Search for Electron Neutrinos in Multiple Topologies with the Microboone Experiment

Search for Electron Neutrinos in Multiple Topologies with the MicroBooNE Experiment

MICROBOONE-NOTE-1085-PUB

The MicroBooNE Collaboration

June 23, 2020

Abstract This note presents the status of the measurement of electron neutrinos from the Fermilab Booster Neutrino Beamline (BNB) with the MicroBooNE experiment. The analysis is aimed at investigating the nature of the low energy excess of electromagnetic activity observed by the MiniBooNE experiment. The νe event selection relies on topological and calorimetric information to characterise particles produced in these interactions, leveraging the Pandora multi-algorithm reconstruction framework as well as custom particle identification and pattern recognition tools. Results presented in this note use 5.88 × 1020 protons on target of data collected between 2015 and 2018. These include the performance of particle identification tools for µ/p and e/γ separation, along with electromagnetic shower calibration with the largest sample of π0 events measured on argon. Progress towards the completion of this analysis is shown through the measurement of high-energy charged-current νe interactions and their kinematic distributions using both inclusive (1eX) and exclusive (1e0p0π and 1eNp0π) channels. Measurements of charged-current νµ interactions aimed at constraining flux and cross-section systematic uncertainties are also shown. We present the analysis’ preliminary sensitivity of an electron-like signal hypothesis to the MiniBooNE excess which includes flux, cross-section, and detector systematic uncertainties.

1 Contents

1 Introduction 3

2 Analysis Approach3

3 Event Reconstruction and Analysis Tools4

4 Electron Neutrino Event Selection7

5 Muon Neutrino Constraint, Systematics, and Analysis Sensitivity 13

6 Selected Electron Neutrinos at High Energy 15

7 Conclusions 16

A Measuring Electron Neutrinos with Particle Identiﬁcation in the MicroBooNE LArTPC for sensitivity to new Physics 17

B Charged-Current Electron Neutrino Measurement with the MicroBooNE De- tector 20 B.1 Electron identiﬁcation...... 23 B.2 Charged-Current Electron Neutrino Event Selection...... 25 B.3 High-Energy Sideband...... 29

C Constraining Systematic Uncertainties for the Electron Neutrino Search at Mi- croBooNE 31 C.1 Event Selection...... 31 C.2 Systematics and Constraint...... 31 C.3 Sensitivity Estimation...... 34

D Measurement of Single Electron Events in MicroBooNE 37

E νe 1eNp Event Displays 39

2 1 Introduction

This document presents the first measurement of electron neutrinos from the Fermilab Booster Neutrino Beamline with the MicroBooNE experiment, and presents the status of the analysis aimed at investigating the low energy excess of electromagnetic activity observed by the MiniBooNE collaboration [1]. MicroBooNE [2] is a liquid argon time projection chamber (LArTPC) collecting data in the same neutrino beamline as MiniBooNE. LArTPC detectors provide detailed topological images of neutrino interactions and calorimetric information about the particles produced in these interactions. This analysis uses the unique capabilities of LArTPCs to perform a high purity measurement of electron neutrinos across multiple signal topologies and a broad range of energies. Background and modeling uncertainties are constrained using data-driven measurements of muon neutrino charged and neutral current interactions. These allow this analysis to test the electron neutrino hypothesis of the MiniBooNE low energy excess. This document presents a brief overview of the analysis, and results from data-sets and sidebands accessed so far in the analysis. The various appendices go into more detail on several key components to this analysis. Each appendix is associated to a specific poster being presented√ at the Neutrino 2020 conference. Throughout this document we use N for the statistical error bar of the data points. plots which show POT-normalized data/MC comparisons show shaded error bands which include ν flux and cross-section uncertainties as well as statistical uncertainties on the MC sample statistics used in the analysis. Detector systematics, while not included in the data/MC ratio plots, are included in the sensitivity estimation reported. Finally, we note that the assessment of systematic uncertainties in this work is preliminary and not finalized.

2 Analysis Approach

Resolving whether the anomalous excess of electromagnetic showers observed by the MiniBooNE collaboration is caused by electrons or photons is the first necessary step in understanding its origin. The primary goal of this analysis is to measure νe interactions with the MicroBooNE detector in the same beamline, and thus contribute to testing the hypothesis of an excess of electron-like events as the origin of the MiniBooNE anomaly. This analysis aims to make a high purity measurement of electron neutrinos across the full spectrum of neutrino energy at the BNB. This analysis does not rely on the kinematics of the νe interaction, and the modelling of final-state particle kinematics. Instead calorimetric and topological information from the final state particles are used. This means that if an anomalous signal is observed, the neutrino interaction kinematics may be used to further understand it. Several event topologies, both with and without visible hadronic activity, are selected. The predicted event distribution of events broken down by expected number of protons and pions is shown in Figure1.

3 MicroBooNE MC 10.1E20 POT

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Figure 1: Expected rate of charged current electron neutrino interactions in the BNB broken into topologies with diﬀerent numbers of protons and pions. Here N > 0. The Proton On Target (POT) to which this plot is normalized corresponds to the dataset collected by MicroBooNE in the ﬁrst four years of running.

Different final-state topologies contribute to the total intrinsic νe spectrum. This analysis aims to measure the rate of pion-less νe events in order to match MiniBooNE’s νe signal definition. Two exclusive selections are developed: one selecting events with no hadronic activity (1e0p0π, or zero- proton), and one with > 0 final state protons and no pions (1eNp0π, or N-proton, N > 0). The two mutually exclusive channels benefit from orthogonal selections which target topological features and backgrounds specific to each one in a tailored way. These two exclusive channels are then combined into a single measurement testing the sensitivity to an electron-like MiniBooNE anomaly. At the same time, the analysis also includes a fully inclusive measurement of νe interactions, which is able to more efficiently select νe events at higher energy and providing a high-statistics measurement of electron kinematics which provides additional validation to the analysis. While the analysis presented here aims to perform a broad and kinematically unbiased measurement of νe events in the BNB, we rely on a specific model choice to test the analysis’ sensitivity to an electron-like MiniBooNE excess. This model is described in ref. [3] and is obtained by unfolding the observed MiniBooNE low-energy excess through the MiniBooNE νe energy-response matrix from simulation, and applied to MicroBooNE’s simulation as an energy-dependent scaling of BNB νe events.

3 Event Reconstruction and Analysis Tools

The analysis relies on a broad set of tools that aim to isolate neutrino interactions and subsequently νe events in the MicroBooNE data-set. It beneﬁts from a rich reconstruction and calibration carried out with the MicroBooNE experiment. The reconstruction used as input to the analysis is performed with the Pandora pattern-recognition framework [4]. MicroBooNE’s location on the surface means there is a large rate of cosmic-ray interactions which continuously occur in the TPC volume. Combined with the slow charge drift time in the

4 TPC, this leads to a 104 : 1 cosmic-to-neutrino event rate, making cosmic-ray rejection a critical first step in the analysis. Triggering, together with a dedicated set of tools which aim to combine information from the TPC pattern recognition with timing and position information provided by scintillation light collected with MicroBooNE’s PMT array allow for a factor of 104 cosmic-rejection. The efficiency in selecting neutrino candidates relative to this level of cosmic-rejection and for the various selections presented in this analysis is shown in Figure2. These efficiencies are at or above 80% above 0.5 GeV, and decrease to 70% in the range 0.2-0.5 GeV.

MicroBooNE Simulation, Preliminary MicroBooNE Simulation, Preliminary MicroBooNE Simulation, Preliminary Efficiency 0p0 Efficiency Np0 (N>0) Efficiency NpM (M>0) 1.0 1.0 1.0

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0.2 0.2 0.2 e CC : 80.9% e CC : 83.2% e CC : 86.0% CC : 80.2% CC : 83.0% CC : 86.2% 0.0 0.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 True neutrino energy [GeV] True neutrino energy [GeV] True neutrino energy [GeV]

Figure 2: The performance of the cosmic removal tools as a function of the true neutrino energy for the topologies considered in the νe CC selection: no vertex activity (left), protons at vertex (middle) and pion production (right) channels. The energy range is 0 GeV to 3 GeV and the bin size is 200 MeV. Shaded bands in the plots represent the statistical error on the measured eﬃciency. The legend shows the integrated eﬃciency of all BNB simulated νe CC and νµ CC events.

