Microboone-Note-1087-Pub

The MicroBooNE Single-Photon Low-Energy Excess Search Public Note 1087

The MicroBooNE Collaboration June 30, 2020

Abstract MicroBooNE is a short baseline neutrino experiment at Fermilab designed to address the low energy excess observed by the MiniBooNE experiment. This note describes and presents preliminary results for the MicroBooNE analysis developed to address this excess as a single photon plus one or zero protons in the ﬁnal state. The analysis assumes neutrino neutral current ∆ resonance production followed by ∆ radiative decay on argon (NC ∆ → Nγ) as the “signal model”; event reconstruction and selection have been developed and optimized in order to maximize eﬃciency and reduce cosmogenic and other beam- related backgrounds to the NC ∆ → Nγ signal. We present the analysis methodology and validation checks performed on limited-statistics open data sets, corresponding to 5×1019 protons on target (POT), following a blind analysis, as well as the projected sensitivities for testing the Standard Model (SM) predicted rate for the NC ∆ → Nγ process and for testing the interpretation of the previously observed MiniBooNE low energy excess as NC ∆ → Nγ events, using the full anticipated MicroBooNE data set of 12.25×1020 POT.

Contents

1 Introduction 3 1.1 The MicroBooNE Detector ...... 4

2 Analysis Overview 4

3 Single Photon Selection 5 3.1 Topological selection and pre-selection ...... 5 3.2 Final Selection ...... 10 3.3 Sideband Validation ...... 22 3.4 Validation of “Dirt” Backgrounds ...... 26

4 NC π0 Selection for In Situ Constraint 34 4.1 Event Selection ...... 34 4.2 BDT Training ...... 35 4.3 Final Selection ...... 38

5 Evaluation of Systematic Uncertainties 43 5.1 Flux and Cross-section Systematic Uncertainties ...... 43 5.2 Detector Systematic Uncertainties ...... 54

6 Final Sensitivities and Preliminary Results 59 6.1 Fit Method ...... 59 6.2 Projected Sensitivity to NC ∆ → Nγ ...... 66

1 7 Summary and Conclusions 71

A Appendix I: GENIE Cross section Systematics 75

2 1 Introduction

The MiniBooNE experiment reported its first observation of an anomalous excess of “low-energy” νe charged current quasi-elastic (CCQE)-like events in 2008 [1]. Since then, additional data collected by the MiniBooNE collaboration in both neutrino and antineutrino running mode have revealed an increasing (in significance) discrepancy between data and the null hypothesis prediction, over the range of 200-475 MeV in neutrino energy reconstructed assuming νe CCQE scattering. Despite becoming more significant with more data and improved analysis, the observed excess has not been definitively attributed to sterile neutrino oscillations or any other interpretation. One of the still-viable interpretations for this excess is that it is contributed by neutral current (NC) single-photon production in neutrino scattering on carbon, where events are generally reconstructed at lower energies and in MiniBooNE contribute as irreducible background. Such process can be either a Standard Model (SM) process that may have been mis-estimated (underestimated) in the MiniBooNE analysis, or a new process involving exotic physics.

Figure 1: The current world’s best bound on the NC ∆ radiative cross-section at O(1GeV) energy by T2K [2]. Shown also in green is the Wang et al. Standard Model (SM) cross-section scaled up by a factor of 3, which is what would be needed to explain the observed MiniBooNE low-energy excess [3].

The analysis presented in this note aims to test the single-photon interpretation of the MiniBooNE low-energy excess under the explicit hypothesis that the excess is contributed by the SM process of NC ∆ baryon resonance production, followed by ∆ radiative decay (NC ∆ → Nγ, where N is a nucleon). MiniBooNE considered contributions from this process to their background prediction, and constrained the overall background rate by tying its branching fraction to the more dominant π0 decay mode of the ∆, which was measured in MiniBooNE in situ. However, as the rate of the NC ∆ resonance production followed by radiative decay has never been directly measured in neutrino scattering, there is motivation to explicitly test this hypothesis with a dedicated MicroBooNE search. Current limits on this process from the T2K experiment [2] only constrain its rate to the level of <100 times the SM prediction at 90% conﬁdence level (CL), as shown in Fig. 1, while a factor of three (3) enhancement of the predicted SM rate can account for the observed MiniBooNE excess [3]. For reference, the uncertainty on the NC ∆ radiative decay rate in the MiniBooNE analysis was 12.5% [4], constrained by an in situ measurement of the NC π0 rate.

3 1.1 The MicroBooNE Detector MicroBooNE is sitting in the same neutrino beam as MiniBooNE, the Fermilab Booster Neutrino Beam (BNB), and is a liquid argon time projection chamber (LArTPC) [5] combining the advantages of high spatial resolution of neutrino interactions, as well as excellent calorimetry, leading to strong particle identification capabilities. The detector consists of a 2.56m × 2.32m × 10.36m TPC filled with 85 tones liquid argon (active mass) serving as both the bulk target mass and for charge detection, and an array of 32 photomultiplier tubes (PMTs) [6] that detect scintillation light for triggering, timing, and reconstruction purposes. Ionization charge deposited in the liquid argon volume is drifted horizontally by a large -70 kV drift voltage, corresponding to a drift field of 273 V/cm. At the edge of the TPC, on the anode side, are three sets of wire planes which are used to read out for reconstruction purposes [7]. Broadly, objects in LArTPC’s can be split into two categories, “tracks” in which the reconstructed ionization charge forms continuously connected lines, most often due to underlying muons, charged pions and protons; and “showers” in which an electromagnetic cascade is formed from an electron or photon undergoing a cascade of bremsstrahlung, pair production, annihilation and Compton scattering. For a more detailed description of the MicroBooNE detector, see Ref. [5].

