinger_cal_proton_rate}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{c c c c c}
\toprule
Target nucleus & Calculation & Experiment & Estimate & Comments \\
%\textbf{Col1}\\
\midrule
$^{27}_{13}$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) & \\
%item1\\
\bottomrule
\end{tabular}
\end{center}
\caption{Calculated of the single proton emission rate and the inclusive
proton emission rate. The experimental data are mostly from Wyttenbach et
al.\cite{WyttenbachBaertschi.etal.1978}}
\label{tab:lifshitzsinger_cal_proton_rate}
\end{table}
A generally good agreement between calculation and experiment can be seen from
Table~\ref{tab:lifshitzsinger_cal_proton_rate}. The rate of $(\mu^-,\nu p)$
reactions for $^{28}\textrm{Al}$ and $^{39}\textrm{K}$ are found to be indeed
data is reproduced in \cref{tab:lifshitzsinger_cal_proton_rate} where
a generally good agreement between calculation and experiment can be seen from.
The rate of $(\mu^-,\nu p)$ reactions for $^{28}\textrm{Al}$ and
$^{39}\textrm{K}$ are found to be indeed
higher than average, though not as high as Vil'gel'mora et
al.~\cite{VilgelmovaEvseev.etal.1971} observed.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l S S[separate-uncertainty=true]
S S[separate-uncertainty=true] c}
\toprule
{Capturing} & {$(\mu,\nu p)$} & {$(\mu,\nu p)$}&
{$\Sigma(\mu,\nu p(xn))$}&
{$\Sigma(\mu,\nu p(xn))$} & {Est.}\\
{nucleus} & {calculation} & {experiment} & {calculation} & {experiment}
&{}\\
%nucleus & calculation & experiment & calculation & experiment \\
%\textbf{Col1}\\
\midrule
$^{27}_{13}$Al & 9.7 & {(4.7)} & 40 & {$> 28 $} &(70)\\
$^{28}_{14}$Si & 32 & 53 \pm 10 & 144 & 150 \pm 30 & \\
$^{31}_{15}$P & 6.7 & {(6.3)} & 35 & {$> 61$}&(91) \\
$^{39}_{19}$K & 19 & 32 \pm 6 & 67 & {} \\
$^{41}_{19}$K & 5.1 & {(4.7)} & 30 & {$> 28$} &(70)\\
$^{51 }_{23}$V &3.7 &2.9 \pm 0.4 &25 &{$>20 \pm 1.8$}& (32)\\
$^{55 }_{25}$Mn &2.4 &2.8 \pm 0.4 &16 &{$>26 \pm 2.5$}& (35)\\
$^{59 }_{27}$Co &3.3 &1.9 \pm 0.2 &21 &{$>37 \pm 3.4$}& (50)\\
$^{60 }_{28}$Ni &8.9 &21.4 \pm 2.3 &49 &40 \pm 5&\\
$^{63 }_{29}$Cu &4.0 &2.9 \pm 0.6 &25 &{$>17 \pm 3 $}& (36)\\
$^{65 }_{29}$Cu &1.2 &{(2.3)} &11 &{$>35 \pm 4.5$}& (36)\\
$^{75 }_{33}$As &1.5 &1.4 \pm 0.2 &14 &{$>14 \pm 1.3$}& (19)\\
$^{79 }_{35}$Br &2.7 &{} &22 & &\\
$^{107}_{47}$Ag &2.3 &{} &18 & &\\
$^{115}_{49}$In &0.63 &{(0.77)} &7.2 &{$>11 \pm 1$} &(12)\\
$^{133}_{55}$Cs &0.75 &0.48 \pm 0.07 &8.7 &{$>4.9 \pm 0.5$} &(6.7)\\
$^{165}_{67}$Ho &0.26 &0.30 \pm 0.04 &4.1 &{$>3.4 \pm 0.3$} &(4.6)\\
$^{181}_{73}$Ta &0.15 &0.26 \pm 0.04 &2.8 &{$>0.7 \pm 0.1$} &(3.0)\\
$^{208}_{82}$Pb &0.14 &0.13 \pm 0.02 &1.1 &{$>3.0 \pm 0.8$} &(4.1)\\
\bottomrule
\end{tabular}
\end{center}
\caption{Probabilities in units of \num{E-3} per muon capture for the
reaction $^A_Z X (\mu,\nu p) ^{A-1}_{Z-2}Y$ and for inclusive proton
emission compiled by Measday~\cite{Measday.2001}. The calculated values
are from Lifshitz and Singer. The experimental data are mostly from
Wyttenbach and colleagues~\cite{WyttenbachBaertschi.etal.1978}. The
inclusive emission the experimental figures are lower limits because only
a few decay channels could be studied. The figures in crescent parentheses
are estimates for the total inclusive rate derived from the measured
exclusive channels by the use of ratio in \eqref{eqn:wyttenbach_ratio}.}
\label{tab:lifshitzsinger_cal_proton_rate}
\end{table}
For protons with higher energies in the range of
40--90 \mega\electronvolt~observed in the emulsion data as well as in later
40--90 \si{\MeV}~observed in the emulsion data as well as in later
experiments~\cite{BudyashovZinov.etal.1971,BalandinGrebenyuk.etal.1978,
KraneSharma.etal.1979}, Lifshitz and Singer~\cite{LifshitzSinger.1988}
suggested another contribution from capturing on correlated two-nucleon
@@ -682,12 +745,12 @@ and it had been shown that the meson exchange current increases the total
capture rate in deuterons by 6\%. The result of this model was a mix, it
accounted well for Si, Mg and Pb data, but predicted rates about 4 times
smaller in cases of Al and Cu, and about 10 times higher in case of AgBr
(Table~\ref{tab:lifshitzsinger_cal_proton_rate_1988}).
\begin{table}[htb]
(\cref{tab:lifshitzsinger_cal_proton_rate_1988}).
\begin{table}[!ht]
\begin{center}
\begin{tabular}{l l c}
\toprule
\textbf{Nucleus} & \textbf{Exp.$\times 10^3$} & \textbf{MEC cal.$\times
\textbf{Nucleus} & \textbf{Experiment$\times 10^3$} & \textbf{Calculation$\times
10^3$}\\
\midrule
Al & $1.38 \pm 0.09$ & 0.3\\
@@ -699,28 +762,30 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr
\bottomrule
\end{tabular}
\end{center}
\caption{Probability of proton emission with $E_p \ge 40$
\mega\electronvolt~as calculated by Lifshitz and
Singer~\cite{LifshitzSinger.1988} in comparison with available data.}
\caption{Probability of proton emission with $E_p \ge \SI{40}{\MeV}$
calculated by Lifshitz and
Singer~\cite{LifshitzSinger.1988} with the two-nucleon capture hypothesis
in comparison with available data.}
\label{tab:lifshitzsinger_cal_proton_rate_1988}
\end{table}
% subsection theoretical_models (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Summary on proton emission from aluminium}
\label{sub:summary_on_proton_emission_from_aluminium}
%%TODO equations, products as in Sobottkas'
There is no direct measurement of proton emission following
muon capture in the relevant energy for the COMET Phase-I of 2.5--10
\mega\electronvolt:
\si{\MeV}:
\begin{enumerate}
\item Spectrum wise, only one energy spectrum (Figure~\ref{fig:krane_proton_spec})
for energies above 40 \mega\electronvolt~is available from Krane et
\item Spectrum wise, only one energy spectrum (\cref{fig:krane_proton_spec})
for energies above 40 \si{\MeV}~is available from Krane et
al.~\cite{KraneSharma.etal.1979},
where an exponential decay shape with a decay constant of
$7.5 \pm 0.4$~\mega\electronvolt. At low energy range, the best one can get is
$7.5 \pm 0.4$~\si{\MeV}. At low energy range, the best one can get is
the charged particle spectrum, which includes protons, deuterons and alphas,
from the neighbouring element silicon (Figure~\ref{fig:sobottka_spec}).
This charged particle spectrum peaks around 2.5 \mega\electronvolt~and
reduces exponentially with a decay constant of 4.6 \mega\electronvolt.
from the neighbouring element silicon (\cref{fig:sobottka_spec}).
This charged particle spectrum peaks around 2.5 \si{\MeV}~and
reduces exponentially with a decay constant of 4.6 \si{\MeV}.
\item The activation data from Wyttenbach et
al.~\cite{WyttenbachBaertschi.etal.1978} only gives rate of
$^{27}\textrm{Al}(\mu^-,\nu pn)^{25}\textrm{Na}$ reaction, and set a lower
@@ -748,25 +813,25 @@ A spectrum shape at this energy range is not available.
\label{sub:motivation_of_the_alcap_experiment}
As mentioned, protons from muon capture on aluminium might cause a very high
rate in the COMET Phase-I CDC. The detector is designed to accept particles
with momenta in the range of 75--120 \mega\electronvolt\per\cc.
Figure~\ref{fig:proton_impact_CDC} shows that protons with kinetic energies of
2.5--8 \mega\electronvolt~will hit the CDC. Such events are troublesome due to
their large energy deposition. Deuterons and alphas at that momentum range is
not of concern because they have lower kinetic energy and higher stopping
power, thus are harder to escape the muon stopping target.
with momenta in the range of \SIrange{75}{120}{\MeV\per\cc}.
\cref{fig:proton_impact_CDC} shows that protons with kinetic energies larger
than \SI{2.5}{\MeV} could hit the CDC. Such events are troublesome due to
their large energy deposition. Deuterons and alphas at the same momentum are
not of concern because they have lower kinetic energy compared with protons and
higher stopping power, thus are harder to escape the muon stopping target.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/proton_impact_CDC}
\caption{Momentum-kinetic energy relation of protons, deuterons and alphas
below 10\mega\electronvolt. Shaded area is the acceptance of the COMET
Phase-I's CDC. Protons with energies in the range of 2.5--8
\mega\electronvolt~are in the acceptance of the CDC. Deuterons and alphas at
low energies should be stopped inside the muon stopping target.}
\includegraphics[width=0.85\textwidth]{figs/alcap_proton_vs_acceptance}
\caption{Momentum - kinetic energy relation of protons, deuterons and alphas
at low energy region below 20\si{\MeV}. Charged particles in the shaded
area could reach the COMET Phase-I's CDC, for protons that corresponds
kinetic energies higher than \SI{2.5}{\MeV}. Deuterons and alphas at low
energies should be stopped inside the muon stopping target.}
\label{fig:proton_impact_CDC}
\end{figure}
The COMET plans to introduce a thin, low-$Z$ proton absorber in between the
target and the CDC to produce proton hit rate. The absorber will be effective
target and the CDC to reduce proton hit rate. The absorber will be effective
in removing low energy protons. The high energy protons that are moderated by
the absorber will fall into the acceptance range of the CDC, but because of the
exponential decay shape of the proton spectrum, the hit rate caused by these
@@ -774,12 +839,11 @@ protons should be affordable.
The proton absorber solves the problem of hit rate, but it degrades the
reconstructed momentum resolution. Therefore its thickness and geometry should
be carefully designed. The limited information available makes it difficult to
be carefully optimised. The limited information available makes it difficult to
arrive at a conclusive detector design. The proton emission rate could be 4\%
as calculated by Lifshitz and Singer~\cite{LifshitzSinger.1980}; or 7\% as
estimated from the $(\mu^-,\nu pn)$ activation data and the ratio
\eqref{eqn:wyttenbach_ratio}~\cite{WyttenbachBaertschi.etal.1978}; or as high
as 15-20\% from silicon and neon.
estimated from the $(\mu^-,\nu pn)$ activation data and the ratio in
\eqref{eqn:wyttenbach_ratio}; or as high as 15-20\% from silicon and neon.
