Final version

analysis/background.tex

@@ -32,7 +32,7 @@ \subsubsection*{Number of reconstructed hits $> 50$}
 
 
 \subsubsection*{Showers energy $>50$~MeV} 
-For the same reason as above, the energy of the showers associated with delta rays of Michel electrons will be peaked at low energies. We require the sum of the energies of the reconstructed showers to be above 50~MeV. In this way we reject a large fraction of the neutrino and cosmic background, without significantly affecting the number of $\nu_e$~CC0$\pi$-Np events, as shown in Figure \ref{fig:shower_energy_integral}.
+For the same reason as above, the energy of the showers associated with delta rays or Michel electrons will be peaked at low energies. We require the sum of the energies of the reconstructed showers to be above 50~MeV. In this way we reject a large fraction of the neutrino and cosmic background, without significantly affecting the number of $\nu_e$~CC0$\pi$-Np events, as shown in Figure \ref{fig:shower_energy_integral}.
 
 \begin{figure}[htbp]
 \centering
@@ -133,7 +133,7 @@ \subsubsection*{Shower distance $d_{s} < 5$~cm}
 \end{figure}
 
 \subsubsection*{Track proton $\chi_{p}^2 < 80$}
-It is possible to perform a $\chi^2$ test on the $dE/dx$ vs. the residual range of the reconstructed track under the hypothesis of a proton stopping in the detector, using the parametrisation of Section \ref{sec:proton_id}. Low values of the $\chi_{p}^2$ score will correspond to proton-like tracks, while a high value will correspond to a MIP-like track. Figure \ref{fig:proton_norm} shows the distributions of the $\chi_{p}^2$ score for background and signal events. Figure \ref{fig:proton_pdg} shows that the protons reconstructed as tracks are peaked around 0 as expected, while the long tail includes muon tracks, photon and electron showers misclassified as tracks, and objects with a misplaced vertex. The comparison between data and Monte Carlo shown in Figure \ref{fig:proton_pdg} and Figure \ref{fig:proton_pot} shows some discrepancies, especially for very low and very high $\chi_{p}^2$ scores. This quantity requires a careful simulation of the signal processing and a correct evaluation of the recombination effect. Our cut is in a region with a good data/Monte Carlo agreement once the systematic uncertainties are taken into account and it is as such deemed safe.
+It is possible to perform a $\chi^2$ test on the $dE/dx$ vs. the residual range of the reconstructed track under the hypothesis of a proton stopping in the detector, using the parametrisation of Section \ref{sec:proton_id}. Low values of the $\chi_{p}^2$ score will correspond to proton-like tracks, while a high value will correspond to a MIP-like track. Figure \ref{fig:proton_norm} shows the distributions of the $\chi_{p}^2$ score for background and signal events. Figure \ref{fig:proton_pdg} shows that the protons reconstructed as tracks are peaked around 0 as expected, while the long tail includes muon tracks, photon and electron showers misclassified as tracks, and objects with a misplaced vertex. The comparison between data and Monte Carlo in Figure \ref{fig:proton_pdg} and Figure \ref{fig:proton_pot} shows some discrepancies, especially for very low and very high $\chi_{p}^2$ scores. This quantity requires a careful simulation of the signal processing and a correct evaluation of the recombination effect. Our cut is in a region with a good data/Monte Carlo agreement once the systematic uncertainties are taken into account and it is as such deemed safe.
 
 \begin{figure}[htbp]
 \centering
@@ -153,7 +153,7 @@ \subsubsection*{Track proton $\chi_{p}^2 < 80$}
 \end{figure}
 
