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\chapter{Data analysis}
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\label{cha:data_analysis}
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\section{Analysis modules}
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\label{sec:analysis_modules}
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A full analysis has not been completed yet, but initial analysis
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based on the existing modules (\cref{tab:offline_modules}) is possible
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thanks to the modularity of the analysis framework.
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\begin{table}[htb]
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\begin{center}
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\begin{tabular}{l p{8cm}}
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\toprule
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\textbf{Module name} & \textbf{Functions}\\
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\midrule
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MakeAnalysedPulses & make a pulse with parameters extracted from
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a waveform\\
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MaxBinAPGenerator & simplest algorithm to get pulse information\\
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TSimpleMuonEvent & sort pulses occur in a fixed time window around the
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muon hits\\
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ExportPulse \& PulseViewer & plot waveforms for diagnostics\\
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PlotAmplitude & plot pulse height spectra\\
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PlotAmpVsTdiff & plot pulse correlations in timing and amplitude\\
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EvdE & identify charged particles using dE/dx\\
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\bottomrule
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\end{tabular}
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\end{center}
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\caption{Available offline analysis modules.}
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\label{tab:offline_modules}
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\end{table}
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The MakeAnalysedPulses module takes a raw waveform, calculates the pedestal
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from a predefined number of first samples, subtracts this pedestal taking
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pulse polarity into account, then calls another module to extract pulse
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parameters. At the moment, the simplest module, so-called MaxBinAPGenerator,
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for pulse information calculation is in use. The module looks for the
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sample that
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has the maximal deviation from the baseline, takes the deviation as pulse
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amplitude and the time stamp of the sample as pulse time. The procedure is
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illustrated on \cref{fig:tap_maxbin_algo}. This module could not account for
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pile-up or double pulses in one \tpulseisland{} in \cref{fig:tap_maxbin_bad}.
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\begin{figure}[htb]
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\centering
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\includegraphics[width=0.85\textwidth]{figs/tap_maxbin_algo}
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\caption{Pulse parameters extraction with MaxBinAPGenerator.}
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\label{fig:tap_maxbin_algo}
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\end{figure}
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\begin{figure}[htb]
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\centering
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\includegraphics[width=0.47\textwidth]{figs/tap_maxbin_bad}
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\includegraphics[width=0.47\textwidth]{figs/tap_maxbin_bad2}
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\caption{Double pulse and pile up are taken as one single pulse by the
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MaxBinAPGenerator}
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\label{fig:tap_maxbin_bad}
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\end{figure}
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The TSimpleMuonEvent first picks a muon candidate, then loops through all
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pulses on all detector channels, and picks all pulses occur in
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a time window of \SI{\pm 10}{\si{\us}} around each candidate to build
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a muon event. A muon candidates is a hit on the upstream plastic scintillator
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with an amplitude higher than a threshold which was chosen to reject MIPs. The
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period of \SI{10}{\si{\us}} is long enough compared to the mean life time of
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muons in the target materials
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(\SI{0.758}{\si{\us}} for silicon, and \SI{0.864}{\si{\us}}
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for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted
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charged particles would be recorded in this time window.
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%\begin{figure}[htb]
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%\centering
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%\includegraphics[width=0.85\textwidth]{figs/tme_musc_threshold}
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%\caption{Pulse height spectrum of the $\mu$Sc scintillator}
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%\label{fig:tme_musc_threshold}
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%\end{figure}
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A pile-up protection mechanism is employed to reject multiple muons events: if
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there exists another muon hit in less than \SI{15}{\si{\us}} from the
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candidate then both the candidate and the other muon are discarded. This
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pile-up protection would cut out less than 11\% total number of events because
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the beam rate was generally less than \SI{8}{\kilo\hertz}.
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%In runs with active silicon targets, another requirement is applied for the
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%candidate: a prompt hit on the target in $\pm 200$ \si{\ns}\ around the
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%time of the $\mu$Sc pulse. The number comes from the observation of the
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%time correlation between hits on the target and the $\mu$Sc
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%(\cref{fig:tme_sir_prompt_rational}).
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%\begin{figure}[htb]
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%\centering
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%\includegraphics[width=0.85\textwidth]{figs/tme_sir_prompt_rational}
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%\caption{Correlation in time between SiR2 hit and muon hit}
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%\label{fig:tme_sir_prompt_rational}
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%\end{figure}
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To make sure that we will analyse good data, a low level data quality checking
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was done on the whole data sets. The idea is plotting the variations of basic
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parameters, such as noise level, length of raw waveforms, pulse rate, time
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correlation to hits on the muon counter on each channel during the data
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collecting period. Runs with significant difference from the averaging
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values were further checked for possible causes, and would be discarded if such
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discrepancy was too large or unaccounted for. Examples of such trend plots are
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shown in \cref{fig:lldq}.
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\begin{figure}[htb]
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\centering
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\includegraphics[width=0.47\textwidth]{figs/lldq_noise}
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\includegraphics[width=0.47\textwidth]{figs/lldq_tdiff}
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\caption{Example trend plots used in the low level data quality checking:
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noise level in FWHM (left) and time correlation with muon hits (right). The
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noise level was basically stable in in this data set, except for one
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channel. On the right hand side, this sanity check helped find out the
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sampling frequency was wrongly applied in the first tranche of the data
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set.}
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\label{fig:lldq}
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\end{figure}
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% section analysis_modules (end)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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This chapter presents initial analysis on subsets of the collected data.
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Purposes of the analysis include:
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\begin{itemize}
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\item testing the analysis chain;
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\item verification of the experimental method, specifically the
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normalisation of number of stopped muons, and particle identification
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using specific energy loss;
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\item extracting a preliminary rate of proton emission from aluminium.
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\end{itemize}
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\section{Charged particles following muon capture on a thick silicon target}
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\label{sec:charged_particles_from_muon_capture_on_silicon_thick_silicon}
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This analysis was done on a subset of the active target runs
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