For the moment, design decisions in the COMET Phase-I are made based on
conservative assumptions: emission rate of 15\% and an exponential decay shape
@@ -787,58 +851,60 @@ are adopted follow the silicon data from Sobottka and Will
~\cite{SobottkaWills.1968}. The spectrum shape is fitted with an empirical
function given by:
\begin{equation}
p(T) = A\left(1-\frac{T_{th}}{T}\right)^\alpha e^{-(T/T_0)},
p(T) = A\left(1-\frac{T_{th}}{T}\right)^\alpha
\exp{\left(-\frac{T}{T_0}\right)},
\label{eqn:EH_pdf}
\end{equation}
where $T$ is the kinetic energy of the proton, and the fitted parameters are
$A=0.105\textrm{ MeV}^{-1}$, $T_{th} = 1.4\textrm{ MeV}$, $\alpha = 1.328$ and
$T_0 = 3.1\textrm{ MeV}$. The baseline
design of the absorber is 1.0 \milli\meter~thick
carbon-fibre-reinforced-polymer (CFRP) which contributes
195~\kilo\electronvolt\per\cc~to the momentum resolution. The absorber also
down shifts the conversion peak by 0.7 \mega\electronvolt. This is an issue as
it pushes the signal closer to the DIO background region. For those reasons,
a measurement of the rate and spectrum of proton emission after muon capture is
required in order to optimise the CDC design.
where $T$ is the kinetic energy of the proton in \si{\MeV}, and the fitted
parameters are $A=0.105\textrm{ MeV}^{-1}$, $T_{th} = 1.4\textrm{ MeV}$,
$\alpha = 1.328$ and $T_0 = 3.1\textrm{ MeV}$. The function rises from the
cut-off value of $T_{th}$, its rising edge is governed by the parameter
$\alpha$. The exponential decay component dominates at higher energy.
The baseline design of the proton absorber for the COMET Phase-I based on
above assumptions is a 0.5-\si{\mm}-thick CFRP layer as has been described in
\cref{ssub:hit_rate_on_the_cdc}. The hit rate estimation is
conservative and the contribution of the absorber to the momentum resolution
is not negligible, further optimisation is desirable. Therefore a measurement
of the rate and spectrum of proton emission after muon capture is required.
% subsection motivation_of_the_alcap_experiment (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Experimental method for proton measurement}
\label{sub:experimental_method}
We planned to use a low energy, narrow momentum spread available at PSI to
We planned to use a low-energy, narrow-momentum-spread available at PSI to
fight the aforementioned difficulties in measuring protons. The beam momentum
is tunable from 28 to 45~\mega\electronvolt\ so that targets at different
thickness from 25 to 100 \micro\meter\ can be studied. The $\pi$E1 beam line
could provide about \sn{}{3} muons\per\second\ at 1\% momentum spread, and
\sn{}{4} muons\per\second\ at 3\% momentum spread. With this tunable beam, the
stopping distribution of the muons is well-defined.
is tunable from \SIrange{28}{45}{\MeV} so that targets at different
thickness from \SIrange{25}{100}{\um} can be studied. The $\pi$E1 beam line
could deliver \sn{}{3} muons/\si{\s} at 1\% momentum spread, and
\sn{}{4} muons/\si{\s} at 3\% momentum spread. The muon stopping distribution
of the muons could be well-tuned using this excellent beam.
The principle of the particle identification used in the AlCap experiment is
that for each species, the function describes the relationship between energy
loss per unit length (dE/dx) and the particle energy E is uniquely defined.
With a simple system of two detectors, dE/dx can be obtained by
measuring energy deposit $\Delta$E in one detector of known thickness
$\Delta$x, and E is the sum of energy deposit in both detector if the particle
is fully stopped.
In the AlCap, we realise the idea with a pair of silicon detectors: one thin
detector of 65~\micron\ serves as the $\Delta$E counter, and one thick detector
of 1500~\micron\ that can fully stop protons up to about 12~MeV. Since the
$\Delta \textrm{d}=65$~\micron\ is known, the function relates dE/dx to
E reduces to a function between $\Delta$E and E. Figure~\ref{fig:pid_sim} shows
that the function of protons can be clearly distinguished from other charged
particles in the energy range of interest.
Emitting charged particles from nuclear muon capture will be identified by the
specific energy loss.
%The specific energy loss is calculated as energy loss
%per unit path length \sdEdx at a certain energy $E$. The quantity is uniquely
%defined for each particle species.
Experimentally, the specific energy loss is measured in the AlCap using a pair
of silicon detectors: a \SI{65}{\um}-thick detector, and a \SI{1500}{\um}-thick
detector. Each detector is $5\times5$ \si{\cm^2} in area.
The thinner one provides $\mathop{dE}$ information, while the sum energy
deposition in the two gives $E$, if the particle is fully stopped. The silicon
detectors pair could help distinguish protons from other charged particles from
\SIrange{2.5}{12}{\MeV} as shown in \cref{fig:pid_sim}.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.75\textwidth]{figs/pid_sim}
\caption{Simulation study of PID using a pair of silicon detectors}
\caption{Simulation study of PID using a pair of silicon detectors. The
detector resolutions follow the calibration results provided by the
manufacturer.}
\label{fig:pid_sim}
\end{figure}
The AlCap uses two pairs of detector with large area, placed symmetrically with
respect to the target provide a mean to check for muon stopping distribution.
The absolute number of stopped muons are inferred
Two pairs of detectors, placed symmetrically with
respect to the target, provide a mean to check for muon stopping distribution
inside the target. The absolute number of stopped muons is calculated
from the number of muonic X-rays recorded by a germanium detector. For
aluminium, the $(2p-1s)$ line is at 346 \kilo\electronvolt. The acceptances of
aluminium, the $(2p-1s)$ line is at \SI{346.828}{\keV}. The acceptances of
detectors will be assessed by detailed Monte Carlo study using Geant4.
% subsection experimental_method (end)
@@ -846,50 +912,63 @@ detectors will be assessed by detailed Monte Carlo study using Geant4.
\subsection{Goals and plan of the experiment}
\label{sub:goals_of_the_experiment}
Our experimental program is organised in three distinct work packages (WP),
The goal of the experiment is measure protons following nuclear muon capture
on aluminium:
\begin{enumerate}
\item emission rate,
\item and spectrum shape in the lower energy region down to \SI{2.5}{\MeV},
\item with a precision of about 5\%.
\end{enumerate}
The measured proton spectrum and rate will be used to assess the hit rate on
the tracking drift chamber of the COMET Phase-I.
The measurement of protons itself is part of the AlCap, where
experimental program is organised in three distinct work packages (WP),
directed by different team leaders, given in parentheses.
\begin{itemize}
\item[WP1:] (Kammel (Seattle), Kuno(Osaka)) \textbf{Charged
Particle Emission after Muon Capture.}\\ Protons emitted after nuclear muon
capture in the stopping target dominate the single-hit rates in the tracking
chambers for both the Mu2e and COMET Phase-I experiments. We plan to measure
both the total rate and the energy spectrum to a precision of 5\% down to
proton energies of 2.5 MeV.
\item[WP2:] (Lynn(PNNL), Miller(BU))
\textbf{Gamma and X-ray Emission after Muon Capture.}\\ A Ge detector will
be used to measure X-rays from the muonic atomic cascade, in order to provide
the muon-capture normalization for WP1, and is essential for very thin
stopping targets. It is also the primary method proposed for calibrating the
number of muon stops in the Mu2e and COMET experiments. Two additional
calibration techniques will also be explored; (1) detection of delayed gamma
rays from nuclei activated during nuclear muon capture, and (2) measurement
of the rate of photons produced in radiative muon decay. The first of these
would use a Ge detector and the second a NaI detector. The NaI
calorimeter will measure the rate of high energy photons from radiative muon
capture (RMC), electrons from muon decays in orbit (DIO), and photons from
radiative muon decay (RMD), as potential background sources for the
conversion measurement. As these rates are expected to be extremely low near
the conversion electron energy, only data at energies well below 100 MeV will
be obtained.
\item[WP3:] (Hungerford(UH), Winter(ANL)) \textbf{Neutron
Emission after Muon Capture.}\\ Neutron rates and spectra after capture in
Al and Ti are not well known. In particular, the low energy region below 10
MeV is important for determining backgrounds in the Mu2e/COMET detectors and
veto counters as well as evaluating the radiation damage to electronic
components. Carefully calibrated liquid scintillation detectors, employing
neutron-gamma discrimination and spectrum unfolding techniques, will measure
these spectra. The measurement will attempt to obtain spectra as low or lower
than 1 MeV up to 10 MeV. \\
\item[WP1:] (P. Kammel (University of Washington), Y. Kuno(Osaka University))
\textbf{Charged Particle Emission after Muon Capture.}\\ Protons emitted
after nuclear muon
capture in the stopping target dominate the single-hit rates in the tracking
chambers for both the Mu2e and COMET Phase-I experiments. We plan to measure
both the total rate and the energy spectrum to a precision of 5\% down to
proton energies of \SI{2.5}{\MeV}.
\item[WP2:] (J. Miller(Boston University))
\textbf{Gamma and X-ray Emission after Muon Capture.}\\ A germanium detector
will be used to measure X-rays from the muonic atomic cascade, in order to
provide
the muon-capture normalisation for WP1, and is essential for very thin
stopping targets. It is also the primary method proposed for calibrating the
number of muon stops in the Mu2e and COMET experiments. Two additional
calibration techniques will also be explored; (1) detection of delayed gamma
rays from nuclei activated during nuclear muon capture, and (2) measurement
of the rate of photons produced in radiative muon decay. The first of these
would use a germanium detector and the second a sodium iodine detector.
The sodium iodine
calorimeter will measure the rate of high energy photons from radiative muon
capture (RMC), electrons from muon decays in orbit (DIO), and photons from
radiative muon decay (RMD), as potential background sources for the
conversion measurement. As these rates are expected to be extremely low near
the conversion electron energy, only data at energies well below 100 MeV will
be obtained.
\item[WP3:] (E. Hungerford (University of Houston), P. Winter(Argonne
National Laboratory)) \textbf{Neutron
Emission after Muon Capture.}\\ Neutron rates and spectra after capture in
Al and Ti are not well known. In particular, the low energy region below 10
MeV is important for determining backgrounds in the Mu2e/COMET detectors and
veto counters as well as evaluating the radiation damage to electronic
components. Carefully calibrated liquid scintillation detectors, employing
neutron-gamma discrimination and spectrum unfolding techniques, will measure
these spectra. The measurement will attempt to obtain spectra as low or lower
than 1 MeV up to 10 MeV. \\
\end{itemize}
WP1 is the most developed
project in this program. Most of the associated apparatus has been built and
optimized. We are ready to start this experiment in 2013, while preparing and
completing test measurements and simulations to undertake WP2 and WP3.
WP1 was the most developed project in this program with most of the associated
apparatus had been built and optimised. Therefore the measurement of proton has
been carried out in November and December 2013, while preparing and completing
test measurements and simulations to undertake WP2 and WP3.
The measurement of proton has been carried out in November and December 2013,
the details are described in following chapters.
% subsection goals_of_the_experiment (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% section the_alcap_experiment (end)

746
thesis/chapters/chap5_alcap_setup.tex
View File

@@ -2,96 +2,105 @@
\label{cha:the_alcap_run_2013}
\thispagestyle{empty}
The first run of the AlCap experiment was performed at the $\pi$E1 beam line
area, PSI (Figure~\ref{fig:psi_exp_hall_all}) from November 26 to December 23,
2013. The goal of the run was to measure protons rate and spectrum following
muon capture on aluminium.
\begin{figure}[p]
\centering
\includegraphics[height=0.85\textheight]{figs/psi_exp_hall_all}
\caption{Layout of the PSI experimental hall, $\pi$E1 experimental area is
marked with the red circle. \\Image taken from
\url{http://www.psi.ch/num/FacilitiesEN/HallenplanPSI.png}}
\label{fig:psi_exp_hall_all}
\end{figure}
area, PSI from November 26 to December 23, 2013. The goal of the run was to
measure protons rate and their spectrum following muon capture on aluminium.
\section{Experimental set up}
\label{sec:experimental_set_up}
The low energy muons from the $\pi$E1 beam line were stopped in thin aluminium
and silicon targets, and charged particles emitted were measured by two pairs
of silicon detectors inside of a vacuum vessel
(Figure~\ref{fig:alcap_setup_detailed}). A stopped muon event is defined by
(\cref{fig:alcap_setup_detailed}). A stopped muon event is defined by
a group of upstream detectors and a muon veto plastic scintillator.