After having identified neutrino interaction candidates, reconstructing individual final state particles becomes crucial in order to determine the neutrino flavor (νe vs. νµ), energy, and event kinematics. Identifying electron neutrinos in the BNB beamline is made particularly challenging 2 by the small νe beam component, sub-dominant to the νµ flux by more than a factor of 10 [5]. This analysis in particular, aiming to measure electron neutrino interactions at low energy, needs to overcome the challenges [6] associated to reconstructing O(100) MeV electromagnetic showers produced by sub-GeV νes. This analysis combines the output of Pandora’s generic pattern-recognition tools with a robust calibration program [7,8] and additional 3D particle tracking tools to provide the particle-identification needed to isolate electron neutrino events. High granularity spatial calorimetric information from all three TPC wire-planes provides the input necessary to perform the particle-identification necessary to the analysis. Figure 3a shows the measured energy loss as a function of residual range for a combination of muon and proton candidates in data. This information is employed in a likelihood-based particle ID algorithm focused on muon-proton separation. The performance of this algorithm is shown in Figure 3b, where one can see the clear separation of highly ionizing protons from lower dE/dx muons or pions. In order to improve the electron identification, hits in the initial shower trunk are identified and fit with a track hypothesis; this technique allows for a more precise determination of the dE/dx at the shower start. Further details on the particle identification (PID) tools developed for this analysis are presented in AppendicesA and B.1.

5 Reconstructed tracks in data Beam ON fully contained, track score > 0.8 only tracks with 0.3 cm <= track pitch Y < 1 cm Collection plane MicroBooNE Preliminary 20 Proton Muon 15

5 dE/dx [MeV/cm]

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(a) dE/dx vs. residual range for tracks in reconstructed neutrino interactions in data.

Trk-score > 0.5 trk-vtx distance < 5 cm, start-end fiducial MicroBooNE Preliminary BNB 4.054e19 POT

DATA ON - OFF 1000 cosmic 800 muon Area normalised pion 600 proton photon 400 Entries / 0.04 200

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(b) PID variable score on data and simulation.

Figure 3: Top: distribution of dE/dx vs. residual range for contained tracks from neutrino interactions recorded in MicroBooNE’s data corresponding to 4.054 × 1019 POT. Bottom: distribution of the log-likelihood-ratio PID variable for neutrino-induced tracks well contained in the fiducial volume. This plot is shown after off-beam subtraction,6 and area-normalized. Reconstructing electromagnetic showers is another crucial aspect of the analysis. High statistics 0 π events, though a background to the νe selection, provide a valuable source for validating the reconstruction and calibration of electromagnetic showers and their energy scale. Figure4 shows the reconstructed Mγγ obtained leveraging the same tools used in the electron neutrino selection. The good agreement between data and simulation, and the alignment between the distribution’s peak with the expected 135 MeV π0 mass help build confidence in the tools used in the analysis.

0 selection 350 MicroBooNE Preliminary 5.89e+20 POT

e CC0 0p: 0.8 CC: 182.9 0 300 e CC0 Np: 3.0 NC : 462.8 e CC: 10.2 CC 0: 1298.2 250 Out. fid. vol.: 41.0 EXT: 210.2 NC: 47.5 BNB: 2452 Cosmic: 107.2 200

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0 Figure 4: Reconstructed Mγγ for candidate π events. The shower energy reconstruction and calibration is performed following the methods of ref. [6]. This plot, aimed to validate shower energy reconstruction, is produced by area normalizing the data and MC distributions scaling the MC π0 contribution.

4 Electron Neutrino Event Selection

The two exclusive channels used in this analysis share a common pre-selection which requires the presence of a contained electromagnetic shower with greater than 70 MeV of energy. This pre- selection suppresses a large fraction of νµ charged current and oﬀ-beam backgrounds, with the energy-cut designed speciﬁcally to remove the frequent Michel electrons from muon decay produced in both cosmic and neutrino interactions. At this stage the 1e0p and 1eNp selections diverge based on whether a reconstructed track associated with the neutrino interaction is found in the event. This requirement makes the two selections fully orthogonal.

7 1000 350 MicroBooNE Preliminary 4.08e+19 POT MicroBooNE Preliminary 4.08e+19 POT

Out. fid. vol.: 56.1 e CC: 11.9 Out. fid. vol.: 36.5 e CC: 4.3 NC: 71.4 e CC0 0p: 4.7 300 NC: 49.6 e CC0 0p: 3.6 0 800 Cosmic: 174.4 e CC0 Np: 18.6 CC : 93.6 e CC0 Np: 14.0 CC: 228.4 MiniBooNE LEE: 4.7 250 Cosmic: 105.8 MiniBooNE LEE: 3.7 CC 0: 256.8 EXT: 451.7 NC 0: 107.0 EXT: 283.0 0 BNB: 1537 BNB: 900 600 NC : 261.7 CC: 160.0 200

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(a) number of showers. (b) number of tracks.

Figure 5: Number of reconstructed showers (left) and tracks (right) after pre-selection. The plot showing the number of tracks is produced further requiring a single reconstructed shower. The number of contained tracks is used to split between the zero and N-proton selections maintaining orthogonality.

After the common pre-selection, backgrounds still dominate over νe events by almost two orders of magnitude, with π0s contributing to about half of the total background events. A series of additional variables and tools are deﬁned to isolate and identify νe interactions. Variables are shared across the zero and N-proton selections, though variables related to proton track candidates are not used in the 1e0p selection. The choice of variables focuses on isolating νe events based on their topological and calorimetric features while limiting reliance on kinematic variables, and possible neutrino interaction modelling dependence. • Cosmic Ray rejection In order to suppress the cosmic background and to select well reconstructed neutrino interactions, all events in this analysis are required to be contained in the TPC. In addition, the proximity of electromagnetic showers to nearby cosmic-ray muons is leveraged as a way to reduce backgrounds induced by cosmic-ray muon Bremmstrahlung showers which are frequently produced in the detector. For events with one or more track, a further requirement that the longest track has a proton-like PID is very eﬀective for the suppression of cosmic-ray muon interactions.

• νµ rejection At low energies, track/shower separation is challenging due to the track-like appearance of O(100) MeV electromagnetic showers. Conversely, low-energy muons and pions which decay producing a Michel electron may be incorrectly reconstructed as a single electromagnetic shower. To reject low-energy track backgrounds to the νe selections, additional variables are constructed with the goal of characterising electromagnetic showers and adding discriminating power complementary to the track/shower classiﬁcation available from Pandora. These variables measure the number of subclusters (Figure 23c) in the shower, the shower Moliere angle (an analysis-deﬁned term aimed to measure the transverse dimension of

8 the shower), and the fraction of hits in the track fit of the shower relative to the total number of hits in the shower (Figure 23a). • π0 rejection The number of reconstructed electromagnetic showers and shower trunk dE/dx are powerful in suppressing π0 backgrounds. For the 1eNp selection, the conversion distance between the proton candidate start point and the electron start point provides an additional powerful discriminant. To mitigate reconstruction deficiencies associated with either uniden- tified low energy sub-leading γ showers or highly co-linear γ pairs, additional variables are defined which aim to identify missing “second showers” and identify merged or overlapping γ showers. Comparisons of data to MC for two of these variables are shown in Figure6.

MicroBooNE Preliminary 4.08e+19 POT 250 MicroBooNE Preliminary 4.08e+19 POT 200 Out. fid. vol.: 35.8 e CC: 3.3 Out. fid. vol.: 36.5 e CC: 4.3 NC: 49.2 e CC0 0p: 2.7 NC: 49.6 e CC0 0p: 3.6 0 0 CC : 88.6 e CC0 Np: 11.1 200 CC : 93.7 e CC0 Np: 14.0 NC 0: 101.6 MiniBooNE LEE: 3.7 Cosmic: 105.8 MiniBooNE LEE: 3.7 150 Cosmic: 102.6 EXT: 272.9 NC 0: 107.1 EXT: 283.1 CC: 159.4 BNB: 875 CC: 160.2 BNB: 901 150

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(a) Number of subclusters in the shower. (b) Fraction of hits in shower-trunk track ﬁt.

Figure 6: Comparison of data and simulation for selected electron neutrino selection variables at pre-selection for events with one shower, and any number of tracks.

These tools are used to deﬁne a series of cuts and are also employed in boosted decision trees (BDTs) used for the ﬁnal selections. The Np selection makes use of two separate BDTs, one trained against backgrounds associated with π0 production and the other against all other backgrounds. The response of the former is shown in Figure7.

9 MicroBooNE Preliminary 4.08e+19 POT 12 MicroBooNE Preliminary 4.08e+19 POT Out. fid. vol.: 26.5 e CC: 5.9 NC: 0.6 e CC: 0.9

600 NC: 51.7 e CC0 0p: 1.1 Out. fid. vol.: 0.7 e CC0 0p: 0.4 0 Cosmic: 91.1 e CC0 Np: 6.9 10 CC : 1.3 e CC0 Np: 5.7 0 500 NC : 175.3 MiniBooNE LEE: 1.8 CC: 1.4 MiniBooNE LEE: 1.0 CC: 186.1 EXT: 217.6 Cosmic: 1.8 EXT: 4.3 0 8 CC : 214.4 BNB: 1022 NC 0: 3.1 BNB: 15 400 6 300

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(a) Low BDT response (0-0.5). (b) High BDT response (0.5-1).