2 Analysis Overview

This analysis builds and significantly expands upon past efforts [8, 9] to develop an efficient and pure selection of events with a topology consistent with neutrino-induced NC ∆ → Nγ events. Two primary final-state-based topologies are examined: one with a single photon and a single proton in the final state and no other tracks or showers reconstructed as part of the interaction (1γ1p), and one with a single photon and zero protons in the final state and no other tracks or showers reconstructed as part of the interaction (1γ0p). These samples are isolated using reconstruction utilizing the Pandora multi-algorithm approach to automated pattern recognition [10]. The selection methodology and preliminary results, following a blind analysis, are presented in Sec. 3. Throughout the development of this selection, it has consistently been observed that the largest background (at final selection stage) is that of NC π0 events, where one of the two daughter photons of the π0 is not reconstructed as such due to (a) leaving the detector, (b) overlapping with the primary shower, (c) pair-converting a significant distance away and thus failing to be associated with the primary neutrino interaction, or (d) failing to reconstruct due to it having too low energy. To make sure that these crucial backgrounds are well understood, two separate (and mutually exclusive) π0 rich selections are developed. One targeting one proton and two photons and no other tracks/showers (2γ1p), and one targeting zero proton and two photons and no other tracks/showers (2γ0p). These are discussed in Sec. 4. The NC π0-targeting selections provide high-statistics samples for data to Monte Carlo comparisons without compromising our signal blindness criteria, which are useful for validating the analysis (including simulation, reconstruction, and event selection), and for directly constraining the rate and potentially shape of the NC π0 background distribution to the single photon selection. Final fits to a potential NC ∆ → Nγ signal are performed with a simultaneous fit to all four selections, considering statistical and systematic uncertainties and systematic correlations, as described in Sec. 6. Systematic uncertainties and correlations are evaluated as described in Sec. 5.

4 Figure 2: Cartoon illustrations of the two topological signatures of NC ∆ → Nγ events targeted by the single-photon low-energy excess search. Left: 1γ1p; right: 1γ0p. A simulated example of what the 1γ1p topology looks like in a LArTPC readout wire plane image is shown in Fig. 3.

3 Single Photon Selection 3.1 Topological selection and pre-selection NC ∆ radiative selection begins with Pandora-reconstructed information. Specifically, per MicroBooNE recorded event, a candidate neutrino interaction vertex is selected and reconstructed by the Pandora al- gorithms. Both the 1γ1p and 1γ0p selections specifically focus on reconstructed vertices which match the corresponding signal topology definitions. These topological selections are defined as:

• 1γ1p - requiring exactly one reconstructed shower and one reconstructed track associated to the candidate vertex;

• 1γ0p - requiring exactly one reconstructed shower associated to the candidate vertex. Cartoon representations of what these topologies look like are shown in Fig. 2. An event display showing a Monte Carlo simulation of a 1γ1p event with a clear proton track and photon shower in the MicroBooNE LArTPC is provided in Fig. 3. In this standard event display, color indicates the amount of charge detected as a function of collection plane wire number (equivalent to distance along the beam direction) on the horizontal axis and time (equivalent to beam-transverse horizontal distance) on the vertical axis. Topological selection eﬃciencies for signal are provided in Tab. 1. For the purposes of comparing how the 1γ1p and 1γ0p selections change as we step through the analysis, two representative distributions have been chosen to highlight at each stage. For the 1γ1p, where we have reconstructed both a proton and photon candidate of the ∆ baryon decay, we show the reconstructed invariant mass of the parent ∆ which for true NC ∆ radiative events should be centered on the ∆ mass of 1,232 MeV. In the case of 1γ0p, however, we have no reconstructed information of the escaping neutron and only have access to the photon candidate, so we instead plot the selected photon’s reconstructed calorimetric energy. These two distributions, after topological selection, are shown in Fig. 4 for the 1γ1p (left) and 1γ0p (right) selection. The distributions compare Run 1 unblinded data to simulated predictions. The Run 1 dataset corresponds to approximately 5 × 1020 POT, or < 5% of the total MicroBooNE data set for Runs 1-5, although after data-quality cuts the available POT that we compare on subsequent plots is closer to 4.1 × 1020 POT. The simulated predictions are broken down according to truth information; the corresponding number of events in the simulation, normalized to the data POT in each distribution, is shown in the legend.

5 As we utilize the same plotting style and legends as is in Fig. 4 for all comparisons between data and simulation in this note, we here briefly describe the breakdown of the various categories. Data points are shown in black, corresponding to the total POT exposure as described on the plot. The remaining histograms are stacked on top of each other and make up the total simulated expectation normalized to the same exposure. Our signal that we search for is the NC ∆ radiative decay, and is included both as the standard model expected rate in GENIE as well as an additional factor of 2 enhancement, which would be needed to explain the MiniBooNE LEE. The various categories including NC 1 π0 Coherent, NC π0 0 0 Non-Coherent, NC 2+ π , CC νµ π and CC νe/νe intrinsic all represent particular sub-components of the total BNB interactions in the MicroBooNE cryostat that we highlight explicitly as they are particularly important backgrounds for this search. All remaining BNB interactions within the cryostat that do not fit into the above 6 definitions are grouped together and referred to as “BNB Other”, the majority of which are 0 CC νµ events with no exiting π . The Dirt category represents all BNB neutrino induced backgrounds that originate outside the cryostat (in the surrounding concrete, steel and dirt) but scatter inside the TPC and produce reconstructable charge. The final histogram is the cosmogenic backgrounds, labeled “cosmic data”, as they are explicitly extracted from MicroBooNE data measured in situ during running, but out of time with the BNB neutrino spills. Simulation error bars include flux and cross-section systematic uncertainty as well as inherent Monte-Carlo statistical uncertainty, with the error bars on the data being their corresponding Poisson errors. Although detector systematics have been evaluated for the purposes of the final sensitivities (see Sec. 5), unless mentioned directly they are omitted from distributions. After topological selection, a series of pre-selection cuts are applied in order to reduce both any obvious and clear backgrounds as well as the number of selected events with reconstruction failures. For the 1γ1p topology, the pre-selection cuts include: • Shower Energy Cut: The reconstructed calorimetric shower energy must be at least 40 MeV. • Track Mean dE/dx Cut: The “truncated mean dE/dx” of the track must be above 2 MeV/cm. The truncated mean is an average of dE/dx along the track, truncating values further than 1 sigma away from a rolling mean, reducing the effects of spurious outliers.

• Angle between Track and Shower Cut: The absolute value of the cosine of the angle formed from the track direction and shower direction must be < 0.99. The shower direction is taken to be the direction from the reconstructed vertex to the reconstructed shower start point.