The number of stopped muons is monitored by a germanium detector placed outside
of the vacuum chamber. In addition, several plastic scintillators were used to
provide veto signals for the silicon and germanium detectors. Two liquid
scintillators for neutron measurements were also tested in this run.
\begin{figure}[htbp]
\begin{figure}[btp]
\centering
\includegraphics[width=0.65\textwidth]{figs/alcap_setup_detailed}
\includegraphics[width=0.95\textwidth]{figs/alcap_setup_detailed}
\caption{AlCap detectors: two silicon packages inside the vacuum vessel,
muon beam detectors including plastic scintillators and a wire chamber,
germanium detector and veto plastic scintillators.}
\label{fig:alcap_setup_detailed}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Muon beam and vacuum chamber}
Muons in the $\pi$E1 beam line are decay products of pions created
as a 590~\mega\electronvolt\ proton beam hit a thick carbon target
(E-target in Figure~\ref{fig:psi_exp_hall_all}). The beam line was designed to
deliver muons with momenta ranging from 10 to 500~\mega\electronvolt\per\cc\
and
momentum spread from 0.26 to 8.0\%. These parameters can be selected by
changing various magnets and slits shown in
Figure~\ref{fig:psi_piE1_elements}~\cite{Foroughli.1997}.
as a \SI{590}{\mega\electronvolt} proton beam hits a thick carbon target. The
beam line was designed to deliver muons with momenta ranging from
\SIrange{10}{500}{\mega\electronvolt\per\cc} and momentum spread from
\SIrange{0.26}{8.0}{\percent}~\cite{Foroughli.1997}. The beam parameters can
be tuned by adjusting magnets and slits along the beam line.
%These parameters can be
%selected by changing various magnets and slits
%\cref{fig:psi_piE1_elements}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.7\textwidth]{figs/psi_piE1_elements}
\caption{The $\pi$E1 beam line}
\label{fig:psi_piE1_elements}
\end{figure}
%(E-target in \cref{fig:psi_exp_hall_all}).
%\begin{figure}[p]
%\centering
%\includegraphics[height=0.85\textheight]{figs/psi_exp_hall_all}
%\caption{Layout of the PSI experimental hall, $\pi$E1 experimental area is
%marked with the red circle. \\Image taken from
%\url{http://www.psi.ch/num/FacilitiesEN/HallenplanPSI.png}}
%\label{fig:psi_exp_hall_all}
%\end{figure}
%\begin{figure}[btp]
%\centering
%\includegraphics[width=0.7\textwidth]{figs/psi_piE1_elements}
%\caption{The $\pi$E1 beam line}
%\label{fig:psi_piE1_elements}
%\end{figure}
One of the main requirements of the AlCap experiment was a low energy muon beam
with narrow momentum bite in order to achieve a high fraction of stopping muons
in the very thin targets. In this Run 2013, muons from 28 to
45~\mega\electronvolt\per\cc\ and momentum spread of 1\% and 3\%were used.
in the very thin targets. In this Run 2013, muons from
\SIrange{28}{45}{\MeV\per\cc} and momentum spread of 1\% and
3\% were used.
For part of the experiment the target was replaced with one of the silicon
detector packages allowed an accurate momentum and range calibration
%(via range-energy relations)
of the beam at the target. Figure~\ref{fig:Rates} shows the measured muon rates
of the beam at the target. \Cref{fig:Rates} shows the measured muon rates
as a function of momentum for two different momentum bites.
Figure~\ref{fig:Beam} shows an example of the resulting energy spectra.
\begin{figure}[htbp]
\Cref{fig:Beam} shows an example of the resulting energy spectra recorded by
our silicon detector.
\begin{figure}[btp]
\centering
\includegraphics[width=0.6\textwidth]{figs/Rates.png}
\caption{Measured muon rate (kHz) at low momenta. Momentum bite of 3 and 1 \%
FWHM, respectively.}
\includegraphics[width=0.65\textwidth]{figs/Rates.png}
\caption{Measured muon rates at low momenta during the Run 2013. Beam rates
at 1 \% FWHM momentum bite were about 3 times smaller than the rates at
3 \% FWHM.}
\label{fig:Rates}
\end{figure}
\begin{figure}[htbp]
\begin{figure}[btp]
\centering
\includegraphics[width=0.9\textwidth]{figs/beam.pdf}
\caption{Energy deposition at 36.4 MeV/c incident muon beam in an
1500-\micron-active
target. The peak at low energy is due to beam electrons, the
peaks at higher energies are due to muons. Momentum bite of 1 and 3\% FWHM
on left and right hand side, respectively.} \label{fig:Beam}
\includegraphics[width=1.00\textwidth]{figs/beam.pdf}
\caption{Energy deposition at \SI{36.4}{/c} incident muon beam in an
\SI{1500}{\micro\meter}-thick active target. The peak at low energy is due
to beam electrons, the peaks at higher energies are due to muons. Momentum
bite of 1 and 3\% FWHM on left and right hand side, respectively. The
electron peak are the same in both plots as beam electrons are minimum
ionisation particles and passed though the detector easily. The muon peak
at the 3 \% FWHM momentum bite is notably broader than that at 1 \% FWHM
setting.}
\label{fig:Beam}
\end{figure}
The targets and charged particle detectors are installed inside the vacuum
chamber as shown in Figure~\ref{fig:alcap_setup_detailed}. The muon beam enters
from the right of the image and hits the target, which is placed at the
centre of the vacuum chamber and orientated at 45 degrees to the beam axis.
chamber as shown in \cref{fig:alcap_setup_detailed}. The muon beam enters
from the right of \cref{fig:alcap_setup_detailed} and hits the target, which is
placed at the centre of the vacuum chamber and orientated at 45 degrees to the
beam axis.
The side walls and bottom flange of the vessel provide several
vacuum-feedthroughs for the high voltage and signal cables for the silicon and
scintillator detectors inside the chamber.
In addition, the chamber is equipped with several lead collimators
%so that muons that are not captured in the target would quickly decay.
to quickly capture muons that do not stop in the actual target.
%\begin{figure}[htbp]
%\begin{figure}[btp]
%\centering
%\includegraphics[width=0.55\textwidth]{figs/SetupOverview.jpg}
%\caption{Vacuum chamber in beam line}
@@ -102,22 +111,25 @@ to quickly capture muons that do not stop in the actual target.
%a silicon detector in the low vacuum region of $10^{-3}$ mbar.
%An interlock mechanism was installed to prevent the bias of the
%silicon detectors from being applied before the safe vacuum level.
For a safe operation of the silicon detector, a vacuum of $<10^{-4}$\,mbar was
necessary. With the help of the vacuum group of PSI, we could consistently
reach $10^{-4}$\,mbar within 45 minutes after closure of the chamber's top
flange.
For a safe operation of the silicon detector, a vacuum of \SI{e-4}{\milli\bar}
was necessary. With the help of the vacuum group of PSI, we could consistently
reach the required vacuum level within 45 minutes after closure of the
chamber's top flange.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Silicon detectors}
The main detectors for proton measurement in the Run 2013 were four large area
silicon detectors. The silicon detectors were grouped into two detector
packages located symmetrically at 90 degrees of the nominal muon beam path, SiL
and SiR in Figure~\ref{fig:alcap_setup_detailed}. Each arm consists of: one
$\Delta$E counter, a 65-\micro\meter-thick silicon detector, divided into
4 quadrants; one E counter made from 1500-\micron-thick silicon; and one
plastic scintillator to identify electrons or high energy protons that pass
through the silicon. The area of each of these silicon detectors and the
scintillators is $50\times50 \textrm{mm}^2$.
and SiR in \cref{fig:alcap_setup_detailed}. Each arm consists of: one
$\Delta$E counter, a \SI{65}{\micro\meter}-thick silicon detector, divided into
4 quadrants; one E counter made from \SI{1500}{\micro\meter}-thick silicon; and
one plastic scintillator to identify electrons or high energy protons that
pass through the silicon. The area of each of these silicon detectors and the
scintillators is $50\times50 \textrm{mm}^2$. There is a dead layer of
\SI{0.5}{\micro\meter} on each side of the silicon detectors according to the
manufacturer Micron Semiconductor
\footnote{\url{http://www.micronsemiconductor.co.uk/}}.
The detectors were named according to their positions relative to the muon
view: the SiL package contains the thin
@@ -129,11 +141,11 @@ SiR1-4.
Bias for the four silicon detectors was supplied by an ORTEC 710 NIM module,
which has a vacuum interlock input to prevent biasing before the safe vacuum
level has been reached. Typical voltage to fully depleted the detectors were
-300~\volt\ and -10~\volt\ for the thick and thin silicon detectors
\SI{-300}{\volt} and \SI{-10}{\volt} for the thick and thin silicon detectors
respectively. The leakage currents at the operating voltages are less than
1.5~\micro\ampere\ for the thick detectors, and about 0.05~\micro\ampere\
for the thin ones (see Figure~\ref{fig:si_leakage}).
\begin{figure}[htb]
\SI{1.5}{\micro\ampere} for the thick detectors, and about
\SI{0.05}{\micro\ampere} for the thin ones (see \cref{fig:si_leakage}).
\begin{figure}[btp]
\centering
\includegraphics[width=0.85\textwidth]{figs/si_leakage}
\caption{Leakage currents of the silicon detectors under bias.}
@@ -146,8 +158,8 @@ output
pulse height on an oscilloscope. One would expect that the maximum pulse height
increases as the bias is raised until the voltage of fully depleted. The effect
can also be seen on the pulse height spectrum as in
Figure~\ref{fig:sir2_bias_alpha}.
\begin{figure}[htb]
\cref{fig:sir2_bias_alpha}.
\begin{figure}[btp]
\centering
\includegraphics[width=0.75\textwidth]{figs/sir2_bias_alpha}
\caption{$^{241}\textrm{Am}$ spectra in cases of fully depleted (top), and
@@ -195,15 +207,15 @@ Figure~\ref{fig:sir2_bias_alpha}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Upstream counters}
\label{sub:upstream_counters}
The upstream detector consists of three counters: a 500~$\mu$m thick
scintillator muon trigger counter ($\mu$SC); a muon anti-coincidence counter
($\mu$SCA) surrounding the trigger counter with a hole
of 35 \milli\meter\ in diameter to define the beam radius; and a multi-wire
proportional chamber ($\mu$PC) that uses 24 X wires and 24 Y wires at
2~\milli\meter~intervals.
The upstream detector consists of three counters: a \SI{500}{\micro\meter}-thick
scintillator muon trigger counter (\Pmu{}SC); a muon anti-coincidence counter
(\Pmu{}SCA) surrounding the trigger counter with a hole
of 35 \si{\milli\meter}\ in diameter to define the beam radius; and a multi-wire
proportional chamber (\Pmu{}PC) that uses 24 X wires and 24 Y wires at
2~\si{\milli\meter}~intervals.
The upstream detectors provide signal of an incoming muon as coincident hits on
the muon trigger and the wire chamber in anti-coincident with the muon
the muon trigger and the wire chamber in anti-coincidence with the muon
anti-coincidence counter.
This set of detectors along with their read-out system
belong to the MuSun experiment, which operated at the same beam line just
@@ -214,7 +226,7 @@ ready to be used in our run without any modification.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Germanium detector}
%\begin{figure}[htbp]
%\begin{figure}[btp]
%\centering
%\includegraphics[width=0.9\textwidth]{figs/neutron.png}
%\caption{Setup of two
@@ -225,9 +237,9 @@ We used a germanium detector to normalise the number of stopped muons by
measuring characteristics muon X-rays from the target material. The primary
X-rays of interest are the 346.828~keV line for aluminium targets, and the
400.177 line for silicon targets. The energies and intensities of the X-rays
listed in Table~\ref{tab:xray_ref} follow measurement results from
listed in \cref{tab:xray_ref} follow measurement results from
Measday and colleagues~\cite{MeasdayStocki.etal.2007}.
\begin{table}[htb]
\begin{table}[btp]
\begin{center}
\begin{tabular}{c l l l l }
\toprule
@@ -250,19 +262,25 @@ The germanium detector is
a GMX20P4-70-RB-B-PL, n-type, coaxial high purity germanium detector produced
by ORTEC. The detector was optimised for low energy gamma and X-rays
measurement with an ultra-thin entrance window of 0.5-mm-thick beryllium and
a 0.3-\micron-thick ion implanted contact (Figure~\ref{fig:ge_det_dimensions}).
This detector is equipped with a transistor reset preamplifier which,
according to the producer, enables it to work in an ultra-high rate environment
up to $10^6$ counts\per\second~ at 1~\mega\electronvolt.
\begin{figure}[htb]
\centering
\includegraphics[width=0.9\textwidth]{figs/ge_det_dimensions}
\caption{Dimensions of the germanium detector}
\label{fig:ge_det_dimensions}
\end{figure}
a 0.3-\si{\micro\meter}-thick ion implanted contact. The germanium crystal is
\SI{52.5}{\mm} in diameter, and \SI{55.3}{\mm} in length. The axial well has
a diameter of \SI{9.9}{\mm} and \SI{47.8}{\mm} deep.