Figure 7: BDT response for the Np selection.

The 0p selection employs a single BDT trained against all backgrounds, and its response is shown in Figure8

MicroBooNE Preliminary 4.08e+19 POT MicroBooNE Preliminary 4.08e+19 POT 14 0 NC: 14.3 e CC: 1.4 CC : 0.5 e CC: 0.2 200 0 CC0 0p: 1.4 CC : 15.1 e CC: 1.0 e CC0 0p: 1.6 CC0 Np: 2.1 12 CC: 23.1 e Out. fid. vol.: 1.5 e CC0 Np: 0.8 Out. fid. vol.: 25.2 MiniBooNE LEE: 1.2 Cosmic: 2.8 MiniBooNE LEE: 0.6 EXT: 180.2 EXT: 6.8 150 Cosmic: 67.9 10 NC: 2.9 NC 0: 73.3 BNB: 389 NC 0: 4.9 BNB: 26 8 100 6

N. Entries / 0.1 N. Entries / 0.1 4 50 2

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(a) Low BDT response (0-0.5). (b) High BDT response (0.5-1).

Figure 8: BDT response for 0p selection.

Figure9 shows the expected reconstructed energy spectrum for the 1 eNp and 1e0p selections scaled to the currently analyzed POT. In both plots, data events are shown for the unblinded regions of the spectrum, above 1.05 and 0.9 GeV of reconstructed energy for the two channels respectively.

10 In both plots green stacked distributions denote νe interactions expected from the intrinsic BNB νe ﬂux, while the orange contribution is the MiniBooNE LEE-signal model, under the νe hypothesis, used to evaluate the analysis’ sensitivity and described in ref. [3]. For the 1eNp selection, in the energy-range 1.05 − 2.05 GeV, 11 data events are observed with an expectation from the simulation of 18.2, 16.6 of which νe. For the 1e0p selection in the energy range 0.9 − 2.00 GeV 3 events are observed with an expectation of 5.5 (4.5 of which νe). Systematics on the expected events in these high-energy bins is in the order 20-30%, depending on the bin.

1eNp BDT cuts

MicroBooNE Preliminary 5.89e+20 POT MicroBooNE Preliminary 5.89e+20 POT 10 CC: 2.4 Cosmic: 0.6 e NC: 0.7 e CC: 0.2 NC: 0.6 CC0 0p: 0.4 8 0 e CC : 0.7 e CC0 0p: 9.1 Out. fid. vol.: 1.1 CC0 Np: 49.8 e CC: 1.3 e CC0 Np: 3.7 8 CC 0: 1.1 MiniBooNE LEE: 8.8 Out. fid. vol.: 3.5 MiniBooNE LEE: 4.2 0 NC : 3.2 EXT: 0.5 NC 0: 3.9 EXT: 5.0 6 BNB: 3 CC: 4.0 BNB: 11 Cosmic: 4.1 6

4 4 N. Entries / 0.1 GeV 2 N. Entries / 0.1 GeV 2

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(a) 1eNp selection. (b) 1e0p selection.

Figure 9: Electron neutrino selections for the 1eNp and 1e0p selections. Data is shown for values of reconstructed energy above 1.05 and 0.9 GeV for the two selections respectively. Data below these thresholds remains blind.

The inclusive selection shares the pre-selection with the exclusive 1e0p and 1eNp selections, and diﬀerentiates afterwards so as to be topology independent. Therefore, the νe CC selection enables the inclusion of events with no vertex activity, arbitrary proton multiplicity and/or pion production. The selection is not tailored to a speciﬁc energy region and is therefore ideal to look at the kinematics of electron showers in charged-current electron neutrino interactions. Results showing the high-statistics measurement of νe interaction rate and the reconstructed lepton kinematics with this selection from available data-sets are presented in Figure 10, and described in more detail in AppendixB. The events selected are not orthogonal to the exclusive selections and therefore are not included in a combined low-energy-analysis.

11 MicroBooNE 5.8e20 POT, Preliminary MicroBooNE 5.8e20 POT, Preliminary MicroBooNE 5.8e20 POT, Preliminary Reconstructed e Energy > 1.05 GeV Reconstructed e Energy > 1.05 GeV Reconstructed e Energy > 1.05 GeV 20.0 2 2 /dof: 4.4/12, p: 0.98 (On-Off)/MC: 0.74±0.15 16 /dof: 11.7/12, p: 0.47 17.5 2/dof: 13.9/12, p: 0.31 40 14 CC purity: 80.6% 15.0 e 12 12.5 30 BNB On: 70 10 BNB Off: 6.5 10.0 e CC: 74.3 8 20 bkgds: 11.4 7.5 6 Events per bin Events per bin Events per bin

5.0 4 10 2.5 2

0.0 0 0 0.5 1.0 1.5 2.0 2.5 0 /4 /2 3 /4 /2 0 /2 2 2 2 C C C M M M n n n + + + O O O f f f f f f B 1 B 1 B 1 O O O N N N B B B B B B N N N B B B 0 0 0 0.5 1.0 1.5 2.0 2.5 0 /4 /2 3 /4 /2 0 /2 Electron shower energy [GeV] Reconstructed electron Reconstructed electron

Figure 10: Electron shower energy (left) and directional angles θ (middle) and φ (right) of the selected νe CC electron candidate. In blue, the neutrino related backgrounds are grouped into one category. The error bars on the data are Poissonian. The errors on the prediction are the ﬂux [5] and cross-section systematic uncertainties [9], combined with the uncertainty originating from the ﬁnite simulated sample size. The used data-set correspond to the high-energy sideband 5.8 × 1020 POT and contains neutrino candidates with a reconstructed energy above 1.05 GeV.

Event displays for several selected electron neutrino events are shown in Figure 11, with additional events from the 1eNp selection available in AppendixE. Additional details on the 1 e0p selection are presented in AppendixD.

12 (a) 1eNp candidate event. (b) 1eNp candidate event.

Figure 11: Event displays of selected events.

5 Muon Neutrino Constraint, Systematics, and Analysis Sen- sitivity

Flux and neutrino interaction cross-section uncertainties limit the ability to predict the expected rate of electron neutrino interactions, and test the hypothesis of the MiniBooNE excess. Muon neutrinos from the BNB can be used to constrain these systematics. Both muon and electron neutrinos are produced by the decay of the same hadrons in the beam, making it possible to constrain νe ﬂux uncertainties by measuring high-statistics νµ events. Similarly, muon and electron neutrinos undergo charged-current weak interactions on the same target nucleus, making it possible to constrain neutrino interaction cross section uncertainties. Most of the neutrinos from the BNB are muon neutrinos, so it is possible to make a high purity measurement of muon neutrinos that have well reconstructed neutrino energy with signiﬁcant statistics [5]. Contained charged current muon neutrinos are selected by identifying events with a contained muon candidate and any number of contained hadron tracks, neither of which exit the detector. The selection as a function of reconstructed neutrino energy is shown in Figure 12.

13 CC INC CC INC

MicroBooNE Preliminary 1.58e+20 POT MicroBooNE Preliminary 1.58e+20 POT 0 0 CC : 724.4 e CC0 0p: 0.4 3500 CC : 901.6 e CC0 0p: 0.5 2000 Cosmic: 425.3 CC 0p + : 1416.5 Cosmic: 445.0 CC 0p + : 1529.1 NC: 338.6 CC 1p + : 3819.5 3000 NC: 360.5 CC 1p + : 4114.2 NC 0: 74.6 NC 0: 84.6 CC 2p + : 1026.1 CC 2p + : 1125.9 Out. fid. vol.: 540.2 2500 Out. fid. vol.: 584.4 1500 CC Np + : 397.8 CC Np + : 462.9 e CC: 9.3 e CC: 13.2 EXT: 840.3 EXT: 878.3 e CC0 Np: 5.2 e CC0 Np: 5.8 BNB: 9924 2000 BNB: 10782 1000 1500

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(a) νµ energy. (b) muon angle w.r.t. beam.

Figure 12: Muon neutrino selection kinematics distributions.