Figure 3: A example simulated ∆+ → pγ event, showing a short proton track with Bragg peak, as well as non-zero conversion distance of the photon before pair-producing into an e+e− pair that subsequently forms an electromagnetic shower in the liquid argon. This event represents a classic example of the topology we are searching for with the 1γ1p selection.

1x SM NC ∆ Radiative 1.50 x2 SM NC ∆ Radiative (LEE) 3.00 1x SM NC ∆ Radiative 1.13 x2 SM NC ∆ Radiative (LEE) 2.26 1400 NC 1 π0 Coherent 2.60 NC 1 π0 Non-Coherent 110.38 NC 1 π0 Coherent 3.10 NC 1 π0 Non-Coherent 56.84 π0 ν π0 π0 ν π0 NC 2+ 4.09 CC µ 1 69.84 250 NC 2+ 2.04 CC µ 1 10.53 BNB Other 796.47 CC ν /ν Intrinsic 13.28 BNB Other 149.13 CC ν /ν Intrinsic 5.56 Events e e Events e e 1200 Dirt 269.26 Run 1 Cosmic Data 1841.44 Dirt 74.85 Run 1 Cosmic Data 423.35 Flux & XS Systematics : 3111.85 Run 1 On-Beam Data 3284.00 Flux & XS Systematics : 728.78 Run 1On-Beam Data 790.00 200 1000 1γ1p 0.41e20 POT 1γ0p 0.41e20 POT MicroBooNE Preliminary MicroBooNE Preliminary 800 150

600 100 400 50 200

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 0 50 100 150 200 250 300 350 400 450 500 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) Corrected Calorimetric Shower Energy [MeV] 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 0 50 100 150 200 250 300 350 400 450 500 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) Corrected Calorimetric Shower Energy [MeV] (Data/MC: 1.06) (KS: 0.526) (χ2/nDOF : 22.88/18) (χ2 Pval: 0.195) (Data/MC: 1.08) (KS: 0.881) (χ2/nDOF : 16.37/18) (χ2 Pval: 0.567)

(a) 1γ1p Selection at Topological Stage (b) 1γ0p Selection at Topological Stage

Figure 4: 1γ1p and 1γ0p Monte Carlo predicted distributions after the topological selection stage. Pre- dictions are scaled to and compared to the open Run 1 data set corresponding to 4.1×1019 POT. Here, the dominant backgrounds are cosmogenic backgrounds, in green (labeled “cosmic data”, as they are directly extracted from MicroBooNE data measured in situ when the BNB is oﬀ), followed by “BNB other” and dirt induced backgrounds, in light blue. Overall, reasonable data to Monte Carlo agreement is observed, within statistical and systematic uncertainties. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

• Shower Fiducial Volume Cut: The reconstructed shower start must be 7 cm from the wire cell space charge boundary. The “wire cell space charge boundary” (SCB) represents the eﬀective active TPC volume [11].

• Track Calorimetric Energy Cut: The calorimetric kinetic energy (KE) of the track, estimated based on the track’s deposited energy, must be < 400 MeV. This forms a consistency check with the previous length-based cut.

• Track Containment Cut: The reconstructed track start and end must both be at least 2 cm from the SCB.

• Vertex Fiducial Volume Cut: The reconstructed vertex must be at least 2 cm from the SCB. • Track Length-Based Energy Cut: The reconstructed KE of the track, estimated based on the length of its travel path in argon under the hypothesis that the track is a proton, must be < 500 MeV. The signal efficiency of these cuts is shown in Tab. 2 (quoted specifically for “well-reconstructed” signal events in which the reconstructed shower and track were correctly matched to the true photon and proton in the interaction). Shown also are the efficiencies for two of our primary backgrounds: (1) mis-identified cosmogenic backgrounds, which are extracted directly from MicroBooNE data taken out-of-time with the BNB spills during Run 11, and (2) mis-identified NC 1π0 events. This demonstrates the significant background reduction achieved with these cuts. Figure 5 shows the effect of these cuts on the signal spectra (red) as well as the measured cosmogenic background spectra (green) and other BNB background spectra (blue). The resulting 1γ1p distribution, following pre-selection, is provided in Fig. 6, left.

In parallel to the 1γ1p pre-selection, the following cuts are applied for the 1γ0p pre-selection:

• Fiducial Volume Cut: The reconstructed shower start must be at least 2cm from the SCB. 1These are also often referred to as BNB-external data.

7 Figure 5: The positions of 6 of the primary precuts used in the 1γ1p selection, highlighted by showing the distributions of the NC ∆ signal (red) as well as Cosmic (green) and BNB other (blue) distributions as well as the cut position.

Sample ν Candidate 1γXp 1γ0p 1γ1p 2γXp 2γ0p 2γ1p BNB All 43.0% 8.1% 0.7% 2.9 % 2.9 % 0.4% 0.8% NC π0 41.9% 16.5% 3.8% 7.1 % 12.4% 3.6% 5.3% NC ∆Rad (All) 62.5% 38.1% 12.8% 17.5 % 9.3% 3.0% 3.8% NC ∆Rad (1γ1p Signal) 72.5% 47.1% 9.63% 28.9 % 8.6% 2.3% 4.1% NC ∆Rad (1γ0p Signal) 64.3% 40.1% 20.6% 11.6 % 10.9% 4.3% 4.0% BNB νe 79.7% 40.3% 6.5% 16.2% 17.4% 2.9 % 6.1% Cosmic Data 15.0% 3.0% 0.37% 1.68% 0.61% 0.13% 0.27% Dirt 22.8% 3.0% 0.49% 1.77% 0.52% 0.14% 0.24%

Table 1: Summary table of showing the percentages of total events that fall into each topological category for various samples used in this analysis. The ﬁrst column shows the overall percentage of events that contain a candidate neutrino vertex, which varies from almost 80% for intrinsic νe events to 15% for cosmogenic backgrounds. Here, BNB All refers to the entire BNB induced νµ and νe (as well as νµ and νe) interactions in the MicroBooNE cryostat. “Dirt” refers to beam-induced backgrounds which originate outside the cryostat volume; those are described in further detail in Sec. 3.4. Here Xp refers to any number of reconstructed tracks, including 0. Note that the analysis considers only 0 and 1 tracks; however expansion in the future to include X > 1 tracks could potentially lead to signal eﬃciency enhancement in the overall analysis.

