73 lines
3.6 KiB
TeX
73 lines
3.6 KiB
TeX
\chapter{Results and discussions}
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\label{cha:results_and_discussions}
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\section{Verification of the experimental method}
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\label{sec:verification_of_the_experimental_method}
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\subsection{Number of stopped muons calculation}
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\label{sub:number_of_stopped_muons_normalisation}
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The number of stopped muons calculated from the muonic X-ray spectrum is shown
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to be consistent with that calculated from the active target spectrum. This
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proves the validity of normalisation using muon X-ray measurement.
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\subsection{Particle identification and unfolding}
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\label{sub:particle_identification_and_unfolding}
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The particle identification using specific energy loss using cut on
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likelihood probability is shown in
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\cref{sub:event_selection_for_the_passive_targets}. Since the distribution of
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$\Delta E$ at a given $E$ is not Gaussian, the fraction of protons that do not
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make the cut is 0.5\%, much larger than the threshold at \num{1E-4}. However,
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that missing fraction is small compared to the statistical uncertainty of the
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measurement (2.3\%) so the threshold is sufficient.
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The observed spectra on the two silicon arms reflect the muon stopping
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distribution discussed in \cref{sub:momentum_scan_for_the_100_} where more
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muons stopped at the downstream side of the target. The proton yields
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calculated from two arms are consistent with each other, and show that the muon
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stopping distribution used to generate the response matrices is reasonable.
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\section{Emission rate of protons and the COMET Phase I's CDC}
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\label{sec:emission_rate_of_protons_and_the_comet_phase_i_s_cdc}
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The proton emission rate from the 100-\si{\um} aluminium target is
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$(3.5 \pm 0.2)$\%. This rate is significantly larger than the calculation rate
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of 0.97\% by Lifshitz and Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980}.
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The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in
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\eqref{eqn:wyttenbach_ratio}.
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The rate smaller that the proton emission rate from silicon of
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5.3\%~\cite{Measday.2001} which is expected since an odd-odd nucleus as
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$^{28}$Al is less stable than an even-odd one.
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For the COMET Phase I experiment, the emission rate of 3.5\% is about 5 times
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smaller than the figure using to design the CDC. The measured spectrum shape
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peaks around \SI{4}{\MeV} rather than \SI{2.5}{\MeV} in the silicon
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spectrum(\cref{fig:sobottka_spec}). Therefore the proton hit rate on the CDC
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should be smaller than the current estimation.
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The CDC proton hit rate is calculated by a toy MC study. The protons with the
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energy spectrum as the parameterisation in \cref{sub:proton_emission_rate} are
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generated inside the COMET's muon stopping targets which are 17
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200-\si{\um}-thick aluminium discs. A proton absorber made of CFRP is placed
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\SI{5}{\cm} far from the inner wall of the CDC.
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A muon stopping rate of \SI{1.3E9}{\Hz} is assumed as in the COMET Phase I's
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TDR. The number of proton emitted is then $\num{1.3E9} \times 0.609 \times
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0.035 = \SI{2.8E7}{\Hz}$. The hit rates on a single cell in the inner most
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layer due to these protons with
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different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}.
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\begin{table}[htb]
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\begin{center}
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\begin{tabular}{l r}
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\toprule
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\textbf{Absorber thickness} & \textbf{Hit rate}\\
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\midrule
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\SI{1}{\mm} & \SI{2}{\Hz}\\
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\SI{0.5}{\mm} & \SI{126}{\Hz}\\
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\SI{0}{\mm} & \SI{1436}{\Hz}\\
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\bottomrule
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\end{tabular}
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\end{center}
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\caption{CDC proton hit rates}
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\label{tab:proton_cdc_hitrate}
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\end{table}
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The proton hit rate even without the absorber is only \SI{1.4}{\kHz}, much
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smaller than the current estimation of \SI{11}{\kHz} (using 1-mm-thick
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absorber). Therefore a proton absorber is not needed for the COMET Phase I's
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CDC.
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