Detector systematic uncertainties are sub-dominant compared to flux and cross-section systematics. They are evaluated separately with dedicated variation samples [10]. More detail is included in AppendixC. The impact of the muon neutrino constraint on the Np selection can be seen by the reduction in errors in Figure 13. The overall reduction in systematic uncertainties from the muon neutrino constraint is 30-50% in the bins ≤ 0.85 GeV. While the analysis’ goal is to perform a comprehensive measurement of electron neutrino events over a broad energy range, sensitivity to a specific model hypothesis [3] for an electron-like excess of events compatible with the MiniBooNE observation is performed. The analysis, folding in detector, cross-section, and flux systematics, and including the constraint from the νµ events, obtains a median sensitivity to exclude a standard model in favor of a MiniBooNE-like 20 νe excess of 2.3σ with the 6.9 × 10 POT of BNB neutrino-mode data analyzed to date. With the full expected data set of 12.5 × 1020 POT, the expected median sensitivity with the same analysis is 3.5σ when considering only the statistical errors and 3.0σ after including the systematics. More details on the analysis approach to systematics, the way in which the muon constraint is performed, and the calculation of the sensitivity are provided in AppendixC.

14 ν π ν π e 1eNp0 selection Systematics Uncertainties, e 1eNp0 selection 1.6 MicroBooNE Simulation, Preliminary 6.9x1020POT ν ν π 16 µ CC: 1.05 µ CC 0 : 3.38 before const. after const. π π0 ν π0 Events NC 0 : 0.30 CC : 1.44 1.4 14 NC 0π: 0.53 ν NC π0: 4.04 ν π π0 ν µ CC 0 : 0.68 e CC: 54.22 uncertainties ν 12 e LEE: 9.64 Dirt: 0.00 1.2 BNB Off: 0.57 Stats. Error 10 1 8

6 0.8

4 0.6 2

0 0.4 0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1 1.2 1.4 Reconstructed Energy [GeV] Reconstructed Energy [GeV]

Figure 13: Impact of muon neutrino constraint on Np selection, scaled to 6.9 × 1020. (Left) Stacked distribution separated by the MC dedicated samples as a function of reconstructed energy. The errors on the plot represent only the statistical uncertainties of the distribution. (Right) The reduction in the systematic uncertainties is visualized as a shrinking in the uncertainty band in the ratio plot. Systematics (including ﬂux, cross-section, and detector uncertainties) before the constraint are shown in grey and after the constraint in red. The dashed line at 1 in the error band is used to guide the eye.

6 Selected Electron Neutrinos at High Energy

This analysis is moving towards a full unblinding in steps in energy and BDT response. To start with, two far side-bands were defined: one at low BDT response, and one at high energy. The low BDT response side-band is used to validate the background model on high data statistics. The data and simulation are found to agree well in this region for the 0p and Np selections. In the high energy side-band, all of the analyzed data was opened above a reconstructed neutrino energy of 1.05 and 0.9 GeV for the N-proton and 0-proton selections, respectively. This high energy side-band provides the opportunity to study νe events with MicroBooNE data for the first time, and provides some of the largest statistics available to date of νe interactions in a LArTPC. The tools and selection cuts developed for the exclusive channels in this analysis have the particular aim of being able to measure νe interactions with high purity at low energy, in order to be sensitive to possible new physics in this regime. With the final selection cuts, 11 events pass the full Np selection above 1.05 GeV, and 3 events pass the full 0p selection above 0.9 GeV, as shown in Figure9. Due to both a smaller rate of backgrounds, and a more efficient reconstruction at high energies, the analysis is able to cleanly isolate νe events at higher energies with loose cuts on a subset of the variables that are used to train the BDT. The inclusive selection (AppendixB) selects 70 events above 1.05 GeV with a νe CC purity of 80.6%. Both the loose-cut exclusive selections and the inclusive selection make it possible to validate the analysis performance with higher statistics of νe CC events, and produce plots such as Figures 14 and 30. These showcase the performance of the calorimetric separation of electrons from photons via their characteristic dE/dx signature.

15 MicroBooNE Preliminary 5.89e+20 POT MicroBooNE Preliminary 5.89e+20 POT NC: 0.9 e CC: 8.5 17.5 NC: 0.2 e CC: 0.9 40 Out. fid. vol.: 1.4 e CC0 0p: 1.7 Out. fid. vol.: 1.2 e CC0 0p: 6.7 CC: 5.6 CC0 Np: 28.7 CC 0: 1.8 CC0 Np: 4.1 e 15.0 e Cosmic: 6.5 MiniBooNE LEE: 0.0 Cosmic: 1.9 MiniBooNE LEE: 0.0 NC 0: 11.9 EXT: 8.5 CC: 3.3 EXT: 5.0 30 0 CC : 42.1 BNB: 122 12.5 NC 0: 9.2 BNB: 28

10.0 20 7.5

5.0

N. Entries / 1 MeV/cm 10 N. Entries / 1 MeV/cm 2.5

0 0.0 2.0 2.0

1.5 1.5

1.0 1.0

0.5 0.5 BNB / (MC+EXT) BNB / (MC+EXT) 0.0 0.0 2 4 6 8 10 2 4 6 8 10 shower dE/dx [MeV/cm] shr tkfit dE/dx (Y plane, 1-5 cm) [MeV/cm]

(a) 1eNp dE/dx calculated on the plane with the (b) 1e0p dE/dx, calculated on the Y plane 1-5 cm most hits 0-4 cm from the vertex. from the vertex.

Figure 14: dE/dx on high energy electron neutrinos after intermediate selection cuts. The left plot comes from the 1eNp selection high-energy sideband (Ereco > 1.05 GeV). The plot on the right is from the 1e0p selection high-energy sideband (Ereco > 0.9 GeV)

7 Conclusions

This document has presented the status of an analysis which aims to measure νe interactions in the BNB beamline with the goal of testing whether the nature of the MiniBooNE excess of EM activity‘[1] is associated with electron-like events. Several of the key measurements of the analysis needed to validate EM shower reconstruction (π0s, e/γ and µ/p separation) and neutrino flux and interaction modeling (νµ CC) are presented, together with a full assessment of the analysis’ sensitivity to a specific interpretation of the MiniBooNE excess under the electron hypothesis [3]. Results shown in this note include 5.9E20 POT of data available thus far. The sensitivity estimation is presented for the total 12.5E20 POT of data collected over MicroBooNE’s five years of running. Finally, this document presented first νe results from the BNB with an applied threshold on reconstructed energy of O(1) GeV, which represent the first step in MicroBooNE’s unblinding procedure towards finalizing the electron neutrino analyses.

16 A Measuring Electron Neutrinos with Particle Identiﬁca- tion in the MicroBooNE LArTPC for sensitivity to new Physics

In this section we describe the calorimetry-based particle identification tools used for tracks and showers that lead to the 1eNp νe selection. First we describe the signature we are looking at using, as an example, one event display coming from the 1eNp high energy sideband (Fig. 15). Afterwards, we describe the way particle identification is performed for tracks and showers in three points. The first one consists in explaining the idea, using a couple of schematics (Fig. 16). The next step is showing plots of the dE/dx versus residual range for muons and protons (Fig. 3a), and of the dE/dx versus distance from the start for electrons and photons (Fig. 17) to show the information available about these particles. The last step describes how the previous information is condensed in one variable, showing plots of the LLR PID for tracks (Fig. 3b), and the shower median dE/dx in the first 4 cm (Fig. 14a). This last couple of plots is shown with selections that emphasise the fact that these variables indeed work to do particle identification. Then, we show the distributions of the particle ID variables used in the analysis in the 1eNp selection sidebands currently explored in two different selection stages in the far sideband (Figs. 18-19). Stage 1 shows the distributions where only a cut on reconstructed energy of 1.05 GeV is applied: it shows how these variables distinguish the signal from the backgrounds. Stage 2 enhances the backgrounds, by selecting only events with low BDT response score (< 0.1). This stage shows how different backgrounds can be classified with these variables, validating the power of particle ID in MicroBooNE. In conclusion, the particle identification tools described in this section are crucial components of the selection chain employed in this analysis; in particular, they are instrumental to achieve levels of purity shown in figure 9a and the expected sensitivity to the MiniBooNE unfolded signal reported in appendixC.

(a) Event display showing a very clear signature of a 1e1p event, with one shwoer and one track in the ﬁnal state.

Figure 15: Event display used to explain the main signature target of the 1eNp analysis.

17 (a) Track PID starts from the Bethe-Bloch func- (b) Shower PID considers the beginning of the shower, tion, which describes the energy deposition as a where a photon shower (in blue) starts with a pair pro- universal function of βγ, and thus the momentum duction of an e+/e- pair, implying a double amount dependence is diﬀerent for diﬀerent particle types. of ionisation with respect to an electron shower (in The plot is taken from the PDG [11]. green) which starts with only one electron.

Figure 16: Schematics to explain the ideas behind particle identiﬁcation for tracks and showers, on the left and right, respectively.