8 • Shower Energy Cut: The calorimetric reconstructed shower energy must be at least 30 MeV. The combined eﬃciency of these two pre-selection cuts on the 1γ0p signal is greater than 95% relative to the topological stage, while 34.6% of cosmogenic backgrounds are removed. These topological eﬃciencies for the 1γ0p selection are given in Table 1. The resulting 1γ0p distribution, following pre-selection, is provided in Fig. 6, right.

1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 1x SM NC ∆ Radiative 1.09 x2 SM NC ∆ Radiative (LEE) 2.17 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 NC 1 π0 Coherent 2.78 NC 1 π0 Non-Coherent 49.89 90 0 0 0 0 NC 2+ π 0.97 CC νµ 1 π 15.56 NC 2+ π 1.59 CC νµ 1 π 9.53 BNB Other 89.82 CC ν /ν Intrinsic 7.52 250 BNB Other 116.23 CC ν /ν Intrinsic 5.31 Events e e Events e e 80 Dirt 15.92 Run 1 Cosmic Data 101.68 Dirt 50.58 Run 1 Cosmic Data 276.90 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 Flux & XS Systematics : 516.08 Run 1On-Beam Data 530.00 70 200 1γ1p 0.41e20 POT 1γ0p 0.41e20 POT 60 MicroBooNE Preliminary MicroBooNE Preliminary 50 150 40 100 30 20 50 10

Data/Prediction 0 Data/Prediction 0 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 0 50 100 150 200 250 300 350 400 450 500 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) Corrected Calorimetric Shower Energy [MeV] (Data/MC: 1.00) (KS: 0.852) (χ2/nDOF : 16.60/18) (χ2 Pval: 0.550) (Data/MC: 1.03) (KS: 0.590) (χ2/nDOF : 13.23/18) (χ2 Pval: 0.778)

(a) 1γ1p Selection at Pre-selection Cut Stage. (b) 1γ0p Selection at Pre-selection Cut Stage.

Figure 6: 1γ1p (left) and 1γ0p (right) Monte Carlo predicted distributions after the pre-selection cut stage. Predictions are scaled to and compared to the open Run 1 data set. At this stage, cosmogenic backgrounds have been reduced signiﬁcantly, to the extent that while they still are the largest single contributing background, they are smaller than the total sum of all BNB-driven backgrounds in the 1γ1p selection. Reasonable data to Monte Carlo prediction agreement is observed, within statistical and systematic uncertainties. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

Cut Signal (Truth Matched) Cosmic Data NC1π0 Vertex Fiducial Volume 99.8% 63.9% 88.1% Track Containment 100.0% 34.3% 79.6% Shower Start Fiducial Volume 97.4% 79.8% 87.0% Shower Energy 97.6% 39.2% 80.3% Track Length-Based Energy 98.6% 53.0% 92.0% Track Calorimetric Energy 99.3% 73.6% 96.2% Track Mean dE/dx 95.1% 51.5% 73.3% Angle between Track and Shower 99.5% 85.8% 96.5% Combined 89.0% 5.59% 44.3%

Table 2: Signal and background efficiencies of 1γ1p pre-selection cuts. Efficiencies are defined relative to the 1γ1p topological selection.

9 3.2 Final Selection After topological and pre-selection cuts, the signal purity for the 1γ1p topology is still < 1% of total selected events. The challenge of the final selection stage is therefore to reject the overwhelming number of remaining backgrounds, while preserving signal events. This is achieved with an ensemble of five separate multivariate Boosted Decision Trees (BDT’s) that each target a different background topology. All vertices which pass the topological selection and pre-selection cuts are passed into these five independent 0 0 BDT’s: cosmic, νe, NC π , second shower veto (SSV) further targeting NC π backgrounds, and then a final BDT that is trained on all remaining BNB neutrino backgrounds that are not directly targeted by the previous three BDTs; this is referred to as the “BNB Other BDT”. The BDT’s are trained separately, based on topological and calorimetric information tailored to the specific background they are targeting. For example, the νe BDT cut makes use of the dE/dx at the start of the shower, while the SSV BDT makes use of the conversion distance of a second candidate 2D reconstructed shower (which fails 3D reconstruction).

Examples of the top training variables for each BDT in the 1γ1p selection are provided in Figs. 7 and 8. Figure 7a, for example, shows the ratio of the shower impact parameter to the shower conversion distance used in the Cosmic BDT. The impact parameter indicates how close the back-projected shower direction comes to the vertex, whereas the conversion distance gives the distance from the shower start to the vertex regardless of the shower direction. If the impact parameter is small relative to the conversion distance, meaning a ratio of approximately 0, that indicates that the shower direction points back well to the vertex and therefore is more likely to be a correctly reconstructed event, whereas events where the shower is incorrectly associated to a vertex do not point back well, and tend to pile up at 1. Figure 7b shows the track truncated mean dE/dx. Given that cosmogenic backgrounds usually contain µ tracks whereas the signal must have a p track, this is a useful training variable.

Figure 7c shows the shower dE/dx where the start of the shower (the trunk) has been ﬁt using a Kalman ﬁtting algorithm, used in the νe BDT. Default behavior is to use the collection plane, but if the shower was not reconstructed on this plane, the plane induction plane with most hits is used instead. Given the e/γ separation power of shower dE/dx it makes sense that this variable ranks highly for discriminating νe backgrounds. Figure 7d shows the logarithm of shower conversion distance, which is also expected to perform well as a training variable given that e backgrounds should not have a gap between the vertex and the shower start unlike the γ signal. Here we see two peaks, corresponding to attached and un-attached showers with majority of signal having a non-zero conversion distance.

Figure 7e shows the reconstructed shower energy, used in the NC π0 BDT. As both the majority of π0 photons and radiative single-photons come from a ∆ resonance, the overall energy available is similar. As in the case of the π0 there are two resulting photons for the same available energy, radiative decay single photons tend to have on average higher energy than NC π0. Figure 7f shows the Photon Transverse Momen- tum, assuming that the photon originated at the reconstructed vertex. NC π0 events in which one photon is missed tend to have a larger transverse (Y-X) momentum spread in the one reconstructed photon, especially when compared to the radiative single photon. All distributions show good data to MC agreement at this stage.

