diff --git a/thesis/chapters/chap1_intro.tex b/thesis/chapters/chap1_intro.tex index 6c2749e..d67d927 100644 --- a/thesis/chapters/chap1_intro.tex +++ b/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) diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index 0bd4bae..e1d0462 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/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 -protons at 0.011 (equivalent to $3\sigma_{\Delta E}$), the band of protons is -shown in (\cref{fig:al100_protons}). +caused by the proton calculated by MC study. A threshold is set at \num{1E-4} to +extract protons, the resulted band of protons is shown in +(\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 -range from \SIrange{4}{8}{\MeV} is 51\% of the total number of protons. The -total proton emission rate is therefore $3.5\times 10^{-2}$. +are shown in \cref{fig:al100_parameterisation}. With such parameterisation, the +integration in range from \SIrange{4}{8}{\MeV} is 51\% of the total number of +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} diff --git a/thesis/chapters/chap7_results.tex b/thesis/chapters/chap7_results.tex index 0e8d39e..39b77bd 100644 --- a/thesis/chapters/chap7_results.tex +++ b/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 normalisation} +\subsection{Number of stopped muons calculation} \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. diff --git a/thesis/thesis.tex b/thesis/thesis.tex index 9aa2d7b..2348c75 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -29,13 +29,14 @@ for the COMET experiment} \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}