Simulated showers purity>90%, start point in the fiducial volume start point accuracy < 2 cm Collection plane MicroBooNE preliminary 6 Photon shower trunk 5 Electron 4

2 dE/dx [MeV/cm] 1

0 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 Distance from the reconstructed start point [cm]

(a) dE/dx versus on the collection plane versus distance from the start point for simulated showers, reconstructed with a start point in the ﬁducial volume and with good accuracy. The contribution from electron and photon showers is clearly visible and distinct, as well as the dependence on the distance from the shower start point.

Figure 17: Calorimetry plot for showers.

18 Run 123 - 1.05 GeV < Reco energy < 2.05 GeV Run 123 - 1.05 GeV < Reco energy < 2.05 GeV 1eNp Presel., 1 shower 1eNp Presel., 1 shower MicroBooNE Preliminary 5.89e+20 POT 150 MicroBooNE Preliminary 5.89e+20 POT CC: 23.4 CC: 19.8 103 Out. fid. vol.: 17.7 e Out. fid. vol.: 15.2 e NC: 35.5 e CC0 0p: 4.2 NC: 28.8 e CC0 0p: 3.4 0 0 NC : 61.4 e CC0 Np: 53.1 125 NC : 52.1 e CC0 Np: 46.2 Cosmic: 76.7 MiniBooNE LEE: 0.0 Cosmic: 64.6 MiniBooNE LEE: 0.0 0 0 CC : 394.1 EXT: 231.5 100 CC : 346.5 EXT: 183.4 102 CC: 424.7 BNB: 1290 CC: 353.3 BNB: 1053 75

1 50

N. Entries / 0.1 10

25 N. Entries / 0.33 MeV/cm

100 0 2.0 2.0

1.5 1.5

1.0 1.0

0.5 0.5 BNB / (MC+EXT) BNB / (MC+EXT) 0.0 0.0 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 0 2 4 6 8 10 Track LLR PID shr tkfit dE/dx (max, 0-4 cm) [MeV/cm]

(a) Track PID (b) Shower dE/dx

Figure 18: Distribution of the track PID and shower dE/dx in the 1eNp far sideband, after applying the Np preselection cuts, requiring the presence of exactly one shower contained, and applying a cut on the reconstructed energy. It is possible to notice that these variables are already able to separate the νeCC0π0p contribution from the background, moving the νµCC background at values of the track PID around 1, and the π0 backgrounds in the peak at 4 MeV/cm.

Run 123 - Low BDT Run 123 - Low BDT 1eNp Presel., 1 shower 1eNp Presel., 1 shower 105 MicroBooNE Preliminary 5.89e+20 POT MicroBooNE Preliminary 5.89e+20 POT Out. fid. vol.: 144.4 e CC: 26.1 600 Out. fid. vol.: 123.1 e CC: 21.7 NC: 430.1 CC0 0p: 3.3 NC: 362.3 CC0 0p: 2.5 104 e e Cosmic: 596.8 e CC0 Np: 25.7 Cosmic: 495.6 e CC0 Np: 20.9 0 500 0 NC : 732.0 MiniBooNE LEE: 5.9 NC : 654.3 MiniBooNE LEE: 4.8 CC 0: 1106.5 EXT: 1618.8 CC 0: 980.7 EXT: 1319.6 3 10 CC: 1778.9 BNB: 6238 400 CC: 1486.6 BNB: 5237

300 102 200 N. Entries / 0.06 101 100 N. Entries / 0.33 MeV/cm

100 0 2.0 2.0

1.5 1.5

1.0 1.0

0.5 0.5 BNB / (MC+EXT) BNB / (MC+EXT) 0.0 0.0 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 0 2 4 6 8 10 Track LLR PID shr tkfit dE/dx (max, 0-4 cm) [MeV/cm]

(a) Track PID (b) Shower dE/dx

Figure 19: Distribution of the track PID and shower dE/dx in the 1eNp far sideband, after applying the Np preselection cuts, requiring the presence of exactly one shower contained, and requiring low PID - i.e. very background like. Aside for not being able to see any signal, these plots emphasise high statistics backgrounds, again showing the capability of these variables of distinguishing diﬀerent backgrounds. Interestingly, the track PID is able to separate NC π0 events, with a proton track, from CC π0 events, characterised by the presence of a muon track.

19 B Charged-Current Electron Neutrino Measurement with the MicroBooNE Detector

The electron neutrino charged-current (νe CC) signal definition used in this section requires a final state lepton with a kinetic energy of at least 20 MeV and a neutrino vertex inside a fiducial volume (Figure 20). The νe CC selection described here selects these events with an efficiency of (18.1 ± 0.1) % and a purity of (53.3 ± 1.0) %. The νe CC events can be categorised by interaction mode or final state topology. The four interaction modes are quasi-elastic scattering, meson-exchange current, resonant production and deep inelastic scattering. Their relative contributions are shown in the left panel of Figure 21. The νe CC signal can be split into three final state topologies:

• 0π0p: No protons or pions in the ﬁnal state with kinetic energy (Ekin) above 40 MeV; a single electron shower.

• 0πNp: At least one proton – N> 0 – with Ekin(p) > 40 MeV in the ﬁnal state and no pions above threshold.

• MπNp: At least one pion – M> 0 – with Ekin(π) > 40 MeV, no restrictions on the number of protons. Their contribution as a function of the simulated neutrino energy is given in the right panel of Figure 21. In the energy range of the Booster Neutrino Beam (BNB), the dominant interaction mode is quasi-elastic scattering, and the dominant final state is νe CC 0πNp. The selection strategy is shown in Figure 22. Cosmic rejection is common in all neutrino analyses described in this note and is obtained by combining the accelerator trigger signals with the prompt light signal and the location of the deposited charge in the TPC. Next, the reconstructed neutrino vertex is required to be located in the same fiducial volume used to define the signal events. Attached to the neutrino vertex, there are reconstructed objects, either electromagnetic showers or track-like charge deposits. The event is required to have an electromagnetic shower, reconstructed on the three wire planes with a reconstructed energy of at least 100 MeV. In the next step, the electron candidate shower is identified as electron-like or photon-like, as is further discussed in Appendix B.1. The other particles attached to the neutrino vertex are used to further reject backgrounds relying on the particle identification tools described in AppendixA. Finally, the combination of the particle identification stage is combined into the event selection, as described in Appendix B.2.

20 Y 116.5 cm

Beam Booster Neutrino Beam 10 cmborders

-116.5 cm

Z X 10 cm border 50 cm border 10 cm borders 0 cm 1036.8 cm 256.4 cm 0 cm

Figure 20: Fiducial volume used in this section for both the signal deﬁnition and the νe CC selection. The yellow cylinder represents the cryostat, the orange structure is the TPC and the green area is the ﬁducial volume. Both the YZ (left) and XY (right) projections are shown.

MicroBooNE Simulation, Preliminary MicroBooNE Simulation, Preliminary 1.0 1.0 e CC Interation Modes e CC Final State

Quasi-elastic scattering: 43% e CC 0 0p: 13% Resonant production: 31% CC 0 Np: 52% 0.8 0.8 e Deep-inselastic scattering: 12% e CC N : 34% Meson exchange current: 12%

0.6 0.6 Fraction Fraction 0.4 0.4

0.2 0.2

0.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 True neutrino energy [GeV] True neutrino energy [GeV]

Figure 21: Breakdown of νe CC events in interaction modes (left) and ﬁnal state topologies (right) as a function of neutrino energy. Note that these are relative fractions and have to be multiplied by the BNB ﬂux to retrieve the interaction rates. The relative contributions to the predicted νe CC interaction rates from the BNB is given in the legend. The shaded bans represent the statistical error arising from limited simulation statistics.

21 Figure 22: (Left) Flowchart indicating the different steps in the νe CC selection. (Right) A hypo- thetical νe CC event with multiple reconstructed showers and tracks. At the pre-selection stage, an electron candidate shower is identified (orange) and electron particle identification is performed on this shower. The other reconstructed objects (purple) are classified to improve background rejection before merging the outputs and perform the final event selection.

22 B.1 Electron identiﬁcation After the electromagnetic shower requirement described in the introduction of this appendix, electrons make up less than 10 % of the selected showers. The majority of showers are caused by neutrino interactions containing π0 → γγ decays. A gradient boosted decision tree [12, 13] is used to discriminate between electron and photon induced showers.

(a) Track ﬁt to shower trunk (b) dE/dx at the start of the shower (c) Number of subclusters

Figure 23: Subset of the variables used for electron identiﬁcation.