 \subsubsection*{Track-shower angle $\mathrm{cos}\alpha > -0.95$}
-Electrons start producing an appreciable shower in the detector after several centimetres. In this case, the patter recognition often identifies the first part of the shower as a track-like object and the latter part of the shower as a shower-like object. 
+Electrons start producing an appreciable shower in the detector after several centimetres. In this case, the pattern recognition often identifies the first part of the shower as a track-like object and the latter part of the shower as a shower-like object. 
 Furthermore, high-energy cosmic rays can produce a shower in the detector, which will be mostly aligned to a cosmic muon track. In order to remove these mis-reconstructed events and reduce this kind of cosmogenic background we require $\mathrm{cos}\alpha > -0.95$, where $\alpha$ is the angle between the most energetic shower and the track with the lowest proton $\chi_{p}^2$ score.
 Figure \ref{fig:angle_integral} shows that there are, in proportion, more background events with a high angular separation between the tracks and the most energetic shower. This cut allows to reject these events while also ensuring that the signal events are well-reconstructed. In fact, signal events with $\mathrm{cos}\alpha \approx -1$ have almost always an electron shower reconstructed as a track-like object in the first part. The agreement shown in Figure \ref{fig:angle_pot} and Figure \ref{fig:angle_pdg} is good. Future improvements in the shower reconstruction will allow for an increased selection efficiency.
 
@@ -198,7 +198,7 @@ \subsubsection*{Most proton-like track length $L < 80~\mathrm{cm}$}
 \subsubsection{Rectangular cuts selection results}
 The goal of the rectangular cuts is to isolate the $\nu_e$ CC0$\pi$-Np events and increase the purity of our selected sample. However, in order to validate our cuts and verify the agreement between data and Monte Carlo after this stage, it is necessary to select a sufficient number of data events. As mentioned before, in this analysis we require at least one data event in the bins in the $[0.2,1.9]$~GeV range, which is the energy region we are most interested into. 
 
-We select 16 data beam-on events, $2.8\pm0.6$ beam-off events, and $12.4\pm3.0$ simulated events (including $\nu_e$ and $\nu_{\mu}$ interactions), corresponding to $4.34\times10^{19}$~POT . The number of selected $\nu_e$ CC0$\pi$-Np events is $3.2\pm0.8$, which corresponds to a final efficiency of $(10.0\pm0.3~\mathrm{(stat)}\pm0.5~\text{(sys)})\%$. 
+We select 16 data beam-on events, $2.8\pm0.6$ beam-off events, and $12.4\pm3.0$ simulated events (including $\nu_e$ and $\nu_{\mu}$ interactions), corresponding to $4.34\times10^{19}$~POT. The number of selected $\nu_e$ CC0$\pi$-Np events is $3.2\pm0.8$, which gives a final efficiency of $(10.0\pm0.3~\mathrm{(stat)}\pm0.5~\text{(sys)})\%$. 
 
 The purity of the sample is defined as:
 \begin{equation}
@@ -212,7 +212,7 @@ \subsubsection{Rectangular cuts selection results}
   \caption{Purity of the selected sample before (green) and after (orange) the application of the rectangular cuts as a function of the reconstructed energy $E_{\mathrm{deposited}}$. Error bars are statistical only.}\label{fig:purity_sel}
 \end{figure}
 
-It is also possible to calculate the overall purity and the efficiency after each cut, to analyse the effect of each cut (Figure \ref{fig:effpurity_cuts}). The largest purity increase is given by the application of the proton $\chi_{p}^2$ score cut. 
+It is also possible to calculate the overall purity and the efficiency after each cut, to analyse its effec (Figure \ref{fig:effpurity_cuts}). The largest purity increase is given by the application of the proton $\chi_{p}^2$ score cut. 
 
 \begin{figure}[htbp]
 \centering

analysis/energy.tex

@@ -138,7 +138,7 @@ \subsection{Deposited Energy Reconstruction}\label{sec:deposited}
 \label{fig:nucalib}
 \end{figure}
 
-In this analysis, we will use the quantity $E_{\mathrm{deposited}}$ defined in Eq. \ref{eq:deposited} as estimate of the total visible energy in the event.
+In this analysis, we will use the quantity $E_{\mathrm{deposited}}$ defined in Equation \ref{eq:deposited} as estimate of the total visible energy in the event.
 