1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 π0 π0 NC 1 Coherent 1.09 NC 1 Non-Coherent 48.09 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 120 π0 ν π0 NC 2+ 0.97 CC µ 1 15.56 160 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 BNB Other 89.82 CC ν /ν Intrinsic 7.52 0 0 Events e e NC 2+ π 0.97 CC νµ 1 π 15.56 Dirt 15.92 Run 1 Cosmic Data 101.68 BNB Other 89.82 CC ν /ν Intrinsic 7.52 Events e e 100 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 140 Dirt 15.92 Run 1 Cosmic Data 101.68 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 1γ1p 0.41e20 POT 120 80 MicroBooNE Preliminary 1γ1p 0.41e20 POT 100 MicroBooNE Preliminary 60 80

40 60

20 40 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Shower Impact Parameter/Shower Conversion Distance 2 3 4 5 6 7 8 9 10 11 12 1.5 Reconstructed Track Truncated Mean dE/dx [MeV/cm] 1.5 1 1 0.5 0.5

Data/Prediction 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Data/Prediction 0 Shower Impact Parameter/Shower Conversion Distance 2 3 4 5 6 7 8 9 10 11 12 Reconstructed Track Truncated Mean dE/dx [MeV/cm] (Data/MC: 1.00) (KS: 0.431) (χ2/nDOF : 10.41/18) (χ2 Pval: 0.918) (Data/MC: 1.00) (KS: 0.997) (χ2/nDOF : 14.76/18) (χ2 Pval: 0.678)

(a) Ratio of Shower Impact Parameter to Shower Con- (b) Track Truncated Mean dE/dx version Distance

1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 60 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 70 0 0 0 0 NC 2+ π 0.97 CC νµ 1 π 15.56 NC 2+ π 0.97 CC νµ 1 π 15.56 BNB Other 89.82 CC ν /ν Intrinsic 7.52 BNB Other 89.82 CC ν /ν Intrinsic 7.52 Events e e Events e e Dirt 15.92 Run 1 Cosmic Data 101.68 50 Dirt 15.92 Run 1 Cosmic Data 101.68 60 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00

50 1γ1p 0.41e20 POT 40 1γ1p 0.41e20 POT MicroBooNE Preliminary MicroBooNE Preliminary 40 30 30 20 20 10 10

0 1 2 3 4 5 6 7 8 9 10 −3 −2 −1 0 1 2 3 4 5 6 7 Shower dEdx [MeV/cm] Reconstructed Shower Conversion Distance Log[cm] 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 1 2 3 4 5 6 7 8 9 10 −3 −2 −1 0 1 2 3 4 5 6 7 Shower dEdx [MeV/cm] Reconstructed Shower Conversion Distance Log[cm] (Data/MC: 1.00) (KS: 0.222) (χ2/nDOF : 14.01/18) (χ2 Pval: 0.728) (Data/MC: 1.00) (KS: 1.000) (χ2/nDOF : 9.31/18) (χ2 Pval: 0.952)

220 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 90 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 0 0 0 0 200 NC 2+ π 0.97 CC νµ 1 π 15.56 NC 2+ π 0.97 CC νµ 1 π 15.56 BNB Other 89.82 CC ν /ν Intrinsic 7.52 BNB Other 89.82 CC ν /ν Intrinsic 7.52 Events e e Events 80 e e 180 Dirt 15.92 Run 1 Cosmic Data 101.68 Dirt 15.92 Run 1 Cosmic Data 101.68 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 160 70 γ γ 140 1 1p 0.41e20 POT 60 1 1p 0.41e20 POT MicroBooNE Preliminary MicroBooNE Preliminary 120 50 100 40 80 30 60 20 40 20 10

0 100 200 300 400 500 600 0 0.05 0.1 0.15 0.2 0.25 0.3 Corrected Calorimetric Shower Energy [MeV] Photon Transverse Momentum [GeV] 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 100 200 300 400 500 600 0 0.05 0.1 0.15 0.2 0.25 0.3 Corrected Calorimetric Shower Energy [MeV] Photon Transverse Momentum [GeV] (Data/MC: 1.00) (KS: 0.973) (χ2/nDOF : 8.85/12) (χ2 Pval: 0.715) (Data/MC: 1.00) (KS: 0.759) (χ2/nDOF : 12.66/18) (χ2 Pval: 0.811)

(e) Reconstructed Shower Energy (f) Photon Transverse Momentum

Figure 7: Monte Carlo prediction to data comparisons for some of the top training variables used for the 1γ1p BDT’s, in terms of the total gain, shown at the pre-selection cut stage. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

11 Figure 8a shows the second shower search closest 2D candidate conversion distance, used in the SSV BDT, while Fig. 8b shows the angle of the 3D second shower search candidate which points back best to the reconstructed vertex, with respect to the primary shower. Clusters which peak at 1 correspond to a small-opening angle between the candidate 3D cluster and the selected reconstructed shower, which means they are quite co-linear with the reconstructed shower. Combining this information with conversion distance can separate out cases of a second shower and cases where it is a fragment of the primary shower incorrectly clustered. Figure 8c shows the log of the maximum distance from a 3D space point that is clustered into the selected reconstructed track to a linear ﬁt to all of the space points in the track, used in the BNB Other BDT. This is a metric of how straight and clean the track is. Figure 8d shows the Pandora shower score assigned to all reconstructed showers, also used in the BNB Other BDT, with 0 corresponding to very shower-like and 0.5 to less shower-like. Here we see that the signal events tend towards low score whereas the backgrounds span the full range of scores.