The nine variables used to discriminate electron showers, and their correlation, are shown in top-left block of Figure 24. The trunk of the shower is ﬁt as a track. The fraction of calorimetric hits in this shower trunk compared to the whole shower is used as one of the variables (see Figure 23a). The start of the trunk is used to measure the ionisation. For reasons introduced in AppendixA, diﬀerent but highly correlated variables are constructed (Figure 23b):

• The dE/dx on the collection plane in the first 4 cm. • The dE/dx on the collection plane in the first 2 cm. • The dE/dx on the collection plane from 1 cm to 4 cm. • The weighted mean of the dE/dx in the first 4 cm using both the two induction planes and the collection plane. As shown in Figure 17, it is possible that an the electron-positron pair at the start of a photon shower only overlaps for a fraction of the first 4 cm. Therefore, the variable using the first 2 cm is important albeit the additional statistical fluctuations. The third variation introduces a 1 cm gap to avoid overlapping charge deposits close to the vertex. The last variation relies on a combination of the three planes and is important when the collection plane has few hits at the beginning of the shower. The number of sub-clusters in the shower (Figure 23c), the Moliere angle of the shower and the distance of the shower start point from the reconstructed neutrino vertex are also used. Finally, the variable Second shower hits takes into account the presence of another shower in the event that might be a signature of a neutral pion decay. The correlations between the input variables and the Electron PID score, seen in Figure 24, indicate a preference for showers with a smaller vertex distance, smaller Moliere angle, and larger

23 hssll evsa eosrto n ooedmninlctwspae nti au nthe in value this on ratio. placed signal-to-background was of B.2 . cut increase Appendix one-dimensional 1 in no : while described and showers, 8 as demonstration photon a selection, a of to final % as 90 corresponding serves reject showers, solely can electron This one of that % found 75 is space. keeping It phase kinemat- separation. kinematics is electron-gamma lepton identification obtained the electron of the that portion demonstration large a a as covering serves unbiased, This ically low. is kinematics based showers. photon The of electron. start an the d d of for specific case the expected the a and in have score occur electrons electron to unlikely that that the is demonstrates between hits variable of correlation tagging amount shower negative substantial second a the with with showers correlation second The sub-clusters. of number simulated their with compared The be are (bottom-left). step. can (middle) group that identification group third kinematics second electron the lepton The the in reconstructed PID. counterparts the electron in the and interest in score of used BDT variables variables the the the contains (top-left) of group matrix first Correlation 24: Figure iuae etioeet asn the passing events truth- neutrino the simulated and , 25 score Figure electron In the between correlation the that see to encouraging is it Finally, Hit fractioninshowertrunk d d d d E E E E / / / / Shower vertexdistance d d d d Number ofsubclusters Reconstructed energy x x x x , , , ,

Second showerhits [ [ [ [ 1 0 0 0 Electron PIDscore , , , , 5 2 4 R 4 R ] ] ] ] e e

c c c c c c Moliere angle m m m o m o True energy n n , , , ,

s c c c a t t o o o r r l l u u l l l

l l l T T p c e e e c r r t l t c c c a e u u e t t t n d e e i i i d o o o e

n n n s E/ dE/dx, [0,4] cm, all planes d

x dE/dx, [0,4] cm, collection

xetto of expectation dE/dx, [0,2] cm, collection dE/dx, [1,5] cm, collection Number of subclusters Hit fraction in shower trunk Moliere angle 24 Shower vertex distance MicroBooNE Simulation,Preliminary Second shower hits ∼ 2 . pre-selection e cm MeV 1 Electron PID score

E/ Reconstructed energy

d Reconstructed x Reconstructed aibe sepandb realising by explained is variables −

1 True energy nta ftedul values double the of instead ,

r sdt eosrt the demonstrate to used are True True 0.00 0.25 0.50 0.75 1.00 1.00 0.75 0.50 0.25

Correlation MicroBooNE Simulation, Preliminary

7 Threshold =0.63 Photons (90% rejected) 6 Electrons (75% accepted) 5

Area normalised 2

0 0.0 0.2 0.4 0.6 0.8 1.0 Electron PID score

Figure 25: e − γ separation performance obtained by the electron classiﬁer on simulation. The electron BDT response is shown for simulated electrons (blue histogram) and for background photons (orange histogram). The green line indicates the score at which 95 % of the background photons are rejected.

B.2 Charged-Current Electron Neutrino Event Selection The final event classification is performed using a gradient boosted decision tree, building on the particle identification performed in AppendicesA and B.1. Figure 26 shows the efficiency in function of the simulated neutrino energy for the three different signal topologies introduced in the beginning of this section. The efficiency is given at three different stages in the selection, corresponding to different levels in Figure 22. NeutrinoID refers to the set of tools introduced in Section3 and corresponds to the first step of cosmic removal in Figure 22. The Pre-selection includes the additional requirements defined by the second block in Figure 22. At this stage, the νe CC purity is (5.74 ± 0.04) %. The final selection combined the output of the electron shower identification with the additional background rejection obtained from the classification of the other reconstructed particles in the event. The response of the event classification is shown for all events passing the pre-selection in the left panel of Figure 27. Here, the unblinded data is used, corresponding to approximately 4 % of the total POT collected by MicroBooNE . The event selection, the final block in Figure 22, corresponds to the requirement of a νe CC event classification score of 0.87 or higher. The purity obtained by the νe CC event selection is (53.3 ± 1.0) %. In Figures 27 and 28 the errors shown on the Beam On data are statistical and modelled by a Poisson distribution. The errors on the prediction, represented by the shaded areas, include the uncertainty arising from the limited simulation and Beam Off data statistics, added in quadrature with the systematic uncertainties arising from the flux and cross-section modelling. The systematic uncertainties are taken into account through a covariance matrix approach. On the figures, the (beam on - beam off)/ simulation ratio is given with corresponding uncertainty. Additionally, the p-value obtained from a two-sample Kolmogorov–Smirnov test is given. The former is indicative for the normalisation agreement while the latter quantifies the shape agreement of the distributions. Additionally, the χ2-test with the corresponding degrees of freedom and p-value is quoted, as defined in [14]. The right panel of Figure 27 shows the reconstructed shower energy of the electron candidate

25 MicroBooNE Simulation, Preliminary MicroBooNE Simulation, Preliminary MicroBooNE Simulation, Preliminary Efficiency e CC 0 0p Efficiency e CC 0 Np Efficiency e CC N 1.0 1.0 1.0

0.8 0.8 0.8 NeutrinoID: 81% NeutrinoID: 83% NeutrinoID: 86% Pre-selection: 33% Pre-selection: 38% Pre-selection: 36% 0.6 Selection: 19% 0.6 Selection: 23% 0.6 Selection: 11%

Efficiency 0.4 Efficiency 0.4 Efficiency 0.4

0.2 0.2 0.2

0.0 0.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 True neutrino energy [GeV] True neutrino energy [GeV] True neutrino energy [GeV]

Figure 26: Efficiency of the different stages in the νe CC selection as a function of the simulated neutrino energy. The three panels correspond to different final state topologies. The shaded band is the statistical uncertainty. The statistical uncertainty on the integrated efficiency in the legend is below 1 % for all cases.

in the selected events, defined as events with a νe CC identification score of 0.87 or higher. In Figure 28, the track multiplicity at vertex is shown before and after the event classification boosted decision tree. It can be appreciated that even in the small unblinded data-set, events with a wide variety in track multiplicity are selected. A further indication of the scope of the selection is given by the collection plane view of three selected events in Figure 29.

26 MicroBooNE 4.8e19 POT, Preliminary MicroBooNE 4.8e19 POT, Preliminary

120 7 (On-Off)/MC: 0.91±0.13 BNB On: 425 (On-Off)/MC: 0.72±0.21 BNB On: 19 2/dof: 25.4/20, p: 0.19 BNB Off: 50. 2/dof: 7.3/12, p: 0.84 BNB Off: 2.5 100 6 e CC purity: 5.7% e CC N : 9.0 e CC purity: 53.3% e CC N : 2.9 KS p-value: 0.58 KS p-value: 0.99 e CC 0 0p: 3.1 5 e CC 0 0p: 1.8 80 e CC 0 Np: 14. e CC 0 Np: 8.9 CC other: 34. 4 CC other: 2.0 60 0 0 CC : 128. 3 CC : 1.5

Events per bin 40 NC: 14. Events per bin NC: 0.68 NC 0: 143. 2 NC 0: 2.8 Cosmic: 34. Cosmic: 0.70 20 1 Out of FV: 34. Out of FV: 1.7 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.5 1.0 1.5 2.0 2.5 2 2 C C M M n n + + O O f f f f B 1 B 1 O O N N B B B B N N B B 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.5 1.0 1.5 2.0 2.5

e CC classification score Electron shower energy [GeV]

Figure 27: (left) BDT response of the νe CC inclusive event classiﬁer. (right) Reconstructed electron shower energy distribution after the selection. The data shown corresponds to the unblinded subsample.