%(\cref{fig:ge_det_dimensions}).
ORTEC quoted the energy resolution of the detector is \SI{1.90}{\keV} at the
\SI{1.73}{\MeV} gamma line. The detector is equipped with a transistor reset
preamplifier which, according to the producer, enables it to work in an
ultra-high rate environment
up to $10^6$ counts\si{\per\second} at \SI{1}{\mega\electronvolt}.
%\begin{figure}[btp]
%\centering
%\includegraphics[width=0.9\textwidth]{figs/ge_det_dimensions}
%\caption{Dimensions of the germanium detector}
%\label{fig:ge_det_dimensions}
%\end{figure}
The detector was installed outside of the vacuum chamber at 32 cm from the
target, seeing the target through a 10-mm-thick aluminium window, behind
target, viewing the target through a 10-mm-thick aluminium window, behind
a plastic scintillator counter used to veto electrons. Liquid nitrogen
necessary for the operation of the detector had to be refilled every 8 hours.
A timer was set up in the data acquisition system to remind this.
@@ -285,15 +303,16 @@ carried out.
% subsection plastic_scintillators (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Front-end electronics and data acquisition system}
The front-end electronics of the AlCap experiment was simple since we employed
a trigger-less read out system with waveform digitisers and flash ADCs
(FADCs). As shown in Figure~\ref{fig:alcapdaq_scheme}, all plastic
(FADCs). As shown in \cref{fig:alcapdaq_scheme}, all plastic
scintillators signals were amplified by PMTs, then fed into the digitisers. The
signals from silicon and germanium detectors were preamplified, and
subsequently shaped by spectroscopy amplifiers and timing filter amplifiers
(TFAs) to provide energy and timing information.
\begin{figure}[htbp]
\begin{figure}[btp]
\centering
\includegraphics[width=0.99\textwidth]{figs/alcapdaq_scheme}
\caption{Schematic diagram of the electronics and DAQ used in the Run 2013}
@@ -304,34 +323,34 @@ The germanium detector has its own transistor reset preamplifier
installed very close to the germanium crystal. Two ORTEC Model 142
preamplifiers were used for the thick silicon detectors. The timing outputs of
the preamplifiers were fed into three ORTEC Model 579 TFAs.
We used an ORTEC Model 673 to shape the germanium signal with 6~\micro\second
We used an ORTEC Model 673 to shape the germanium signal with 6~\si{\micro\second}
shaping time.
A more modern-style electronics was used for thin silicon detectors where the
preamplifier, shaping and timing amplifiers were implemented on one compact
package, namely a Mesytec MSI-8 box. This box has 8 channels, each channel
consists of one preamplifier board and one shaper-and-timing filter board which
can be fine-tuned independently. The shaping time was set to 1~\micro\second\
can be fine-tuned independently. The shaping time was set to 1~\si{\micro\second}\
for all channels.
The detector system produced signals that differs significantly in time scale,
ranging from very fast (about 40~\nano\second\ from scintillators) to very slow
(several \micro\second\ from shaping outputs of semiconductor detectors). This
lead to the use of several sampling frequencies from 17~\mega\hertz\ to
250~\mega\hertz, and three types of digitisers were employed:
ranging from very fast (about 40~\si{\nano\second}\ from scintillators) to very slow
(several \si{\micro\second}\ from shaping outputs of semiconductor detectors). This
lead to the use of several sampling frequencies from 17~\si{\mega\hertz}\ to
250~\si{\mega\hertz}, and three types of digitisers were employed:
\begin{itemize}
\item custom-built 12-bit 170-MHz FADCs which was designed for the
MuCap experiment. Each FADC board has dimensions the same as those of
MuCap experiment. Each FADC board has the same dimensions as those of
a single-width 6U VME module, but is hosted in a custom built crate due to
its different power supply mechanical structure. The FADC communicates with
a host computer through a 100-Mb/s Ethernet interface using a simple
Ethernet-level protocol. The protocol only allows detecting
incomplete data transfers but no retransmitting is possible due to the
limited size of the module's output buffer. The FADCs accept clock signal
at the frequency of 50~\mega\hertz\ then multiply that internally up to
170~\mega\hertz. Each channel on one board can run at different sampling
at the frequency of 50~\si{\mega\hertz}\ then multiply that internally up to
170~\si{\mega\hertz}. Each channel on one board can run at different sampling
frequency not dependent on other channels. The FADC has 8 single-ended
LEMO inputs with 1~\volt pp dynamic range.
LEMO inputs with 1~\si{\volt} pp dynamic range.
\item a 14-bit 100-MS/s CAEN VME FADC waveform digitiser model V1724. The
module houses 8 channels with 2.25~Vpp dynamic range on single-ended MCX
coaxial inputs. The digitiser features an optical link for transmission of
@@ -347,7 +366,7 @@ lead to the use of several sampling frequencies from 17~\mega\hertz\ to
proprietary binary drivers and libraries.
\end{itemize}
All digitisers were driven by external clocks which were derived from the same
500-\mega\hertz\ master clock, a high precision RF signal generator Model SG382
500-\si{\mega\hertz}\ master clock, a high precision RF signal generator Model SG382
of Stanford Research System.
The silicon detectors were read out by FADC boards feature network-based data
@@ -355,14 +374,14 @@ readout interface. To maximize the data throughput, each of the four FADC
boards was read out through separate network adapter.
The CAEN digitisers were used to read out
the germanium detector (timing and energy, slow signals) or scintillator
detectors (fast signals). For redundancy, all beam monitors ($\mu$SC, $\mu$SCA
and $\mu$PC) were also read out by a CAEN time-to-digital converter (TDC)
detectors (fast signals). For redundancy, all beam monitors (\Pmu{}SC, \Pmu{}SCA
and \Pmu{}PC) were also read out by a CAEN time-to-digital converter (TDC)
model V767 which was kindly provided by the MuSun experiment.
The Data Acquisition System (DAQ) of the AlCap experiment, so-called AlCapDAQ,
provided the readout of front-end electronics, event assembling, data logging,
hardware monitoring and control, and the run database of the experiment
(Figure~\ref{fig:alcapdaq_pcs}). It was based on MIDAS framework~\footnote{
(\cref{fig:alcapdaq_pcs}). It was based on the MIDAS framework~\footnote{
MIDAS is a general purpose DAQ software system developed at PSI and TRIUMF:\\
\url{http://midas.triumf.ca}} and consisted of two circuits, {\em i})
a detector circuit for synchronous data readout from the front-end electronics
@@ -375,7 +394,7 @@ running Linux operating system and connected into a private subnetwork.
%\hl{TODO: storage and shift monitor}
\begin{figure}[htb]
\begin{figure}[btp]
\centering
\includegraphics[width=0.95\textwidth]{figs/alcapdaq_pcs}
\caption{AlCapDAQ in the Run 2013. The {\ttfamily fe6} front-end is
@@ -397,18 +416,329 @@ correlation between detectors would be established in the analysis stage.
At the beginning of each block, the time counter in each digitiser is reset to
ensure time alignment across all modules. The period of 110~ms was chosen to be:
{\em i} long enough compares to the time scale of several \micro\second\ of the
physics of interest, {\em ii} short enough so that there is no timer rollover
on any digitiser (a FADC runs at its maximum speed of 170~\mega\hertz\ could
handle up to about 1.5 \second\ with its 28-bit time counter).
{\em i}) long enough compared to the time scale of several \si{\micro\second}\
of the physics of interest, {\em ii}) short enough so that there is no timer
rollover on any digitiser (a FADC runs at its maximum speed of
\SI{170}{\mega\hertz} could handle up to about \SI{1.5}{\second} with its
28-bit time counter).
To ease the task of handling data, the data collecting period was divided into
short runs, each run stopped when the logger had recorded 2 GB of data.
The data size effectively made each run last for about 5 minutes. The DAQ
automatically starts a new run with the same parameters after about 6 seconds.
automatically started a new run with the same parameters after about 6 seconds.
The short period of each run also allows the detection, and helps to reduce the
influence of effects such as electronics drifting, temperature fluctuation.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Detector calibration}
\label{sec:detector_calibration}
The calibration was done mainly for the silicon and germanium detectors
because they would provide energy information. The plastic scintillators were
only checked by oscilloscopes to make sure that the minimum ionisation
particles (MIPs) could be observed. The upstream plastic scintillation
counters and wire chamber, as mentioned, were well-tuned by the MuSun group.
\subsection{Silicon detector}
\label{sub:silicon_detector}
The energy calibration for the silicon detectors were done routinely during the
run, by:
\begin{itemize}
\item a \SI{79.5}{\becquerel} $^{241}\textrm{Am}$ alpha source. The most
prominent alpha particles have energies of \SI{5.484}{\MeV} (85.2\%)
and \SI{5.442}{\MeV} (12.5\%). The alpha particles from the source
would lose about \SI{66}{\kilo\eV} in the \SI{0.5}{\um}-thick dead layer,
and the peak would appear at \SI{5418}{\kilo\eV} (\cref{fig:toyMC_alpha});
\item a tail pulse generator, A tail pulse with amplitude of
\SI{66}{\milli\volt}~was used to simulate the response of the silicon
detectors' preamplifiers to a particle with \SI{1}{\MeV} energy
deposition; and
\item during data taking period, electrons in the beam were were also used
for energy calibration of thick silicon detectors where energy deposition
is large enough. The muons at different momenta provided another mean of
calibration in the beam tuning period.
\end{itemize}
\begin{figure}[htb]
\centering
\includegraphics[width=0.6\textwidth]{figs/toyMC_alpha}
\caption{Energy loss of the alpha particles after a dead layer of
\SI{0.5}{\um}.}
\label{fig:toyMC_alpha}
\end{figure}
The conversion from ADC value to energy is done with a first-order polynomial:
\begin{equation}
\textrm{E [keV]} = \textrm{Slope} \times \textrm{ADC} + \textrm{Offset}.
\end{equation}
The calibration coefficients for the silicon channels are listed in
\cref{tab:cal_coeff}.
\begin{table}
\begin{center}
\pgfplotstabletypeset[
% separator
col sep=comma,
% columns displayed
display columns/0/.style={column name = \textbf{Detector}, string type,
column type=l},
display columns/1/.style={column name = \textbf{Slope}, column type=c,
dec sep align},
display columns/2/.style={column name = \textbf{Offset}, column type=r,
dec sep align},
% format the line breaks
every head row/.style={
before row={\toprule},
after row={\midrule},
%%TODO unit of coeffcients
%after row={ \arraybackslash
%{ }& { keV/channel } & { keV }\\
%\midrule},
%{}& {(keV/channel)} & {(keV)}\\ \midrule},
columns/Detector/.style={column type=c},
columns/Slope/.style={column type=c},
columns/Offset/.style={column type=c}
},
every last row/.style={after row=\bottomrule},
]{raw/si_cal_effs.csv}
\caption{Calibration coefficients of the silicon detector channels}
\label{tab:cal_coeff}
\end{center}
\end{table}
% subsection silicon_detector (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Germanium detector}
\label{sub:germanium_detector}
The germanium detector was calibrated using a $^{152}\textrm{Eu}$
source
\footnote{Energies and intensities of gamma rays are taken from the
X-ray and Gamma-ray Decay Data Standards for Detector Calibration and Other
Applications, which is published by IAEA at \\
\url{https://www-nds.iaea.org/xgamma_standards/}},
the recorded pulse height spectrum is shown in \cref{fig:ge_eu152_spec}. The
source was placed at the target position so that the absolute efficiencies can
be calculated. The peak centroids and areas were obtained by fitting a Gaussian
peak on top of a first-order polynomial background. The only exception is the
\SI{1085.84}{\keV} line because of the interference of the \SI{1089.74}{\keV}
gamma, the two were fitted with two Gaussian peaks on top of a first-order
polynomial background.