1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 100 0 0 0 0 NC 2+ π 0.97 CC νµ 1 π 15.56 120 NC 2+ π 0.97 CC νµ 1 π 15.56 BNB Other 89.82 CC ν /ν Intrinsic 7.52 BNB Other 89.82 CC ν /ν Intrinsic 7.52 Events e e Events e e Dirt 15.92 Run 1 Cosmic Data 101.68 Dirt 15.92 Run 1 Cosmic Data 101.68 80 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 100 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 1γ1p 0.41e20 POT 1γ1p 0.41e20 POT 80 60 MicroBooNE Preliminary MicroBooNE Preliminary 60 40 40

20 20

0 10 20 30 40 50 60 70 80 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 sss2d closest candidate conversion Distance [cm] sss3d min IOC implied angle w.r.t primary shower [cos] 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 10 20 30 40 50 60 70 80 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 sss2d closest candidate conversion Distance [cm] sss3d min IOC implied angle w.r.t primary shower [cos] (Data/MC: 1.00) (KS: 0.249) (χ2/nDOF : 37.41/18) (χ2 Pval: 0.005) (Data/MC: 1.00) (KS: 0.539) (χ2/nDOF : 10.68/18) (χ2 Pval: 0.907)

(a) (b)

1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 160 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 π0 ν π0 π0 ν π0 100 NC 2+ 0.97 CC µ 1 15.56 NC 2+ 0.97 CC µ 1 15.56 BNB Other 89.82 CC ν /ν Intrinsic 7.52 140 BNB Other 89.82 CC ν /ν Intrinsic 7.52 Events e e Events e e Dirt 15.92 Run 1 Cosmic Data 101.68 Dirt 15.92 Run 1 Cosmic Data 101.68 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 120 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 80 1γ1p 0.41e20 POT 1γ1p 0.41e20 POT MicroBooNE Preliminary 100 MicroBooNE Preliminary 60 80

40 60

40 20 20

−2 −1.5 −1 −0.5 0 0.5 1 1.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Reconstructed Track Max Distance Spacepoint from Line [cm] Shower Score 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 −2 −1.5 −1 −0.5 0 0.5 1 1.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Reconstructed Track Max Distance Spacepoint from Line [cm] Shower Score (Data/MC: 1.00) (KS: 0.499) (χ2/nDOF : 9.41/18) (χ2 Pval: 0.950) (Data/MC: 1.00) (KS: 0.749) (χ2/nDOF : 20.46/18) (χ2 Pval: 0.307)

Figure 8: Monte Carlo prediction to data comparisons for some of the top training variables used for the 1γ1p BDT’s, in terms of the total gain, shown at the pre-selection cut stage. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

12 Similarly, several BDT training variables are shown for the 1γ0p selection in Fig. 9. Figure 9a shows the reconstructed photon transverse momentum, a top training variable for the BNB BDT, which shows good data-MC agreement at this stage. Figure 9b shows the Pandora neutrino score, a top training variable for the cosmic BDT, which also shows good agreement and as expected we see that true showers like those 0 from the νe and π backgrounds peak at low shower score. Variable importance here is deﬁned in terms of the variable’s “gain” which is a measure of the improvement in accuracy of a model when the variable in question is used in a BDT branch. Figure 9c shows the ratio of the shower energy to geometric size, also used in the cosmic BDT. If the ratio is large, this indicates that the energy is high relative to the size of the reconstructed shower which is useful for removing tracks mis-reconstructed as showers or highly energetic cosmogenic showers. Finally, Fig. 9d shows the dE/dx calculated with the Kalman track ﬁtter and all planes, used in the BNB BDT.

1x SM NC ∆ Radiative 1.09 x2 SM NC ∆ Radiative (LEE) 2.17 1x SM NC ∆ Radiative 1.09 x2 SM NC ∆ Radiative (LEE) 2.17 NC 1 π0 Coherent 2.78 NC 1 π0 Non-Coherent 49.89 NC 1 π0 Coherent 2.78 NC 1 π0 Non-Coherent 49.89 π0 ν π0 π0 ν π0 140 NC 2+ 1.59 CC µ 1 9.53 NC 2+ 1.59 CC µ 1 9.53 BNB Other 116.23 CC ν /ν Intrinsic 5.31 250 BNB Other 116.23 CC ν /ν Intrinsic 5.31 Events e e Events e e Dirt 50.58 Run 1 Cosmic Data 276.90 Dirt 50.58 Run 1 Cosmic Data 276.90 120 Flux & XS Systematics : 516.08 Run 1On-Beam Data 530.00 Flux & XS Systematics : 516.08 Run 1On-Beam Data 530.00 200 100 1γ0p 0.41e20 POT 1γ0p 0.41e20 POT MicroBooNE Preliminary MicroBooNE Preliminary 80 150

60 100 40 50 20

0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Photon Transverse Momentum [GeV] Neutrino Slice Score 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Photon Transverse Momentum [GeV] Neutrino Slice Score (Data/MC: 1.03) (KS: 0.686) (χ2/nDOF : 12.02/24) (χ2 Pval: 0.980) (Data/MC: 1.03) (KS: 0.910) (χ2/nDOF : 14.51/24) (χ2 Pval: 0.934)

(a) Reconstructed Photon Transverse Momentum (b) Pandora Neutrino Score

1x SM NC ∆ Radiative 1.09 x2 SM NC ∆ Radiative (LEE) 2.17 1x SM NC ∆ Radiative 1.09 x2 SM NC ∆ Radiative (LEE) 2.17 250 NC 1 π0 Coherent 2.78 NC 1 π0 Non-Coherent 49.89 NC 1 π0 Coherent 2.78 NC 1 π0 Non-Coherent 49.89 0 0 0 0 NC 2+ π 1.59 CC νµ 1 π 9.53 NC 2+ π 1.59 CC νµ 1 π 9.53 BNB Other 116.23 CC ν /ν Intrinsic 5.31 BNB Other 116.23 CC ν /ν Intrinsic 5.31 Events e e Events 100 e e Dirt 50.58 Run 1 Cosmic Data 276.90 Dirt 50.58 Run 1 Cosmic Data 276.90 200 Flux & XS Systematics : 516.08 Run 1On-Beam Data 530.00 Flux & XS Systematics : 516.08 Run 1On-Beam Data 530.00 1γ0p 0.41e20 POT 80 1γ0p 0.41e20 POT 150 MicroBooNE Preliminary MicroBooNE Preliminary 60

100 40

50 20

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0 1 2 3 4 5 6 7 8 9 10 Ratio of Calorimetric Shower Energy to Shower Length x Opening Angle [GeV/cm*rad] Shower dEdx [MeV/cm] 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0 1 2 3 4 5 6 7 8 9 10 Ratio of Calorimetric Shower Energy to Shower Length x Opening Angle [GeV/cm*rad] Shower dEdx [MeV/cm] (Data/MC: 1.03) (KS: 0.763) (χ2/nDOF : 21.66/24) (χ2 Pval: 0.600) (Data/MC: 1.03) (KS: 0.520) (χ2/nDOF : 33.66/24) (χ2 Pval: 0.091)