 \subsection{Deposited energy binning}\label{sec:depositedenergy}
 The binning of the deposited energy distribution must be carefully evaluated, since it is of fundamental importance in the calculation of the significance of an eventual excess. In this analysis, we require the events in a true $E_{\mathrm{k}}$ bin to fall in the same reconstructed $E_{\mathrm{deposited}}$ bin in at least 50\% of the cases for $\nu_e$~CC0$\pi$-Np events. A combination which satisfies this condition and maximises the number of bins in the $[0,3]$~GeV range is:
@@ -164,7 +164,7 @@ \subsection{Measurement of the electromagnetic shower energy loss}\label{sec:ded
 \end{equation}
 where $T_{\mathrm{max}}$ is the maximum possible energy transfer in a single collision, $I$ is the mean excitation energy, and $\delta(\beta\gamma)$ is a density correction. 
 
-In materials of moderate thickness such as LAr, the energy loss probability distribution is described by the asymmetric Landau distribution \cite{Landau:1944if}, which drives the mean of the energy loss of Eq. \ref{eq:bethe} into the tail of the distribution. For this reason, ``the
+In materials of moderate thickness such as LAr, the energy loss probability distribution is described by the asymmetric Landau distribution \cite{Landau:1944if}, which drives the mean of the energy loss of Equation~\ref{eq:bethe} into the tail of the distribution. For this reason, ``the
 mean of the energy loss given by the Bethe equation [\dots] is thus ill-defined
 experimentally and is not useful for describing energy loss by single particles'' \cite{PhysRevD.98.030001}.
 The most probable value of the Landau distribution, which should be used instead, is given by: 
@@ -188,7 +188,7 @@ \subsection{Measurement of the electromagnetic shower energy loss}\label{sec:ded
 
 Subsequently, the $dQ/dx$ for each hit is measured dividing the collected charge ($dQ$) by the pitch ($dx$) between each hit and the next one along the shower direction. The pitch corresponds to the distance in the TPC that a particle travels between its two projections  on adjacent wires, which is \emph{at least} the wire spacing (3~mm for MicroBooNE \cite{Acciarri:2016smi}). Electromagnetic showers aligned with the wire direction correspond to a much larger value of the pitch. 
 
-The $dE/dx$ is calculated from the $dQ/dx$ using the calibration factor measured in Section \ref{sec:showerenergy}, Eq. \ref{eq:calib}.
+The $dE/dx$ is calculated from the $dQ/dx$ using the calibration factor measured in Section \ref{sec:showerenergy}, Equation~\ref{eq:calib}.
 Since the Landau distribution of the $dE/dx$ hit values has an asymmetric tail, we assign to the shower the median (and not the mean) of the $dE/dx$ hit distribution, as an estimation the most probable value. The median metric has been demonstrated in \cite{Acciarri:2016sli} to be to most robust over a variety of box lengths.
 
 \begin{figure}[htbp]

analysis/introduction.tex

@@ -4,7 +4,7 @@
 
 The MicroBooNE detector, being a LArTPC, provides detailed  calorimetry, which makes it possible to measure the $dE/dx$ of ionisation tracks and electromagnetic showers \cite{Acciarri:2016sli}, and excellent granularity, which allows to measure the gap between the neutrino interaction vertex and the start of the electromagnetic shower. These two methods provide powerful electron/photon separation.% and are not normally available in a Cherenkov detector. 
 
-In this chapter we will describe a fully-automated electron neutrino selection using the Pandora multi-algorithm pattern recognition. This is the first fully-automated electron neutrino search in MicroBooNE. The selection will be validated with two orthogonal side-bands and with an independent sample of events acquired with the NuMI beam. The systematic uncertainties will evaluated in Chapter \ref{sec:systematics} and the current sensitivity to the MiniBooNE low-energy excess in the electron hypothesis will be estimated in Chapter \ref{sec:sensitivity}.
+In this chapter we will describe a fully-automated electron neutrino selection using the Pandora multi-algorithm pattern recognition. This is the first fully-automated electron neutrino search in a LArTPC. The selection will be validated with two orthogonal side-bands and with an independent sample of events acquired with the NuMI beam. The systematic uncertainties will evaluated in Chapter \ref{sec:systematics} and the current sensitivity to the MiniBooNE low-energy excess in the electron hypothesis will be estimated in Chapter \ref{sec:sensitivity}.
 