The relation between pulse height in ADC value and energy is found to be:
\begin{equation}
\textrm{ E [keV]} = 0.1219 \times \textrm{ADC} + 1.1621
\end{equation}
The energy resolution (full width at half maximum - FWHM) was better than
2.6~\si{\keV}\ for all the $^{152}\textrm{Eu}$ peaks. It was
a little worse at 3.1~\si{\keV}~for the annihilation photons at
511.0~\si{\keV}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.70\textwidth]{figs/ge_eu152_spec}
\caption{Energy spectrum of the $\rm^{152}\textrm{Eu}$ calibration source
recorded by the germanium detector. The most prominent peaks of
$^{152}\textrm{Eu}$ along with their energies are
annotated in red; the 1460.82 \si{\keV}~line is background from
$^{40}\textrm{K}$; and the annihilation 511.0~\si{\keV}~photons
come both from the source and the surrounding environment.}
\label{fig:ge_eu152_spec}
\end{figure}
\begin{figure}[htb]
\centering
\includegraphics[width=0.89\textwidth]{figs/ge_ecal_fwhm}
\caption{Germanium energy calibration and resolution.}
\label{fig:ge_fwhm}
\end{figure}
Following corrections for the peak areas are considered:
\begin{enumerate}
\item Correction for counting loss due to finite response time of the
detector system, where two gamma rays arrive at the detector within a time
interval short compared to that response time. This correction is
significant in our germanium system because of the current pulse
information extracting method does not count the second pulse (see
\cref{sub:offline_analyser}).
\item Correction of counting time loss in the reset periods of the transistor
reset preamplifier. A preamplifier of this type would reset itself after
accumulating a predetermined amount of charge. During a reset, the
preamplifier is insensitive so this can be counted as a dead time.
\item True coincidence summing correction: two cascade gamma rays hit the
detector at the same time would cause loss of counts under the two
respective peaks and gain under the sum energy peak.
\item Correction for self-absorption of a gamma ray by the source itself.
\end{enumerate}
The corrections for the first two mechanisms can be estimated by examining
pulse length and intervals between two consecutive pulses in the germanium
detector (\cref{fig:ge_cal_rate_pulselength}). The average pulse
length is \SI{45.7}{\um}, the average count rate obtained from the decay rate
of the interval spectrum is \SI{240}{\per\s}.
The correction factor for the finite response time of the detector system is
calculated as:
\begin{align}
k_{\textrm{finite response time}} &= e^{2\times \textrm{(pulse length)}
\times \textrm{(count rate)}}\\
&= e^{2\times 47.5\times10^{-6} \times 241} \nonumber\\
&= 1.02 \label{eqn:finite_time_response}
\end{align}
The resets of the preamplifier show up as a peak around \SI{2}{\ms},
consistent with specification of the manufacturer. Fitting the peak on top of
an exponential background gives the actual reset pulse length of
\SI{1947.34}{\us} and the number of resets during the calibration runs is
2335.0. The total time loss for resetting is hence:
$1947.34\times 10^{-6} \times 2335.0 = 4.55$ \si{\s}. That is a 0.14\% loss
for a measuring time of \SI{3245.5}{\s}. This percentage loss is insignificant
compared with the loss in \eqref{eqn:finite_time_response} and the statistical
uncertainty of peak areas.
\begin{figure}[htb]
\centering
\includegraphics[width=0.95\textwidth]{figs/ge_cal_rate_pulselength}
\caption{Germanium detector pulse length (left) and intervals between pulses
on that detector (right). The peak around \SI{2}{\ms} corresponds to the
resets of the preamplifier. The peak at \SI{250}{\us} is due to triggering
by the timing channel which is on the same digitiser.}
\label{fig:ge_cal_rate_pulselength}
\end{figure}
The true coincidence summing probability is estimated to be very small, about
\num{5.4d-6}, thanks to the far geometry of the calibration. The absorption in
the source cover made of \SI{22}{\mg\per\cm^2} polyethylene is less than
\num{4d-4} for a \SI{100}{\keV} photon. Therefore these two corrections are
omitted.
The absolute efficiencies of the reference gamma rays show agreement with those
obtained from a Monte Carlo (MC) study where a point source made of $^{152}$Eu
is placed at the target position (see \cref{fig:ge_eff_cal}). A comparison
between efficiencies in case of the point-like source and a finite-size
source is also done by MC simulation. The differences between the two sources
are generally smaller than 3\%, which are comparable with the uncertainties of
the efficiency calibration. That means the point-like efficiencies can be used
for a finite-sized source without correction.
%As shown in \cref{fig:ge_eff_cal}, the
%differences are in line with the uncertainties of the measured efficiencies.
%The dimensions of the latter are set to
%resemble the distribution of muons inside the target: Gaussian spreading
%\SI{11}{\mm} vertically, \SI{13}{\mm} horizontally, and \SI{127}{\um} in
\begin{figure}[htb]
\centering
\includegraphics[width=0.40\textwidth]{figs/ge_eff_cal}
\includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root}
\caption{Absolute efficiency of the germanium detector (right) and
MC comparison of efficiencies in case of point-like and finite-sized
sources (left). The efficiencies curve is fitted on
7 measured energy points from \SIrange{244}{1408}{\keV}, the shaded area is
95\% confidence interval of the fit. The ratios on the left plot are
normalised to the efficiencies of the point-like case at each energy point.}
%because it is known that the linearity between
%$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better.
\label{fig:ge_eff_cal}
\end{figure}
The absolute efficiencies of the referenced points, and calculated efficiencies
at X-rays of interest are listed in \cref{tab:xray_eff}.
\begin{table}[htb]
\begin{center}
\pgfplotstabletypeset[
% separator
col sep=comma,
% columns displayed
% column type={S} means leave formatting to siunitx
display columns/0/.style={column name = \textbf{Photons (\si{\keV})},
string type,
column type={S[table-format=4.3, table-alignment=center]}},
display columns/1/.style={column name = \textbf{Efficiency},
string type,
column type={S[parse-numbers = true,
round-precision=3,
round-mode=figures,
fixed-exponent=-4,
scientific-notation=fixed,
table-format=1.2e-1,
%table-omit-exponent,
]}},
display columns/2/.style={column name = \textbf{Uncertainty},
string type,
column type={S[parse-numbers = true,
round-precision=3,
round-mode=figures,
fixed-exponent=-5,
scientific-notation=fixed,
table-format=1.3e-1,
%table-omit-exponent,
]}},
% format the line breaks
every head row/.style={
before row={\toprule},
after row={
%\textbf{\si{\keV}} & \textbf{\num{E-4}} & \textbf{\num{E-4}}\\
\midrule},
columns/0/.style={column type=r},
columns/1/.style={column type=c},
columns/2/.style={column type=c}
},
every last row/.style={after row=\bottomrule},
every nth row={8}{before row={\midrule}},
]{raw/ge_eff.csv}
\end{center}
\caption{Absolute efficiencies of the germanium detector in case of
a point-like source placed at the centre of the target (upper half), and
the calculated efficiencies for the X-rays of interest (lower half).}
\label{tab:xray_eff}
\end{table}
% subsection germanium_detector (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Beam tuning and muon momentum scanning}
%\label{sub:muon_momentum_scanning}
%Before taking any data, we carried out the muon momentum scanning to understand
%the muon beam, as well as calibrate the detector system. The nominal muon
%momentum used in the Run 2013 had been tuned to 28~MeV\cc\ before the run. By
%changing simultaneously the strength of the key magnet elements in the $\pi$E1
%beam line with the same factor, the muon beam momentum would be scaled with the
%same factor.
%The first study was on the range of muons in an active silicon target. The SiL2
%detector was placed perpendicular to the nominal beam path, after an oval
%collimator. The beam momentum scaling factor was scanned from 1.10 to 1.60,
%muon momenta and energies in the measured points are listed in
%\cref{tab:mu_scales}.
%\begin{table}[htbp]
%\begin{center}
%\begin{tabular}{c c c c}
%\toprule
%\textbf{Scaling} & \textbf{Momentum} & \textbf{Kinetic energy}
%& \textbf{Momentum spread}\\
%\textbf{factor} & \textbf{(MeV\per\cc)} & \textbf{(MeV)}
%& \textbf{(MeV\per\cc, 3\% FWHM)}\\
%\midrule
%1.03 & 28.84 & 3.87& 0.87\\
%1.05 & 29.40 & 4.01& 0.88\\
%1.06 & 29.68 & 4.09& 0.89\\
%1.07 & 29.96 & 4.17& 0.90\\
%1.10 & 30.80 & 4.40& 0.92\\
%1.15 & 32.20 & 4.80& 0.97\\
%1.20 & 33.60 & 5.21& 1.01\\
%1.30 & 36.40 & 6.09& 1.09\\
%1.40 & 39.20 & 7.04& 1.18\\
%1.43 & 40.04 & 7.33& 1.20\\
%1.45 & 40.60 & 7.53& 1.22\\
%1.47 & 41.16 & 7.73& 1.23\\
%1.50 & 42.00 & 8.04& 1.26\\
%\bottomrule
%\end{tabular}
%\end{center}
%\caption{Muon beam scaling factors, energies and momenta.}
%\label{tab:mu_scales}
%\end{table}
% subsection muon_momentum_scanning (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% section detector_calibration (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Data sets and statistics}
\label{sec:data_sets}
@@ -431,14 +761,14 @@ different targets were carried out for silicon targets:
As the emitted protons deposit a significant amount of energy in the target
material, thin targets and thus excellent momentum resolution of the low energy
muon beam are critical. Aluminium targets of 50-\micro\meter\ and
100~\micron\ thick were used. Although a beam with low momentum spread of
1\% is preferable, it was used for only a small portion of the run due to the
low beam rate (see Figure~\ref{fig:Rates}). The beam momentum for each target
was chosen to maximise the number of stopped muons. The collected data sets are
shown in Table~\ref{tb:stat}.
muon beam are critical, aluminium targets of 50-\si{\micro\meter}\ and
100-\si{\micro\meter}\ thick were used. Although a beam with low momentum
spread of 1\% is preferable, it was used for only a small portion of the run
due to the low beam rate (see \cref{fig:Rates}). The beam momentum for each
target was chosen to maximise the number of stopped muons. The collected data
sets are shown in \cref{tb:stat}.
\begin{table}[htb!]
\begin{table}[btp!]
\begin{center}
\vspace{0.15cm}
\begin{tabular}{l c c c}
@@ -446,38 +776,39 @@ shown in Table~\ref{tb:stat}.
\textbf{Target} &\textbf{Momentum} & \textbf{Run time} & \textbf{Number}\\
\textbf{and thickness}&\textbf{scaling factor} & \textbf{(h)} &\textbf{of muons}\\
\midrule
Si 1500 \micro\meter& 1.32& 3.07& $2.78\times 10^7$\\
Si 1500 \si{\micro\meter}& 1.32& 3.07& $2.78\times 10^7$\\
& 1.30& 12.04& $2.89 \times 10^8$\\
& 1.10& 9.36& $1.37 \times 10^8$ \\
\midrule
Si 62 \micro\meter & 1.06& 10.29& $1.72 \times 10^8$\\
Si 62 \si{\micro\meter} & 1.06& 10.29& $1.72 \times 10^8$\\
\midrule
Al 100 \micro\meter& 1.09& 14.37&$2.94 \times 10^8$\\
Al 100 \si{\micro\meter}& 1.09& 14.37&$2.94 \times 10^8$\\
& 1.07& 2.56& $4.99 \times 10^7$\\
\midrule
Al 50 \micro\meter m & 1.07& 51.94& $8.81 \times 10^8$\\
Al 50 \si{\micro\meter} & 1.07& 51.94& $8.81 \times 10^8$\\
\bottomrule
\end{tabular}
\end{center}
\caption{Run statistics. Momentum scaling
normalized to 28 MeV/c.}
\caption{Run statistics. Momentum scaling factors are normalised to
\SI{28}{\MeV\per\cc}.}
\label{tb:stat}
\end{table}
% section data_sets (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Analysis framework}
\label{sec:analysis_framework}
\subsection{Concept}
\label{sub:concept}
Since the AlCapDAQ is a trigger-less system, it stored all waveforms of the
hits occured in 100-ms-long blocks without considering their physics
significance The analysis code therefore must be able to extract parameters of
the waveforms, then organises the pulses into physics events correlated to
stopped muons (Figure~\ref{fig:muon_event}). In addition, the analyser is
significance. The analysis code therefore must be able to extract parameters of
the waveforms, then organises the pulses into the physics events correlated to
stopped muons (\cref{fig:muon_event}). In addition, the analyser is
intended to be usable as a real-time component of a MIDAS DAQ, where simple
analysis could be done online for monitoring and diagnostic during the run.
\begin{figure}[htb]
\begin{figure}[btp]
\centering
\includegraphics[width=0.9\textwidth]{figs/muon_event.pdf}
\caption{Concept of the AlCap analysis code: pulses from individual detector
@@ -487,9 +818,9 @@ analysis could be done online for monitoring and diagnostic during the run.