Figure 9: Monte Carlo prediction to data comparisons for some of the training variables for the 1γ0p BDT’s, shown at the pre-selection cut stage. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

13 After training, the BDT cuts are optimized simultaneously on the final selected sample (1γ1p or 1γ0p), in order to maximize signal to background. Distributions of the BDT responses, after training, are provided in Figs. 10 and 11 for 1γ0p and 1γ1p, respectively. As can be seen in several of these BDT responses, the NC ∆ signal events, while generally peaking at high BDT score response as expected, also has smaller peaks at low BDT score. This is primarily due to the fact that the ∆ radiative histogram is showing all events in which a NC ∆ radiative scattering took place, regardless of whether or not the reconstructed shower and/or track candidates are reconstructed well. We break this down for the Cosmic BDT further in Fig. 12, where we split the NC ∆ radiative sample into five categories. In this breakdown it can be seen that over 93% of the well-reconstructed events that are defined to have one visible proton and photon have a cosmic BDT response score above 0.95. The flatness of the signal BDT response for NCπ0 and SSV BDT, is partially due to this same effect, but also stresses the fact that kinematically a certain fraction of NC π0 decays in which one shower is missed look almost indistinguishable from our signal, meaning separation is extremely difficult.

4 1x SM NC ∆ Radiative 1.09 x2 SM NC ∆ Radiative (LEE) 2.17 4 1x SM NC ∆ Radiative 1.09 x2 SM NC ∆ Radiative (LEE) 2.17 10 NC 1 π0 Coherent 2.78 NC 1 π0 Non-Coherent 49.89 10 NC 1 π0 Coherent 2.78 NC 1 π0 Non-Coherent 49.89 0 0 0 0 NC 2+ π 1.59 CC νµ 1 π 9.53 NC 2+ π 1.59 CC νµ 1 π 9.53 BNB Other 116.23 CC ν /ν Intrinsic 5.31 BNB Other 116.23 CC ν /ν Intrinsic 5.31 Events e e Events e e 3 Dirt 50.58 Run 1 Cosmic Data 276.90 3 Dirt 50.58 Run 1 Cosmic Data 276.90 10 Flux & XS Systematics : 516.08 Run 1On-Beam Data 530.00 10 Flux & XS Systematics : 516.08 Run 1On-Beam Data 530.00 γ γ 2 1 0p 0.41e20 POT 2 1 0p 0.41e20 POT 10 MicroBooNE Preliminary 10 MicroBooNE Preliminary

10 10

1 1

10−1 10−1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Cosmic BDT Score BNB Other BDT Score 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Cosmic BDT Score BNB Other BDT Score (Data/MC: 1.03) (KS: 0.999) (χ2/nDOF : 24.46/24) (χ2 Pval: 0.436) (Data/MC: 1.03) (KS: 0.866) (χ2/nDOF : 19.16/24) (χ2 Pval: 0.743)

(a) 1γ0p Cosmic BDT Response (b) 1γ0p BNB Other BDT Response

4 1x SM NC ∆ Radiative 1.09 x2 SM NC ∆ Radiative (LEE) 2.17 10 NC 1 π0 Coherent 2.78 NC 1 π0 Non-Coherent 49.89 0 0 NC 2+ π 1.59 CC νµ 1 π 9.53 BNB Other 116.23 CC ν /ν Intrinsic 5.31 Events e e 3 Dirt 50.58 Run 1 Cosmic Data 276.90 10 Flux & XS Systematics : 516.08 Run 1On-Beam Data 530.00 γ 2 1 0p 0.41e20 POT 10 MicroBooNE Preliminary

10−1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 NCπ0 BDT Score 1.5 1 0.5

Data/Prediction 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 NCπ0 BDT Score (Data/MC: 1.03) (KS: 0.905) (χ2/nDOF : 23.58/24) (χ2 Pval: 0.486)

Figure 10: BDT response distributions for the 1γ0p selection. The Monte Carlo predictions are scaled to 5×1019 POT, and compared to corresponding data from Run 1. The data and Monte Carlo agree reasonably within statistical and systematic uncertainties, and each BDT is capable of providing noticeable signal to background diﬀerentiation. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

4 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 10 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 104 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 0 0 0 0 NC 2+ π 0.97 CC νµ 1 π 15.56 NC 2+ π 0.97 CC νµ 1 π 15.56 BNB Other 89.82 CC ν /ν Intrinsic 7.52 BNB Other 89.82 CC ν /ν Intrinsic 7.52 Events e e Events 3 e e 3 Dirt 15.92 Run 1 Cosmic Data 101.68 10 Dirt 15.92 Run 1 Cosmic Data 101.68 10 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00

1γ1p 0.41e20 POT 2 1γ1p 0.41e20 POT 2 10 10 MicroBooNE Preliminary MicroBooNE Preliminary

10 10

1 1

− 10−1 10 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Cosmic BDT Score ν BDT Score 1.5 1.5 E 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ν Cosmic BDT Score E BDT Score (Data/MC: 1.00) (KS: 0.805) (χ2/nDOF : 23.54/24) (χ2 Pval: 0.488) (Data/MC: 1.00) (KS: 0.988) (χ2/nDOF : 16.85/24) (χ2 Pval: 0.855)

(a) 1γ1p Cosmic BDT Response (b) 1γ1p νe BDT Response

∆ ∆ ∆ ∆ 1x SM NC Radiative 0.92 x2 SM NC Radiative (LEE) 1.84 4 1x SM NC Radiative 0.92 x2 SM NC Radiative (LEE) 1.84 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 10 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 0 0 0 0 NC 2+ π 0.97 CC νµ 1 π 15.56 NC 2+ π 0.97 CC νµ 1 π 15.56 3 BNB Other 89.82 CC ν /ν Intrinsic 7.52 BNB Other 89.82 CC ν /ν Intrinsic 7.52 Events 10 e e Events e e Dirt 15.92 Run 1 Cosmic Data 101.68 3 Dirt 15.92 Run 1 Cosmic Data 101.68 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 10 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00