 \section{Signal definition}
 The MiniBooNE experiment showed an excess of CCQE-like events in the 200-475~MeV neutrino energy range \cite{Aguilar-Arevalo:2018gpe}, therefore this analysis will focus on a similar topology.
@@ -22,7 +22,7 @@ \section{Signal definition}
 \end{description}
 
 
-As an example, figure \ref{fig:evd} shows a simulated $\nu_{e}$ CC0$\pi$-Np event display on the collection plane with an electron and two protons in the final state, with the corresponding reconstructed shower and reconstructed tracks. In this case, the patter recognition is able to correctly identify the electromagnetic shower and both proton tracks.
+As an example, Figure \ref{fig:evd} shows a simulated $\nu_{e}$ CC0$\pi$-Np event display on the collection plane with an electron and two protons in the final state, with the corresponding reconstructed shower and reconstructed tracks. In this case, the patter recognition is able to correctly identify the electromagnetic shower and both proton tracks.
 
 \begin{figure}[htbp]
 	\begin{center}

analysis/methodology.tex

@@ -40,7 +40,7 @@ \subsection{Overview of the analysis}
 \begin{figure}[htbp]
 \centering
   \includegraphics[width=0.9\linewidth]{figures/selection.png}
-  \caption{Schematics of the $\nu_e$ CC0$\pi$-Np event selection stages.}
+  \caption{Schematics of the $\nu_e$ CC0$\pi$-Np event selection stages, from the cosmic-ray removal to the rejection of the neutrino and cosmogenic backgrounds.}
   \label{fig:selection}
 \end{figure}
 
@@ -278,11 +278,11 @@ \subsection{Selection performances in BNB events}\label{sec:numu}
 The background caused by the neutrino interactions happening outside the cryostat has been evaluated using the \emph{dirt} sample.
 We divide the selected events (signal and background) into 8 categories:
 \paragraph{Signal}
-\begin{description}
-\item[beam intrinsic $\nu_{e}$ CC$0\pi$-Np:] charged-current $\nu_{e}$ neutrino interaction, at least one proton (N > 1), one electron, and no other visible particles above detection threshold. This category represents the signal of our analysis.
+\begin{description}[labelindent=1cm]
+\item[Beam intrinsic $\nu_{e}$ CC$0\pi$-Np:] charged-current $\nu_{e}$ neutrino interaction, at least one proton (N > 1), one electron, and no other visible particles above detection threshold. This category represents the signal of our analysis.
 \end{description}
 \paragraph{Backgrounds}
-\begin{description}
+\begin{description}[labelindent=1cm]
 \item[Beam intrinsic $\nu_{e}$ CC:] charged-current $\nu_{e}$ neutrino interaction that is not $\nu_{e}$ CC$0\pi$-Np or where the electron or protons were below the detection threshold defined above.
 \item[Beam intrinsic $\nu_{\mu}$:] charged-current $\nu_{\mu}$ neutrino interaction.
 \item[Beam intrinsic NC:] neutral current neutrino interaction (both $\nu_{\mu}$ and $\nu_{e}$).

analysis/validation.tex

@@ -29,28 +29,32 @@ \subsubsection{NC-enhanced selection}
 It is possible to enhance the neutral-current component (defined as \emph{beam intrinsic NC} in our analysis) by (1) inverting the cut on the shower $dE/dx$, and (2) removing the cut on the shower distance (see Figures \ref{fig:dedx_norm}, \ref{fig:showerd_norm}). The $dE/dx$ of the most energetic shower must be within 3.2~MeV/cm and 5~MeV/cm to select electromagnetic cascades that were initiated by a photon. It also ensures that this NC-enhanced sample is orthogonal to the $\nu_{e}$ CC0$\pi$-Np selected sample. The cut on the shower distance is removed to include events where the photon conversion is far from the neutrino interaction vertex.
 Thus, our final sample will mainly contain NC events, with some contamination of $\nu_{\mu}$ CC$\pi^{0}$ events where the muon track was tagged as a proton-like track.
 
