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thesis/chapters/chap1_intro.tex

@@ -83,6 +83,6 @@ 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:results_and_discussions}.
 
 % chapter introduction (end)

thesis/chapters/chap6_analysis.tex

@@ -343,9 +343,9 @@ calculated as:
 where $\Delta E_{\textrm{meas.}}$ is energy deposition measured by the thin
 silicon detector by a certain  proton at energy $E_i$, $\Delta E_i$  and
 $\sigma_{\Delta E}$ are the expected and standard deviation of the energy loss
-caused by the proton calculated by MC study. A threshold is set to extract
+caused by the proton calculated by MC study. A threshold is set at \num{1E-4} to
-protons at 0.011 (equivalent to $3\sigma_{\Delta E}$), the band of protons is
+extract protons, the resulted band of protons is shown in
-shown in (\cref{fig:al100_protons}).
+(\cref{fig:al100_protons}).  
 \begin{figure}[htb]
   \centering
     \includegraphics[width=0.47\textwidth]{figs/al100_protons}
@@ -510,9 +510,15 @@ The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore:
 
 The total proton emission rate can be estimated by assuming a spectrum shape
 with the same parameterisation as in \eqref{eqn:EH_pdf}. The fit parameters
-are shown in . With such parameterisation, the integration in
+are shown in \cref{fig:al100_parameterisation}. With such parameterisation, the
-range from \SIrange{4}{8}{\MeV} is 51\% of the total number of protons. The
+integration in range from \SIrange{4}{8}{\MeV} is 51\% of the total number of
-total proton emission rate is therefore $3.5\times 10^{-2}$.
+protons. The total proton emission rate is therefore $3.5\times 10^{-2}$.
+\begin{figure}[htb]
+  \centering
+  \includegraphics[width=0.85\textwidth]{figs/al100_parameterisation}
+  \caption{Fitting of the unfolded spectra.}
+  \label{fig:al100_parameterisation}
+\end{figure}
 
 \subsection{Uncertainties of the emission rate}
 \label{sub:uncertainties_of_the_emission_rate}

thesis/chapters/chap7_results.tex

@@ -2,13 +2,71 @@
 \label{cha:results_and_discussions}
 \section{Verification of the experimental method}
 \label{sec:verification_of_the_experimental_method}
-
+\subsection{Number of stopped muons calculation}
-\subsection{Number of stopped muons normalisation}
 \label{sub:number_of_stopped_muons_normalisation}
-
+The number of stopped muons calculated from the muonic X-ray spectrum is shown
+to be consistent with that calculated from the active target spectrum. This
+proves the validity of normalisation using muon X-ray measurement.
 \subsection{Particle identification and unfolding}
 \label{sub:particle_identification_and_unfolding}
+The particle identification using specific energy loss using cut on
+likelihood probability is shown in
+\cref{sub:event_selection_for_the_passive_targets}. Since the distribution of
+$\Delta E$ at a given $E$ is not Gaussian, the fraction of protons that do not
+make the cut is 0.5\%, much larger than the threshold at \num{1E-4}. However,
+that missing fraction is small compared to the statistical uncertainty of the
+measurement (2.3\%) so the threshold is sufficient. 
+
+The observed spectra on the two silicon arms reflect the muon stopping
+distribution discussed in \cref{sub:momentum_scan_for_the_100_} where more
+muons stopped at the downstream side of the target. The proton yields
+calculated from two arms are consistent with each other, and show that the muon
+stopping distribution used to generate the response matrices is reasonable.
 
 \section{Emission rate of protons and the COMET Phase I's CDC}
 \label{sec:emission_rate_of_protons_and_the_comet_phase_i_s_cdc}
+The proton emission rate from the 100-\si{\um} aluminium target is 
+$(3.5 \pm 0.2)$\%. This rate is significantly larger than the calculation rate
+of 0.97\% by Lifshitz and Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980}.
+The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in
+\eqref{eqn:wyttenbach_ratio}.
+The rate smaller that the proton emission rate from silicon of
+5.3\%~\cite{Measday.2001} which is expected since an odd-odd nucleus as
+$^{28}$Al is less stable than an even-odd one.
 
+For the COMET Phase I experiment, the emission rate of 3.5\% is about 5 times
+smaller than the figure using to design the CDC. The measured spectrum shape
+peaks around \SI{4}{\MeV} rather than \SI{2.5}{\MeV} in the silicon
+spectrum(\cref{fig:sobottka_spec}). Therefore the proton hit rate on the CDC
+should be smaller than the current estimation.
+
+The CDC proton hit rate is calculated by a toy MC study. The protons with the
+energy spectrum as the parameterisation in \cref{sub:proton_emission_rate} are
+generated inside the COMET's muon stopping targets which are 17
+200-\si{\um}-thick aluminium discs. A proton absorber made of CFRP is placed
+\SI{5}{\cm} far from the inner wall of the CDC.
+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 thickness are shown in \cref{tab:proton_cdc_hitrate}.
+\begin{table}[htb]
+  \begin{center}
+    \begin{tabular}{l r}
+      \toprule
+      \textbf{Absorber thickness} & \textbf{Hit rate}\\
+      \midrule 
+      \SI{1}{\mm} & \SI{2}{\Hz}\\
+      \SI{0.5}{\mm} & \SI{126}{\Hz}\\
+      \SI{0}{\mm} & \SI{1436}{\Hz}\\
+      \bottomrule
+    \end{tabular}
+  \end{center}
+  \caption{CDC proton hit rates}
+  \label{tab:proton_cdc_hitrate}
+\end{table}
+
+The proton hit rate even without the absorber is only \SI{1.4}{\kHz}, much
+smaller than the current estimation of \SI{11}{\kHz} (using 1-mm-thick
+absorber). Therefore a proton absorber is not needed for the COMET Phase I's
+CDC.

thesis/thesis.tex

@@ -29,13 +29,14 @@ for the COMET experiment}
 \end{frontmatter}
 
 \mainmatter
-%\input{chapters/chap1_intro}
+\input{chapters/chap1_intro}
-%\input{chapters/chap2_mu_e_conv}
+\input{chapters/chap2_mu_e_conv}
-%\input{chapters/chap3_comet}
+\input{chapters/chap3_comet}
-%\input{chapters/chap4_alcap_phys}
+\input{chapters/chap4_alcap_phys}
-%\input{chapters/chap5_alcap_setup}
+\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}