MicroBooNE 4.8e19 POT, Preliminary MicroBooNE 4.8e19 POT, Preliminary

200 (On-Off)/MC: 0.91±0.13 BNB On: 425 (On-Off)/MC: 0.72±0.21 BNB On: 19 12 175 2/dof: 1.6/6, p: 0.96 BNB Off: 50. 2/dof: 9.7/6, p: 0.14 BNB Off: 2.5 e CC purity: 5.7% e CC N : 9.0 e CC purity: 53.3% e CC N : 2.9 150 10 KS p-value: 0.61 e CC 0 0p: 3.1 KS p-value: 1.00 e CC 0 0p: 1.8 125 e CC 0 Np: 14. 8 e CC 0 Np: 8.9 CC other: 34. CC other: 2.0 100 CC 0: 128. 6 CC 0: 1.5 75

Events per bin NC: 14. Events per bin NC: 0.68 0 4 0 50 NC : 143. NC : 2.8 Cosmic: 34. 2 Cosmic: 0.70 25 Out of FV: 34. Out of FV: 1.7 0 0 0 1 2 3 4 5 0 1 2 3 4 5 2 2 C C M M n n + + O O f f f f B 1 B 1 O O N N B B B B N N B B 0 0 0 1 2 3 4 5 0 1 2 3 4 5 Track multiplicity at vertex Track multiplicity at vertex

Figure 28: Track multiplicity at vertex at the pre-selection stage (left) and after the ﬁnal selection stage (right).

27 Figure 29: Collection-plane displays of selected events by the νe CC selection. Note the diﬀer- ences in the reconstructed angle and energy of the electromagnetic shower in the three events, demonstrating the wide range of kinematics covered by the selection.

28 B.3 High-Energy Sideband In this section, a sideband containing neutrinos with a reconstructed energy above 1.05 GeV is studied. The exposure corresponds to 5.8 × 1020 POT, roughly 50 % of the collected data. Figure 30 shows the two variables with the strongest e − γ separation power after the pre-selection. As stated in Appendix B.2, the selection does not rely directly on the kinematics of the event, and is therefore suited to explore the kinematics of νe candidate events. The resolution, obtained from simulation and the data-simulation comparisons for the three kinematic variables of the electron after selection are given in 31 and 10 respectively. After the unblinding of a signiﬁcant data-set, the inclusive νe CC selection described in this section will serve as a validation of the electron neutrino modelling in MicroBooNE and be used to measure the intrinsic electron ﬂavour component in the Booster Neutrino Beam.

MicroBooNE 5.8e20 POT, Preliminary MicroBooNE 5.8e20 POT, Preliminary Reconstructed e Energy > 1.05 GeV Reconstructed e Energy > 1.05 GeV

2 120 /dof: 18.5/20, p: 0.56 (On-Off)/MC: 0.82±0.11 2 80 /dof: 16.2/20, p: 0.70 BNB On: 636 CC purity: 18.6% 100 e BNB Off: 81. p: 1.6 60 80 : 8.1 ±: 4.3 60 40 K: 0.059 Cosmic: 89. Events per bin 40 Events per bin : 430. 20 e: 140. 20

0 0 0 2 4 6 8 10 0 2 4 6 8 10 2 2 C C M M n n + + O O f f f f B 1 B 1 O O N N B B B B N N B B 0 0 0 2 4 6 8 10 0 2 4 6 8 10 dE Shower vertex distance [cm] Shower dx (collection plane) [MeV/cm]

Figure 30: Data/MC comparisons for the two variables of the electron shower classiﬁer with the strongest separation power: The dE/dx at the start of the shower (left) and the shower vertex distance (right). The used data-set corresponds to the high-energy sideband 5.8 × 1020 POT and contains neutrino candidates with a reconstructed energy above 1.05 GeV.

29 MicroBooNE Simulation, Preliminary MicroBooNE Simulation, Preliminary MicroBooNE Simulation, Preliminary 1.75 103 median + 68% CI median + 68% CI median + 68% CI 1.50

n n

o 3 /4 o /2 r r

1.25 t t c c 102 e e l l e e 1.00 d d

e /2 e 0 t t c c

0.75 u u r r t t

s s 101 n n

0.50 o /4 o /2 c c e e Electron showers per bin R R 0.25 Electron shower energy [GeV] 0 100 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 /4 /2 3 /4 /2 0 /2 True electron energy [GeV] True electron True electron

(a) Resolution for the reconstructed electron variables after the νe CC selection. The colour scale is logarithmic. In black, the median and 68 % conﬁdence interval are given, binned in the simulated electron kinematics.

Figure 31: Resolution of νe CC electron kinematic variables.

30 C Constraining Systematic Uncertainties for the Electron Neutrino Search at MicroBooNE

MicroBooNE is designed to investigate the anomalous excess in the electron neutrino event spectrum observed by the MiniBooNE experiment. MicroBooNE runs in the same Booster Neutrino Beamline (BNB) as MiniBooNE and is located at a baseline of 470 m. To achieve the level of sensitivity to probe this low energy excess, it is necessary to ensure a significant reduction of uncertainties related to the expected neutrino energy spectrum. This section outlines the strategy to constrain the systematic uncertainties in electron neutrino modeling using a high-statistics muon neutrino sample. It also discusses the different sources of systematic uncertainties, the constraint approach that accounts for known correlations between different electron final-states and muon neutrino fluxes and cross-sections, and the implementation of the constraint given this correlation to improve the sensitivity.

C.1 Event Selection

The strategy to constrain the systematic uncertainties leverages a variety of channels in the νe selection. The νe selection is divided into two ﬁnal state topologies: • 1eNp0π : One single electron shower and at least one proton in the ﬁnal state and no pions above 40 MeV kinetic energy. This selection is the most sensitive to the unfolded LEE signal (see Fig.9a)

• 1e0p0π : One single electron shower and no protons or pions in the ﬁnal state above 40 MeV kinetic energy. This selection is utilised to constrain the less understood protons kinematics and reconstructions (see Fig. 9b)

A high-statistics νµ sample and the correlations to the νe sample is leveraged to constrain ﬂux and neutrino cross-section uncertainties. These correlations are due to the νµ and νe sharing the same neutrino parents from the BNB and interacting via the same mechanism in the liquid argon medium. The νµ’s selection is designed to maximize its phase-space overlap with the νe’s selection and to prioritize low-energy performance where the constraining power is most needed. Requiring contained tracks, for example, ﬁlters out higher energy muons and ensures the use of both range- based and multiple-coulomb scattering-based calorimetry techniques on muon tracks for higher precision energy reconstruction (see Figure 12a).

C.2 Systematics and Constraint Systematic uncertainties in this analysis are associated to the level of precision of the model used in the event generation (argon cross section/GENIE ref. [15]), to the knowledge of the neutrino beam (ﬂux), and to the limitation of our detector simulation (detector response). Two approaches are used to estimate the uncertainties: unisim and multisim. • Unisim: a single variation of given analysis input parameter. The diﬀerence between number of events in the variation and the central value is taken as the uncertainty in that bin. This approach is implemented to estimate the detector response systematics by using dedicated variation samples. These systematics are treated as uncorrelated.

31 • Multisim: several variations of given analysis input parameter, called universes. The correlations in the various bins of the distributions of the selected events are preserved. This approach is implemented when calculating the ﬂux and cross-section uncertainties. Systematics which impact TPC’s responses can impact calorimetric energy reconstruction important for shower, and thus νe event energy reconstruction. The impacts of these systematics are generally at the few percent as shown in Fig 32.

Figure 32: This ﬁgure displays the impact of the TPC variation on the selection eﬃciency as a function of dE/dx for true backtracked electrons. TPC variations which impact spatial and calorimetric reconstruction can impact particle ID discriminant variables such as the LLR trkpid used for µ/p separation and dE/dx used for e/γ separation. The impact of TPC detector variations (after 1eNp0π pre-selection) on electron PID cuts in 1eNp0π box-cuts is subdominant overall at few percent variation.

For each uncertainty, a covariance matrix correlating the variation “sys” universe k = 1,...,N k CV in the measured number of events (Ni ) and the central value (Ni ) between bins is calculated as follows: N 1 X V sys = (N CV − N k)(N CV − N k), (1) ij N i i j j k where only the diagonal elements are considered to calculate the systematics in the unisim approach. The constraint is exercised through the covariance matrix constructed from the energy spectrums of the νe and νµ selections described above. Figure 33 displays the covariance matrix between 1eNp0π νe, 1e0p0π νe, and νµ channels for the full systematics accounting ﬂux, cross-section, and detector response systematics. The correlation between the elements in the matrix allow to constrain νe ﬂux and cross-section modelling uncertainties through the measurements of correlated νµ events as shown in Figure 34.