The analysis framework of the AlCap consists of two separate programs.
A MIDAS-based analyser framework, \alcapana{}, processes the raw data and
passes its ROOT data output to a second
passes its ROOT data output to the second
stage, \rootana{}, where most of the physics analysis is performed.
Both programs were designed to be modularised, which allowed us to develop
Both of the programs were designed to be modularised, which allowed us to develop
lightweight analysis modules that were used online to generate plots quickly,
while more sophisticated modules can be applied in offline analysis.
@@ -520,12 +851,12 @@ algorithm that takes the pulse parameters from the peak of the waveform. In
parallel, a pulse finding and template fitting code is being developed because
it would provide more accurate pulse information. The first iteration of this
code has been completed and is being tested.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/analysis_scheme}
\caption{Concept of the analysis framework in \rootana{}}
\label{fig:rootana_scheme}
\end{figure}
%\begin{figure}[btp]
%\centering
%\includegraphics[width=0.85\textwidth]{figs/analysis_scheme}
%\caption{Concept of the analysis framework in \rootana{}}
%\label{fig:rootana_scheme}
%\end{figure}
After obtaining pulse parameters for individual channel, the pairing up of
fast and slow pulses from the same physical detector needs to be done. This
@@ -545,7 +876,7 @@ detectors. These particle hits are still stored in the time-ordered tree
corresponds to the 110 ms block length from the AlCapDAQ. By iterating through
the tree to find stopped muons and taking any hits within a certain window
around this muon from every detector, a stopped-muon-centred tree shown in
Figure~\ref{fig:muon_event} can be produced. This will make it much easier to
\cref{fig:muon_event} can be produced. This will make it much easier to
look for coincidences and apply cuts, thereby bringing the end
goal of particle numbers and energy distributions.
@@ -558,8 +889,8 @@ The online analyser was developed and proved to be very useful during the run.
A few basic modules were used to produce plots for diagnostic purposes
including: persistency view of waveforms, pulse height
spectra, timing correlations with respect to the upstream counters. The
modules and their purposes are listed in Table~\ref{tab:online_modules}.
\begin{table}[htb]
modules and their purposes are listed in \cref{tab:online_modules}.
\begin{table}[btp]
\begin{center}
\begin{tabular}{l p{6cm}}
\toprule
@@ -604,35 +935,142 @@ groups such as upstream counters, silicon arms. It could also periodically
update the plots to reflect real-time status of the detector system.
%Screen
%shots of the {\ttfamily online-display} with several plots are shown in
%Figure~\ref{fig:online_display}.
%\cref{fig:online_display}.
%\hl{Screen shots}
\subsection{Offline analyser}
\label{sub:offline_analyser}
Some offline analysis modules has been developed during the beam time and could
Some offline analysis modules have been developed during the beam time and could
provide quick feedback in confirming and guiding the decisions at the time. For
example, the X-ray spectrum analysis was done to confirm that we could observe
the muon capture process (Figure~\ref{fig:muX}), and to help in choosing optimal
momenta which maximised the number of stopped muons.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.7\textwidth]{figs/muX.png}
\caption{Germanium
detector spectra in the range of 300 - 450 keV with different setups: no
target, 62-\micron-thick silicon target, and 100-\micron-thick aluminium
target. The ($2p-1s$) lines from
aluminium (346.828 keV) and silicon (400.177 keV) are clearly visible,
the double peaks at 431 and 438 keV are from the lead shield, the peak at
351~keV is a background gamma ray from $^{211}$Bi.}
\label{fig:muX}
\end{figure}
the muon capture process and to help in choosing optimal momenta which
maximised the number of stopped muons.
Although the offline analyser is still not fully developed yet, several modules
are ready. They are described in detailed in the next chapter.
Although the offline analyser is still not fully available yet, several modules
are ready (\cref{tab:offline_modules}). An initial analysis is possible using
the existing modules thanks to the modularity of the analysis framework.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l p{8cm}}
\toprule
\textbf{Module name} & \textbf{Functions}\\
\midrule
MakeAnalysedPulses & make a pulse with parameters extracted from
a waveform\\
MaxBinAPGenerator & simplest algorithm to get pulse information\\
TSimpleMuonEvent & sort pulses occur in a fixed time window around the
muon hits\\
ExportPulse \& PulseViewer & plot waveforms for diagnostics\\
PlotAmplitude & plot pulse height spectra\\
PlotAmpVsTdiff & plot pulse correlations in timing and amplitude\\
EvdE & plot \sdEdx histograms\\
\bottomrule
\end{tabular}
\end{center}
\caption{Available offline analysis modules.}
\label{tab:offline_modules}
\end{table}
The MakeAnalysedPulses module takes a raw waveform, calculates the pedestal
from a predefined number of first samples, subtracts this pedestal taking
pulse polarity into account, then calls another module to extract pulse
parameters. At the moment, the simplest module, so-called MaxBinAPGenerator,
for pulse information calculation is in use. The module looks for the
sample that has the maximal deviation from the baseline, takes the deviation as
pulse amplitude and the time stamp of the sample as pulse time. The procedure
is illustrated on \cref{fig:tap_maxbin_algo}. This module could not handle
pile-up or double pulses in one \tpulseisland{} in \cref{fig:tap_maxbin_bad}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/tap_maxbin_algo}
\caption{Pulse parameters extraction with MaxBinAPGenerator.}
\label{fig:tap_maxbin_algo}
\end{figure}
\begin{figure}[htb]
\centering
\includegraphics[width=0.47\textwidth]{figs/tap_maxbin_bad}
\includegraphics[width=0.47\textwidth]{figs/tap_maxbin_bad2}
\caption{Double pulse and pile up are taken as one single pulse by the
MaxBinAPGenerator}
\label{fig:tap_maxbin_bad}
\end{figure}
The TSimpleMuonEvent first picks a muon candidate, then loops through all
pulses on all detector channels, and picks all pulses occur in
a time window of \SI{\pm 10}{\si{\us}} around each candidate to build
a muon event. A muon candidate is a hit on the upstream plastic scintillator
with an amplitude higher than a threshold which was chosen to reject MIPs. The
period of \SI{10}{\si{\us}} is long enough compared to the mean life time of
muons in the target materials
(\SI{0.758}{\si{\us}} for silicon, and \SI{0.864}{\si{\us}}
for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted
charged particles would be recorded in this time window.
%\begin{figure}[htb]
%\centering
%\includegraphics[width=0.85\textwidth]{figs/tme_musc_threshold}
%\caption{Pulse height spectrum of the $\mu$Sc scintillator}
%\label{fig:tme_musc_threshold}
%\end{figure}
A pile-up protection mechanism is employed to reject multiple muons events: if
there exists another muon hit in less than \SI{15}{\us} from the
candidate then both the candidate and the other muon are discarded. This
pile-up protection would cut out less than 11\% total number of events because
the beam rate was generally less than \SI{8}{\kilo\hertz}.
%In runs with active silicon targets, another requirement is applied for the
%candidate: a prompt hit on the target in $\pm 200$ \si{\ns}\ around the
%time of the $\mu$Sc pulse. The number comes from the observation of the
%time correlation between hits on the target and the $\mu$Sc
%(\cref{fig:tme_sir_prompt_rational}).
%\begin{figure}[htb]
%\centering
%\includegraphics[width=0.85\textwidth]{figs/tme_sir_prompt_rational}
%\caption{Correlation in time between SiR2 hit and muon hit}
%\label{fig:tme_sir_prompt_rational}
%\end{figure}
To make sure that we will analyse good data, a low level data quality checking
was done on the whole data sets. The idea is to plot the variations of basic
parameters, such as noise level, length of raw waveforms, pulse rate, time
correlation to hits on the muon counter on each channel during the data
collecting period. Runs with significant difference from the averaging
values were further checked for possible causes, and would be discarded if such
discrepancy was too large or unaccounted for. Examples of such trend plots are
shown in \cref{fig:lldq}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.47\textwidth]{figs/lldq_noise}
\includegraphics[width=0.47\textwidth]{figs/lldq_tdiff}
\caption{Example trend plots used in the low level data quality checking:
noise level in FWHM (left) and time correlation with muon hits (right).
The horizontal axis is run number, the vertical axis is the channel name
(left), or the time difference between hit in the germanium
detector and a hit in upstream counter (right). Colors in both plots
indicate the number of events. In the left plot, the
noise level was basically stable in in this data set, except for one
channel where there was a sudden jump in a range of runs. On the right hand
side, this sanity check helped find out the sampling frequency was wrongly
applied in the first tranche of the data
set.}
\label{fig:lldq}
\end{figure}
% subsection offline_analyser (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% section analysis_strategy (end)
\section{Monte Carlo simulation}
\label{sec:monte_carlo_simulation}
A full Monte Carlo (MC) simulation of the experimental set up has been developed
based on Geant4~\cite{Agostinelli.etal.2003}. The geometrical implementation
was detailed as much as possible and could be modified via configuration
scripts at run time. Descriptions of the muon beam came from the beam line optic
calculation provided by the accelerator experts at PSI.
The MC model greatly assisted the design of the experiment, such as alignment
of the detectors with respect to the target, and shielding of scattered muons.
It also helped make a sense of the observed results during the run and data
analysing.
% chapter the_alcap_run_2013 (end)

1909
thesis/chapters/chap6_analysis.tex
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210
thesis/chapters/chap7_results.tex
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@@ -1,74 +1,154 @@
\chapter{Discussions}
\label{cha:discussions}
\chapter{Impact to the COMET Phase-I}
\label{cha:discussions_on_the_impact_to_the_comet_phase_i}
The measured proton emission rate of 3.5\% is about 5 times
smaller than the figure using to make the baseline design of the CDC in COMET
Phase-I. The spectrum shape is softer than that of silicon,
peaks around \SI{4}{\MeV} rather than at \SI{2.5}{\MeV}
(\cref{fig:sobottka_spec}). Therefore CDC hit rate due to proton should be
smaller than the current estimation.
\section{Thick aluminium target measurement}
\label{sub:active_target_measurement}
With a thick and active silicon target, I have tried to reproduce an existing
result from Sobottka and Wills~\cite{SobottkaWills.1968}. This is important in
giving confidence in our experimental method. The idea is the same as that of
the old measurement, where muons were stopped inside a bulk active target and
the capture products were measured. Due to the limitation of the
currently available analysis tool, a direct comparison with the result of
Sobottka and Wills is not practical at the moment.
The CDC proton hit rate is calculated by a toy MC study. The dimensions of the
geometry shown in \cref{fig:cdc_toy_mc} are from \cref{ssub:CDC_configuration}.
The inner wall of the CDC is \SI{0.5}{\mm} thick CFRP.
A proton absorber made
of CFRP is placed \SI{5}{\cm} far from the inner wall of the CDC. The
absorber's thickness is varied from 0 (no absorber) to \SI{1}{\mm}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.55\textwidth]{figs/cdc_toy_mc}
\caption{Geometry of the toy MC study for hit rate study.}
\label{fig:cdc_toy_mc}
\end{figure}
But a partial comparison is available for a part of the spectrum from 8 to
10~MeV, where my result of $(1.22 \pm 0.19) \times 10^{-2} $ is consistent with
the derived value $(1.28\pm0.19)\times10^{-2}$ from the paper of Sobottka and
Wills. The agreement was partly because of large error bars in both results.
In my part, the largest error came from the uncertainty on choosing the
integration window. This can be solved with a more sophisticated pulse
finding/calculating algorithm so that the contribution of muons in the energy
spectrum can be eliminated by imposing a cut in pulse timing. The
under-testing pulse template fitting module could do this job soon.
The protons with the energy spectrum shape as in
\cref{sub:proton_emission_rate} are generated inside the COMET's muon stopping
targets which are 17 200-\si{\um}-thick aluminium discs. The spatial
distribution of protons resembles the stopping distribution of muons inside the
target discs calculated from the full MC simulation of the COMET detectors
(\cref{fig:cdc_toy_mc_init_pos}).
\begin{figure}[htb]
\centering
\includegraphics[width=0.65\textwidth]{figs/cdc_toy_mc_init_pos_xy}
\includegraphics[width=0.60\textwidth]{figs/cdc_toy_mc_init_pos_z}
\caption{Spatial distribution of the generated protons in X, Y (top) and
Z (bottom). Z is the axis of the CDC, X, Y are the horizontal and vertical
axes respectively.}
\label{fig:cdc_toy_mc_init_pos}
\end{figure}
The range of 8--10~MeV was chosen to be large enough so that the uncertainty of
integration window would not to be too great; and at the same time be small
enough so the protons (and other heavier charged particles) would not escape
the active target. This range is also more convenient for calculating the
partial rate from the old paper of Sobottka and Wills.