-Figure \ref{fig:photon} shows the comparison between data and Monte Carlo for the reconstructed energy spectrum $E_{deposited}$ of the NC-enhanced event spectrum. The agreement is good both in shape and normalisation: the data points are within the systematic uncertainties of the simulation in every bin.
-%The reconstructed energy $E_{corr}$ here corresponds to the sum of the reconstructed energies of the shower-like objects and the reconstructed energies of the track-like objects $E_{corr} = E_{corr}^{p}+E_{corr}^{e}$.
-
 \begin{figure}[htbp]
 \centering
   \includegraphics[width=0.7\linewidth]{figures/nc_reco.pdf}
   \caption{Reconstructed energy spectrum of the events selected with the NC-enhanced reverse cuts. The black points represent the data with statistical uncertainties. The coloured stacked histograms represent the simulated events, with the hatched histogram corresponding to the data beam-off sample. The shaded area represents the systematic uncertainty.}\label{fig:photon}
 \end{figure}
 
+Figure \ref{fig:photon} shows the comparison between data and Monte Carlo for the reconstructed energy spectrum $E_{deposited}$ of the NC-enhanced event spectrum. The agreement is good both in shape and normalisation: the data points are within the systematic uncertainties of the simulation in every bin.
+%The reconstructed energy $E_{corr}$ here corresponds to the sum of the reconstructed energies of the shower-like objects and the reconstructed energies of the track-like objects $E_{corr} = E_{corr}^{p}+E_{corr}^{e}$.
+
+
+
 \subsubsection{CC \texorpdfstring{$\nu_{\mu}$}{numu}-enhanced selection}
 It is possible to enhance the presence of the CC $\nu_{\mu}$ background (defined as \emph{beam intrinsic $\nu_{\mu}$} in our analysis) by (1) removing the cut on the total number of hits in the collection plane, (2) removing the cut on the fraction of shower hits, (3) requiring a minimum track length, (4) requiring at least a track with $40 < \chi_p^{2} < 220$ (muon-like track), and (5) requiring that the event is selected by the external $\nu_{\mu}$ CC-inclusive analysis \cite{ubxsec} (see Figures \ref{fig:nhits_integral}, \ref{fig:ratio_norm}, \ref{fig:length_norm}, and \ref{fig:proton_norm}). Also in this case the CC $\nu_{\mu}$-enhanced sample will be orthogonal to the $\nu_{e}$ CC0$\pi$-Np selected sample.
 A CC $\nu_{\mu}$ event has, by definition, a muon in the final state: as such, requiring a track length larger than 20~cm and changing the cut on the proton $\chi^2_p$ score decreases our muon-rejection power. The goal of the external analysis is to select CC $\nu_{\mu}$ events, so instead of vetoing those events as described in Section \ref{sec:numu}, we invert this requirement by allowing only these events.
 
-Figure \ref{fig:numu_inverted} shows the agreement between data and Monte Carlo for the reconstructed energy spectrum of the CC $\nu_{\mu}$-enhanced event sample.
-The agreement is good both in shape and normalisation: the data points are within the systematic uncertainties of the simulation in every bin.
-
 \begin{figure}[htbp]
 \centering
   \includegraphics[width=0.7\linewidth]{figures/numu_reco.pdf}
   \caption{Reconstructed energy spectrum of the events selected with the CC~$\nu_{\mu}$-enhanced reverse cuts. The black points represent the data with statistical uncertainties. The coloured stacked histograms represent the simulated events, with the hatched histogram corresponding to the data beam-off sample. The shaded area represents the systematic uncertainty. The bottom part of the plot shows the ratio between the data beam-on events and the stacked histograms.}\label{fig:numu_inverted}
 \end{figure}
 
+Figure \ref{fig:numu_inverted} shows the agreement between data and Monte Carlo for the reconstructed energy spectrum of the CC $\nu_{\mu}$-enhanced event sample.
+The agreement is good both in shape and normalisation: the data points are within the systematic uncertainties of the simulation in every bin.
+
+
+
 % \subsection{Future Validation Studies}
 
 % \subsubsection{Cosmic-ray studies}