32 Figure 33: Total uncertainties of the ﬂux modelling, neutrino interaction modelling, and detector modeling systematics. The detector response systematics are treated as uncorrelated and increase the size of the fractional errors of the diagonal elements. This has the eﬀect of degrading the power of the correlation between the νµ channels and the 1eNp0π and 1e0p0π channels.

(a) Flux Correlation Matrix (b) Cross-section (GENIE) Correlation Matrix

Figure 34: (a) Flux modelling systematics has the highest correlation in the low-energy, where the uncertainties from model parameterization for short Berilium target π+ production cross section dominates. (b) Signiﬁcant uncertainty in νµ/νe CC cross section models due to limited experimental data in low neutrino energy. Good correlation at very low energy between 1eNp0π and 1e0p0π channels selections provided additional constraint in the combined ﬁt.

The maximum systematics constraint can be estimated using the correlation elements between

33 the νe and νµ events as follows 1. Minimize the χ2 between the data and MC in selections by using the covariance matrix − inversion, (Vij) 1.

2. Assume that the observed events (NData) is equal to the predicted events (NMC ) within the statistical uncertainties, and ﬁt the NMC to the statistical uncertainties in each bin of the spectrum, as follows −1 new −1 1 (Vij ) = Vij + MC . (2) Ni

−1 new new 3. Invert back the new inverse matrix, (Vij ) to give the new constrained matrix, (Vij) . The new constrained matrix is plotted as the red shade in Figure 13.

This method demonstrates the best estimation of the constraint power that we can expect from utilizing the νµ constraint. Overall, systematics reduction of up to 50% in ﬂux, cross section, and detector response systematics at the low energy region where it is most needed. The impact of the constraint is shown on Figure 13.

C.3 Sensitivity Estimation The sensitivity of the selection to the MiniBooNE unfolded LEE signal is calculated by generating toy experiments under two hypotheses, which deﬁnitions can be used interchangeably:

• H0 is the Standard Model hypothesis and H1 is the MiniBooNE unfolded LEE hypothesis.

• H0 is the MiniBooNE unfolded LEE hypothesis and H1 is the Standard Model hypothesis.

The median, ±1σ, ±2σ of the sensitivity are calculated relative to the H1. Following this convention, a test statistic is employed to rule out the H0 hypothesis in favor of the H1 hypothesis. 2 The calculation uses the χCNP formalism [14] that approximates Poisson statistical errors for the covariance matrix diagonals and it is deﬁned as follows:

2 T stat syst −1 (χCNP )COV = (N − µ(H)) (VCNP + V ) (N − µ(H)), (3) where N is the observed number of entries in a bin, µ(H)) is the expected number of entries under syst the H0 or H1 hypothesis, V is the systematic covariance matrix on the H0 hypothesis, and the statistical covariance matrix is deﬁned as stat 1 2 VCNP ij ≡ 3/ + δij. (4) Ni µi(H)

The median sensitivity of the selection is estimated for the current open dataset of 6.9 × 1020 POT and the full dataset of 12.5×1020 POT. The systematics uncertainties is only assumed for the Standard Model (SM) hypothesis, and no systematics uncertainties is attached to the MiniBooNE LEE signal model. These estimates are reported considering the following scenarios: • The median sensitivity projected for 6.9 × 1020 POT to rule out the Standard Model (SM) hypothesis in favor of the LEE hypothesis is 2.3σ, shown in Figure 35

34 • The median sensitivity projected for 6.9 × 1020 POT to rule out the LEE hypothesis in favor of the SM hypothesis is 1.9σ. • The median sensitivity projected for 12.5 × 1020 POT to rule out the SM hypothesis in favor of the LEE hypothesis is 3.0σ shown in Figure 36.

• The median sensitivity projected for 12.5 × 1020 POT to rule out the LEE hypothesis in favor of the SM hypothesis is 2.4σ.

MicroBooNE Simulation, Preliminary +2 +1 Median -1 -2 σ

PDF 0.14 σ σ σ H0 0.12 H1

0.1 +2σ 1-β(0.977) α(0.527 | -0.1σ)

0.08 +1σ 1-β(0.841) α(0.129 | 1.1σ)

0.06 Median 1-β(0.500) α(0.010 | 2.3σ)

0.04 -1σ 1-β(0.159) α(10-3.37 | 3.3σ)

σ 0.02 -2 1-β(0.023) α(10-inf | inf )

0 −60 −40 −20 0 20 40 60 80 100 ∆ χ2 = χ2 - χ2 H0 H1

Figure 35: Sensitivity estimate to the MiniBooNE LEE unfolded signal on the combined 1eNp0π 20 and 1e0p0π selection with the νµ constraint for an integrated POT of 6.9 × 10 . In this plot, H0 is the Standard Model hypothesis and H1 is the MiniBooNE unfolded LEE hypothesis

Leveraging multiple selections in the fit brings an overall improvement to the sensitivity. For the current open dataset of 6.9×1020 POT, incorporating the 1e0p0π with the 1eNp0π in the combined fit improves the median sensitivity to rule out the standard model in favor of the LEE from 1.8σ to 2.0σ. And including the νµ selection in the combined fit, we observe an improvement from 2.0σ to 2.3σ.

35 MicroBooNE Simulation, Preliminary +2 +1 Median -1 -2 σ

PDF 0.14 σ σ σ H0 0.12 H1

0.1 +2σ 1-β(0.977) α(0.315 | 0.5σ)

0.08 +1σ 1-β(0.841) α(0.040 | 1.7σ)

0.06 Median 1-β(0.500) α(0.002 | 3.0σ)

0.04 -1σ 1-β(0.159) α(10-4.52 | 4.0σ)

σ 0.02 -2 1-β(0.023) α(10-inf | inf )

0 −60 −40 −20 0 20 40 60 80 100 ∆ χ2 = χ2 - χ2 H0 H1

Figure 36: Sensitivity estimate to the MiniBooNE LEE unfolded signal on the combined 1eNp0π 20 and 1e0p0π selection with the νµ constraint for an integrated POT of 12.5 × 10 . In this plot, H0 is the Standard Model hypothesis and H1 is the MiniBooNE unfolded LEE hypothesis

36 D Measurement of Single Electron Events in MicroBooNE

Electron neutrinos can create a wide variety of topologies when interacting in liquid argon, and this analysis measures events both with (1eNp0π) and without (1e0p0π) visible protons. This section presents the measurement of single electron events in the MicroBooNE detector, which includes events at low energies and are important for understanding the excess observed by MiniBooNE. The single electron selection is orthogonal to the 1eNp0π selection which makes it possible to allow migrations between the two channels in a joint ﬁt, and constrain uncertainties associated with low energy protons such as those related to reconstruction, multiplicity and their kinematics. A selection of plots summarizing the development of the 1e0p0π selection, and not already included in the main body of this document, are shown in Fig. 37.

(a) Reconstructed Visible Energy (b) BDT Response

Figure 37: Reconstructed visible energy and BDT score in the low BDT score region of the far sideband after the 1e0p0π pre-selection stage. Additional cuts were applied to reduce the EXT contribution. Simulation in agreement with data measurement.

In liquid argon, a minimum ionizing particle (MIP) has an energy loss per unit distance about of 2 MeV/cm [16]. Separation of showers of one MIP (mostly 1e0p0π events) and showers of two MIPs (mostly NCπ0 events) is observed in 14b. The selection framework shows great capability at selecting true 1e0p0π events in the high energy sideband region, as can be seen from the event displays in Fig. 11.

37 (a) High Energy and BDT score > 0.4

Figure 38: Selection of single shower events in the high energy region (> 0.9 GeV) and a BDT score > 0.4. This is at the 1e0p0π pre-selection and after applying cuts on the shower/track ﬁtter start and end points in Y.

38 E νe 1eNp Event Displays This section shows a collection of event displays for selected 1eNp events. In the images, reconstructed showers are displayed as cones, while tracks are displayed as lines. The recosntructed neutrino interaction vertex is represented with a white dot, and has been slightly oﬀset from the actual point for better readability.

Figure 39: Selected 1eNp νe candidate from high-energy (> 1.05 GeV) sideband.

39 Figure 40: Selected 1eNp νe candidate from high-energy (> 1.05 GeV) sideband.

Figure 41: Selected 1eNp νe candidate from high-energy (> 1.05 GeV) sideband.

40 Figure 42: Selected 1eNp νe candidate from high-energy (> 1.05 GeV) sideband.

Figure 43: Selected 1eNp νe candidate from high-energy (> 1.05 GeV) sideband.

41 Figure 44: Selected 1eNp νe candidate from high-energy (> 1.05 GeV) sideband.

Figure 45: Selected 1eNp νe candidate from high-energy (> 1.05 GeV) sideband.

42 Figure 46: Selected 1eNp νe candidate from high-energy (> 1.05 GeV) sideband.

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