The protons are then tracked in a \SI{1}{\tesla} magnetic field. The protons
reaching the absorber, inner wall and the sensitive volume of the CDC are
recorded (see \cref{fig:cdc_toy_mc_p_spec_500um}).
\begin{figure}[!htb]
\centering
\includegraphics[width=0.75\textwidth]{figs/cdc_toy_mc_p_spec_500um}
\caption{Proton energy spectra at different stages from birth to the
sensitive volume of the CDC. The baseline design of \SI{0.5}{\mm} thick
absorber and \SI{0.5}{\mm} thick inner wall was used to produce this
plot.}
\label{fig:cdc_toy_mc_p_spec_500um}
\end{figure}
% section protons_following_muon_capture_on_silicon (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A muon stopping rate of \SI{1.3E9}{\Hz} is assumed as in the COMET Phase I's
TDR. The number of proton emitted is then $\num{1.3E9} \times 0.609 \times
0.035 = \SI{2.8E7}{\Hz}$. The hit rates on a single cell in the inner most
layer due to these protons with
different absorber configurations are listed in
\cref{tab:proton_cdc_hitrate_comp}.
\section{Thin silicon target measurement}
\label{sub:thin_and_passive_target_measurement}
The charged particles in the low energy region of 2.5--8~MeV were measured by
dE/dx method. The particle identification was good in lower energy part, but
losing its resolution power as energy increases. The current set up could do
the PID up to about 8~MeV for protons. This energy range is exactly the
relevant range to the COMET experiment (Figure~\ref{fig:proton_impact_CDC}).
\begin{table}[htb]
\begin{center}
\begin{tabular}{S S S S S}
\toprule
{\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}&
{\textbf{Proton hit rate}} & {\textbf{Proton hit rate}}\\
{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}&
{\textbf{Phase-I TDR}} & {\textbf{New estimation}}\\
{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}& {(\si{\Hz})}\\
\midrule
1 &0.5&1.5 & 4E+3 & 2 \\
0.5 &0.5&1.0 & 11E+3& 126 \\
0 &0.5&0.5 & 30E+3& 1436 \\
\bottomrule
\end{tabular}
\end{center}
\caption{CDC proton hit rates in this study in comparison with the expected
rates in COMET Phase-I's Technical Design Report~\cite{COMET.2014} at
different configurations of proton absorber and inner wall.}
\label{tab:proton_cdc_hitrate_comp}
\end{table}
In that useful energy range, the analysis showed a good separation of protons
from other heavy charged particles. The contribution of protons in the total
charged particles is 87\%. This is the high limit only since the heavier
particles at this energy range are most likely to stopped in the thin
detectors. More statistic would be needed to estimate the contributions from
other particles.
%\begin{table}[htb]
%\begin{center}
%\begin{tabular}{S S S S S S}
%\toprule
%{\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& {\textbf{Proton}} & {\textbf{Momentum}} & {\textbf{Integrated charge}}\\
%{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& {\textbf{hit rate}} &{\textbf{spread $\Delta p$}} &{\textbf{300 days}}\\
%{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})} & {(\si{\keV\per\cc)}} &{(mC/cm)}\\
%\midrule
%1 &0.5&1.5 & 2 & 195 & 25\\
%0.5 &0.5&1.0 & 126 & 167 & 60\\
%0 &0.5&0.5 & 1436 & 133 & 160\\
%\bottomrule
%\end{tabular}
%\end{center}
%\caption{CDC proton hit rates at different configuration of proton absorber
%and inner wall. The momentum spreads for \SI{0.5}{\mm} thick inner wall are
%taken from \cref{tab:comet_absorber_impact}.}
%\end{table}
At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz},
much smaller than the current estimation at \SI{11}{\kHz}. Even without the
absorber, proton hit rate remains lower than that level at \SI{1.4}{\kHz}.
Therefore the absorber is not necessary as far as the hit rate is concerned.
%Therefore a proton
%absorber is not needed for the COMET Phase I's CDC.
The effective emission rate of protons per muon capture in this measurement is
4.20\%, with a large uncertainty contribution comes from limitation of the
timing determination. The spectral integral in the region 2.5--8~MeV on
Figure~\ref{fig:sobottka_spec} is about 70\% of the spectrum from 1.4 to
26~\MeV, and corresponds to an emission rate of about 10\% per muon capture.
The two figures are not in disagreement.
In order to have a better comparison, a correction or unfolding for energy
loss and more MC simulation study are needed. I am on progress of these study.
% subsection thin_and_passive_target_measurement (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Aluminium target measurement}
\label{sec:aluminium_target_measurement}
The proton emission rate was derived as 2.37\%, but the problem on the SiL1-1
channel was not solved yet. One possible cause is the muons captured on other
lighter material inside the chamber. More investigation will be made on this
matter.
The rate of 2.37\% on aluminium appears to be smaller on that of silicon but
the two results are both effective rates, modified by energy loss inside the
target. Unfolding and MC study for the correction are ongoing.
% section aluminium_target_measurement (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% chapter discussions (end)
If the proton absorber is not used, the momentum spread of the signal electron
reduces from \SI{167}{\keV\per\cc} to \SI{131}{\keV\per\cc} (\cref{tab:proton_cdc_hitrate}).
This is a small improvement since the momentum resolution is dominated by
intrinsic spread of \SI{197}{\keV\per\cc} due to multiple scattering in gas
and wires.
The last column of \cref{tab:proton_cdc_hitrate} shows the integrated charge
per unit length of a wire. The TDR deems an integrated charge level of
\SI{200}{\milli\coulomb\per\cm} safe. So even with the pessimistic estimation using
silicon rate and spectrum and without the proton absorber, the integrated
charge level in the CDC is still below the requirement. Therefore removing the
absorber will not worsen the ageing process of the wires.
\begin{table}[htb]
\begin{center}
\begin{tabular}{S S S S S}
\toprule
{\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}&
{\textbf{Momentum}} & {\textbf{Integrated charge}}\\
{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}&
{\textbf{spread $\Delta p$}} &{\textbf{300 days}}\\
{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})}
& {(\si{\keV\per\cc)}} &{(mC/cm)}\\
\midrule
1 &0.5&1.5 & 195 & 25\\
0.5 &0.5&1.0 & 167 & 60\\
0 &0.5&0.5 & 133 & 160\\
%0 &0.3&0.3 & 8281 & {-} & {-}\\
%0 &0.1&0.1 & 15011& {-} & {-}\\
\bottomrule
\end{tabular}
\end{center}
\caption{Momentum spreads due to the inner wall and absorber, and integrated
charge per unit length of wire as calculated in the COMET Phase-I's TDR.
The momentum spreads were calculated for signal electrons at
\SI{104.96}{\MeV\per\cc}. The integrated charge is estimated assuming 300
days of operation.}
\label{tab:proton_cdc_hitrate}
\end{table}
%In case a lower momentum spread is desired, it is possible to reduce the
%thickness of the inner wall. The last
%two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at
%\SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at
%manageable levels. However, reducing the wall thickness would be governed by
%other requirements such as mechanical structure and gas-tightness.
In summary, the toy MC study with the preliminary proton rate and spectrum
shows that a proton absorber is not needed. It confirms the known fact that the
estimation used in COMET Phase-I is conservative, and provides a solid
prediction of the hit rate caused by protons.

47
thesis/chapters/chap8_conclusions.tex Normal file
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@@ -0,0 +1,47 @@
\chapter{Conclusions}
\label{cha:conclusions}
The AlCap is an experiment proposed at PSI to study charged particles, neutrons
and photons emitting after nuclear muon capture on aluminium. These
measurements are important for backgrounds and hit rates estimation of the new
generation of \mueconv experiments, COMET and Mu2e. In the first stage of the
COMET experiment, hit rate on its main tracking detector is anticipated to be
dominated by low energy protons following muon capture on an aluminium target,
which has never been measured.
The first run of the AlCap which aims for proton measurement has been carried
out in 2013. Data analysis is in progress. Before finishing the complete AlCap
analysis, an initial analysis on partial data
was made. The main results are:
\begin{enumerate}
\item demonstration of the analysis chain from trigger-less waveforms to
correlated physics events;
\item validation of the experimental method including: number of nuclear
capture muons normalisation by muonic X-ray measurement, charged particle
identification by specific energy loss, and unfolding of the proton energy
spectrum using the iterative Bayesian method;
\item obtaining preliminary results on proton emission rate and spectrum:
the proton spectrum has a peak at \SI{3.7}{\MeV}, then reduces exponentially
with a decay constant of \SI{2.6}{\MeV}. The partial emission rate in the
energy range from \SIrange{4}{8}{\MeV} is $(1.7 \pm 0.1)\%$ per nuclear
muon capture, and the total
emission rate assuming the shape holds for the whole spectrum is
$(3.5\pm0.2)\%$ per nuclear muon capture.
\end{enumerate}
The emission rate is consistent with the lower limit of 2.8\% set by
Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978}. It is also compatible
with the theoretical calculation by Lifshitz and
Singer~\cite{LifshitzSinger.1980}. Compared with the existing result on
silicon~\cite{SobottkaWills.1968}, the emission rate from aluminium is
significantly smaller and the spectrum is softer.
The proton rate and spectrum have been used to optimise the planned proton
absorber for the drift chamber of the COMET Phase-I. The resulted proton hit
rate with the baseline configuration is very small compared with the current
figure.The recommendation to the COMET Phase-I is to remove the proton
absorber altogether. The momentum resolution of the drift chamber will be
slightly improved, and the level of integrated charge will still remain below
the safe level for the chamber.
The AlCap experiment is going to
submit a beam time request for the 2015 run to collect more data and other
measurements for neutrons and gamma rays.

52
thesis/chapters/frontmatter.tex
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@@ -10,11 +10,11 @@ Osaka University}
\begin{abstract}
%[\smaller \thetitle\\ \vspace*{1cm} \smaller {\theauthor}]
\thispagestyle{empty}
COMET [1] is an experiment that aims to search for a charged lepton flavor
COMET [1] is an experiment that aims to search for a charged lepton flavour
violation (CLFV) process, the muon-to-electron conversion in the presence of
a nucleus,
\muec. The process is forbidden in the Standard Model (SM), however is
predicted to occur in various extensions of SM, such as . Current experimental
predicted to occur in various extensions of SM. Current experimental
upper limit of the branching ratio is $BR(\mu^{-} + Au \rightarrow e^{-} + Au)
< 7 \times 10^{-13}$, set by the SINDRUM II experiment [2].
@@ -25,11 +25,21 @@ approach in which the first phase, COMET Phase-I [3], starts in 2013 and
initial data taking in around 2017.
In order to optimize detector design for the Phase-I, backgrounds from nuclear
muon capture are crucial. We have proposed a dedicated experiment , namely
AlCap, at PSI, Switzerland to study the backgrounds, including: heavy charged
particles, neutrons and photons. The measurements of heavy charged particles
have been carried out in the 2013 run and the preliminary analysis results are
presented in this thesis.
muon capture are crucial. We have proposed a dedicated experiment, namely
AlCap, at PSI, Switzerland to study the backgrounds, including protons,
neutrons and photons. The measurements of proton rate and spectrum on
aluminium have been carried out in the 2013 run. The second run to study
neutrons and photons is planned in 2015.
The preliminary results from the analysis of the 2013 run are presented in this
thesis. The measured proton spectrum peaks at \SI{3.7}{\MeV} and decays
exponentially with the decay constant of \SI{2.6}{\MeV}. The emission
rate of protons in the energy range from \SIrange{4}{8}{\MeV} is
$(1.7\pm0.1)\%$. The total proton emission rate is estimated to be
$(3.5\pm0.2)\%$ assuming the spectrum shape holds.
The resulted proton rate and spectrum were used to optimise the tracking
detector hit rate of the COMET Phase-I.
\end{abstract}
@@ -47,18 +57,34 @@ presented in this thesis.
% Acknowledgements
%\begin{acknowledgements}
%\thispagestyle{empty}
%Of the many people who deserve thanks, some are particularly prominent,
%such as my supervisor Professor Yoshitaka Kuno.
%\end{acknowledgements}
\begin{acknowledgements}
\thispagestyle{empty}
First and foremost I would like to thank my supervisor Yoshitaka
Kuno, for his great support and almost infinite patience in last four years.
I am also grateful to all members of the Kuno group, Department of
Physics, Osaka University. Thanks to Akira Sato, Hideyuki Sakamoto for the
knowledge and supervision they have provided. And to Takahisa Itahashi
for the advice and allowing me to practice on his expensive silicon detectors.
The measurement described in this thesis is the product of effort of all
members of the AlCap Collaboration. Special thanks to Peter Kammel for
always pushing the experiment forward and your very helpful advices.
I enjoyed the stays at your group at University of Washington in Seattle
a lot. I would also like to thank the
fellow graduate students in the collaboration Andy, John, Ben, Damien for
all the hard work in the beam time, in the analysis phase, and also for
the beers. I wish you all success with your work.
Finally, I would like to thank my family and friends. Without your love and
support I wouldn't make it through these long years of graduate school.
\end{acknowledgements}
%% Preface
%\begin{preface}
%\thispagestyle{empty}
%The thesis is about measurements of products of nuclear muon capture on an
%aluminum target, which is important for optimization of a tracking detector
%aluminium target, which is important for optimization of a tracking detector
%of a search for muon to electron conversion, the E21 experiment - so called
%COMET - at Japan Proton Accelerator Complex (J-PARC).
%\end{preface}

3
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@@ -50,6 +50,9 @@ $\mu^- \rightarrow e^- \nu_\mu \overline{\nu}_e e^+ e^-$\xspace
\newcommand{\cc}{$c$\xspace}
\newcommand{\dEdx}{$\dfrac{\mathop{dE}}{\mathop{dx}}$\xspace}
\newcommand{\sdEdx}{$\sfrac{\mathop{dE}}{\mathop{dx}}$\xspace}
\newcommand{\rootana}{{\ttfamily rootana}}
\newcommand{\alcapana}{{\ttfamily alcapana}}
\newcommand{\tpulseisland}{{\ttfamily TPulseIsland}}

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thesis/mythesis.sty
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@@ -12,10 +12,11 @@ inner=1.25in, outer=1in, twoside]{geometry}
%$ Hyper-link ..
\RequirePackage[%
colorlinks=true,% color links instead of using boxes
linkcolor=red,% color for internal (intra-document) links
citecolor=green,% color for bibliographic links
urlcolor=blue,% color for URL links
%colorlinks=false,% color links instead of using boxes
%linkcolor=red,% color for internal (intra-document) links
%citecolor=green,% color for bibliographic links
%urlcolor=blue,% color for URL links
hidelinks,
hyperfootnotes=false,% disable links to footnotes (because feature broken)
hyperindex,% make page numbers in index into hyperlinks
pdfstartview={FitH},% startup page view: fit width of page to window
@@ -36,6 +37,9 @@ bookmarks
\RequirePackage{emptypage}
%% Others
\RequirePackage{booktabs}
\RequirePackage{caption}
\RequirePackage{pgfplotstable}
\RequirePackage{cite}
%\RequirePackage{morefloats}
\RequirePackage{mathrsfs} % script font
@@ -51,12 +55,14 @@ bookmarks
\RequirePackage{setspace}
\RequirePackage{verbatim}
\RequirePackage{lipsum}
\RequirePackage{datatool}
\RequirePackage[capitalise]{cleveref}
\RequirePackage[final]{listings}
\RequirePackage{xfrac}
%% Units
\RequirePackage[]{siunitx}
%\RequirePackage[]{siunitx}
\RequirePackage[detect-weight=true, detect-family=true]{siunitx}
\RequirePackage{hepnames}
\RequirePackage{array}
%% Various fonts ...
%\RequirePackage[T1]{fontenc}
%\RequirePackage{charter}
@@ -76,6 +82,8 @@ bookmarks
%\linespread{1.025} % Palatino leads a little more leading
%\usepackage[small]{eulervm}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\RequirePackage{tabularx}
\RequirePackage{color}
\RequirePackage{pifont}
@@ -188,6 +196,26 @@ bookmarks
\ignorespacesafterend%
}
\newenvironment{acknowledgements}{%
\cleardoublepage%
\adjustwidth{\@declarationextramargin}{\@declarationextramargin}%
\vspace*{\@frontmattertopskip}%
\begin{center}%
\begingroup
\ifx\@sftitles\@empty\else\sf\fi
{\LARGE\textbf{Acknowledgements}}%
\endgroup
\end{center}%
\vspace*{1cm}%
}{%
%\newline \newline \newline%
%\begin{flushright}
% \thesisauthor\newline
% \today\newline
%\end{flushright}
\endadjustwidth%
\ignorespacesafterend%
}
%% Change the spacing of lines
\DeclareRobustCommand{\setspacing}[1]{%
\setfrontmatterspacing{#1}%
@@ -270,3 +298,6 @@ bookmarks
\endgroup%
}
\renewcommand{\maketitle}[1]{\titlepage{}}
%% Cleveref should be the last package to not be messed up by others
\RequirePackage[noabbrev]{cleveref}

348
thesis/thesis.bib
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@@ -112,6 +112,41 @@
Timestamp = {2014-04-09}
}
@Article{Agostinelli.etal.2003,
Title = {{GEANT4: A Simulation toolkit}},
Author = {Agostinelli, S. and others},
Journal = {Nucl. Instrum. Meth.},
Year = {2003},
Pages = {250-303},
Volume = {A506},
Collaboration = {GEANT4},
Doi = {10.1016/S0168-9002(03)01368-8},
Owner = {NT},
Reportnumber = {SLAC-PUB-9350, FERMILAB-PUB-03-339},
Slaccitation = {%%CITATION = NUIMA,A506,250;%%},
Timestamp = {2014-10-11}
}
@Article{AhmadAzuelos.etal.1988a,
Title = {Search for muon-electron and muon-positron conversion},
Author = {Ahmad, S. and Azuelos, G. and Blecher, M. and Bryman, D. and Burnham, R. and Clifford, E. and Depommier, P. and Dixit, M. and Gotow, K. and Hargrove, C. and Hasinoff, M. and Leitch, M. and Macdonald, J. and Mes, H. and Navon, I. and Numao, T. and Poutissou, J-M. and Poutissou, R. and Schlatter, P. and Spuller, J. and Summhammer, J.},
Journal = {Phys. Rev. D},
Year = {1988},
Month = {Oct},
Pages = {2102--2120},
Volume = {38},
Doi = {10.1103/PhysRevD.38.2102},
Issue = {7},
Numpages = {19},
Owner = {NT},
Publisher = {American Physical Society},
Timestamp = {2014-12-10},
Url = {http://link.aps.org/doi/10.1103/PhysRevD.38.2102}
}
@Article{AhmadAzuelos.etal.1988,
Title = {Search for muon-electron and muon-positron conversion},
Author = {Ahmad, S and Azuelos, G and Blecher, M and Bryman, DA and Burnham, RA and Clifford, ETH and Depommier, P and Dixit, MS and Gotow, K and Hargrove, CK and others},
@@ -131,7 +166,7 @@
@Article{AhmadAzuelos.etal.1987,
Title = {Searches for muon-electron and muon-positron conversion in titanium},
Author = {Ahmad, S and Azuelos, G and Blecher, M and Bryman, D and Burnham, RA and Clifford, ETH and Depommier, P and Dixit, MS and Gotow, K and Hargrove, CK and others},
Journal = {Physical review letters},
Journal = {Phys. Rev. Lett.},
Year = {1987},
Number = {9},
Pages = {970},
@@ -145,11 +180,11 @@
}
@TechReport{COMET.2012,
Title = {Experimental Proposal for Phase-I of the COMET
Experiment at J-PARC},
Title = {Experimental Proposal for Phase-I of the COMET Experiment at J-PARC},
Author = {R. Akhmetshin and A. Bondar and L. Epshteyn and
G. Fedotovich and D. Grigoriev and V. Kazanin and A. Ryzhenenkov and
D. Shemyakin and Yu. Yudin and others},
Institution = {KEK},
Year = {2012},
Month = {7},
Number = {KEK/J-PARC-PAC 2012-10},
@@ -273,7 +308,7 @@
@Article{AndreevBanks.etal.2013a,
Title = {Measurement of Muon Capture on the Proton to 1\% Precision and Determination of the Pseudoscalar Coupling g P},
Author = {Andreev, VA and Banks, TI and Carey, RM and Case, TA and Clayton, SM and Crowe, KM and Deutsch, J and Egger, J and Freedman, SJ and Ganzha, VA and others},
Journal = {Physical review letters},
Journal = {Phys. Rev. Lett.},
Year = {2013},
Number = {1},
Pages = {012504},
@@ -307,10 +342,28 @@
Timestamp = {2014-05-02}
}
@Article{AudiWapstra.etal.2003,
Title = {The Ame2003 atomic mass evaluation: (II). Tables, graphs and references },
Author = {G. Audi and A.H. Wapstra and C. Thibault},
Journal = {Nucl. Phys. A},
Year = {2003},
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Owner = {NT},
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}
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Timestamp = {2014-04-24}
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Url = {http://www.sciencedirect.com/science/article/pii/0375947482900495}
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@@ -352,6 +441,22 @@
Timestamp = {2014.02.10}
}
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}
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Timestamp = {2014-04-09}
}
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Timestamp = {2014-04-03}
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}
@TechReport{COMET.2009,
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}
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@@ -1049,7 +1258,6 @@
Pages = {741--757},
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__markedentry = {[NT:]},
Doi = {10.1103/PhysRevC.36.741},
File = {Published version:GadioliGadioli.1987.pdf:PDF},
Issue = {2},
@@ -1150,7 +1358,7 @@
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Timestamp = {2014-04-09}
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}
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Timestamp = {2014-04-01}
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Reportnumber = {SIN-PR-81-12},
Slaccitation = {%%CITATION = NUPHA,A392,385;%%},
Timestamp = {2014-10-16}
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Title = {An Analysis of the Charged Particles Emitted Following Negative Muon Absorptions in Photographic Emulsions},
Author = {Ishii, Chikai},
@@ -1465,7 +1711,7 @@
@Article{KotelchuckTyler.1968,
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}
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Timestamp = {2014-10-16}
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Timestamp = {2014-10-16}
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Primaryclass = {physics},
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Title = {{Exotic Decays of the Muon and Heavy Leptons in Gauge
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@@ -1812,6 +2121,7 @@
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@@ -1856,7 +2166,7 @@
@Article{MeasdayStocki.etal.2007,
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@@ -2284,7 +2594,6 @@
Pages = {135--141},
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__markedentry = {[NT:]},
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File = {Published version:SchlepuetzComiso.etal.1979.pdf:PDF},
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@@ -2348,7 +2657,7 @@
@Article{SobottkaWills.1968,
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@@ -2471,7 +2780,6 @@
Pages = {MOLT007},
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Eprint = {physics/0306116},
File = {arXiv v1:VerkerkeKirkby.2003-eprintv1.pdf:PDF},

21
thesis/thesis.tex
View File

@@ -21,21 +21,22 @@ following nuclear muon capture\\
\vspace{2mm}
for the COMET experiment}
\author{Nam Hoai Tran}
\date{September, 2014}
\date{October, 2014}
\begin{document}
%\begin{frontmatter}
%\input{chapters/frontmatter}
%\end{frontmatter}
\begin{frontmatter}
\input{chapters/frontmatter}
\end{frontmatter}
\mainmatter
%\input{chapters/chap1_intro}
%\input{chapters/chap2_mu_e_conv}
%\input{chapters/chap3_comet}
%\input{chapters/chap4_alcap_phys}
%\input{chapters/chap5_alcap_setup}
%%%\input{chapters/chap1_intro}
\input{chapters/chap2_mu_e_conv}
\input{chapters/chap3_comet}
\input{chapters/chap4_alcap_phys}
\input{chapters/chap5_alcap_setup}
\input{chapters/chap6_analysis}
%\input{chapters/chap7_results}
\input{chapters/chap7_results}
\input{chapters/chap8_conclusions}
\begin{backmatter}
\input{chapters/backmatter}