2 γ γ 10 1 1p 0.41e20 POT 2 1 1p 0.41e20 POT MicroBooNE Preliminary 10 MicroBooNE Preliminary

10 10

1 1

− 10 1 10−1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 NCπ0 BDT Score SSV BDT Score 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 NCπ0 BDT Score SSV BDT Score (Data/MC: 1.00) (KS: 0.944) (χ2/nDOF : 9.91/24) (χ2 Pval: 0.995) (Data/MC: 1.00) (KS: 0.419) (χ2/nDOF : 26.32/24) (χ2 Pval: 0.337)

104 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 NC 1 π0 Coherent 1.09 NC 1 π0 Non-Coherent 48.09 0 0 NC 2+ π 0.97 CC νµ 1 π 15.56 BNB Other 89.82 CC ν /ν Intrinsic 7.52 Events e e 103 Dirt 15.92 Run 1 Cosmic Data 101.68 Flux & XS Systematics : 283.39 Run 1 On-Beam Data 283.00 γ 102 1 1p 0.41e20 POT MicroBooNE Preliminary

10−1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 BNB Other BDT Score 1.5 1 0.5

Data/Prediction 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 BNB Other BDT Score (Data/MC: 1.00) (KS: 0.674) (χ2/nDOF : 22.56/24) (χ2 Pval: 0.546)

(e) 1γ1p BNB Other BDT Response

Figure 11: BDT response distributions for the 1γ1p selection. The Monte Carlo predictions are scaled to 4.1×1019 POT, and compared to corresponding data from Run 1. The data and Monte Carlo agree reasonably within statistical and systematic uncertainties, and each BDT is capable of providing noticeable signal to background diﬀerentiation. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

15 Figure 12: A breakdown of the NC ∆ Radiative MC sample’s cosmic BDT response, as shown in yellow and orange stacked histograms in Fig. 11a. For the purposes of counting visibility, protons and photons must have greater than 20 MeV KE (e.g, protons with < 20 MeV are counted as 0 proton events) and cosmic contamination is deﬁned as an event in which either the track or shower contains more than 50% of its hits coming from cosmic events. Bad reconstruction (”Bad reco”) is an event where the track or shower are not matched to the ∆ decay proton or photon respectively. Note the logarithmic scale on the y axis. In this breakdown it can be seen that over 93% of the well-reconstructed signal events that are deﬁned to have one visible proton and photon have a cosmic BDT response score above 0.95.

16 The eﬀect of each BDT score cut, applied independently on pre-selected events, is shown in Figs. 13 and 14 for 1γ0p and 1γ1p, respectively. Final selection is performed with the optimized BDT cuts provided in Tab. 3.

1x SM NC ∆ Radiative 0.60 x2 SM NC ∆ Radiative (LEE) 1.20 60 1x SM NC ∆ Radiative 0.76 x2 SM NC ∆ Radiative (LEE) 1.51 30 NC 1 π0 Coherent 2.01 NC 1 π0 Non-Coherent 14.29 NC 1 π0 Coherent 1.51 NC 1 π0 Non-Coherent 18.35 0 0 0 0 NC 2+ π 0.34 CC νµ 1 π 2.51 NC 2+ π 0.34 CC νµ 1 π 2.78 BNB Other 4.26 CC ν /ν Intrinsic 2.02 BNB Other 8.85 CC ν /ν Intrinsic 1.42 Events e e Events 50 e e 25 Dirt 0.58 Run 1 Cosmic Data 0.96 Dirt 2.02 Run 1 Cosmic Data 16.95 Flux & XS Systematics : 28.77 Run 1On-Beam Data 22.00 Flux & XS Systematics : 54.48 Run 1On-Beam Data 58.00

20 1γ0p 0.41e20 POT 40 1γ0p 0.41e20 POT MicroBooNE Preliminary MicroBooNE Preliminary 15 30

10 20

5 10

0 50 100 150 200 250 300 350 400 450 500 0 50 100 150 200 250 300 350 400 450 500 Corrected Calorimetric Shower Energy [MeV] Cosmic Only Cut Corrected Calorimetric Shower Energy [MeV] BNB Other Only Cut 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 50 100 150 200 250 300 350 400 450 500 0 50 100 150 200 250 300 350 400 450 500 Corrected Calorimetric Shower Energy [MeV] Cosmic Only Cut Corrected Calorimetric Shower Energy [MeV] BNB Other Only Cut (Data/MC: 0.76) (KS: 0.035) (χ2/nDOF : 11.13/4) (χ2 Pval: 0.025) (Data/MC: 1.06) (KS: 0.558) (χ2/nDOF : 9.31/6) (χ2 Pval: 0.157)

(a) After Pre-selection and Cosmic BDT >0.988 (b) After Pre-selection and BNB Other BDT > 0.893.

1x SM NC ∆ Radiative 0.60 x2 SM NC ∆ Radiative (LEE) 1.19 NC 1 π0 Coherent 0.69 NC 1 π0 Non-Coherent 8.76 0 0 60 NC 2+ π 0.23 CC νµ 1 π 1.33 BNB Other 19.26 CC ν /ν Intrinsic 1.40 Events e e Dirt 3.38 Run 1 Cosmic Data 26.54 50 Flux & XS Systematics : 63.39 Run 1On-Beam Data 68.00 1γ0p 0.41e20 POT 40 MicroBooNE Preliminary

0 50 100 150 200 250 300 350 400 450 500 Corrected Calorimetric Shower Energy [MeV] NC π0 Only Cut 1.5 1 0.5

Data/Prediction 0 0 50 100 150 200 250 300 350 400 450 500 Corrected Calorimetric Shower Energy [MeV] NC π0 Only Cut (Data/MC: 1.07) (KS: 0.896) (χ2/nDOF : 8.29/6) (χ2 Pval: 0.218)

Figure 13: 1γ0p predicted distributions and comparisons to Run 1 open data after pre-selection cuts and each optimized BDT cut applied as indicated on each sub-ﬁgure caption. Reasonable data to Monte Carlo agreement is observed for all distributions. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

1x SM NC ∆ Radiative 0.73 x2 SM NC ∆ Radiative (LEE) 1.46 1x SM NC ∆ Radiative 0.69 x2 SM NC ∆ Radiative (LEE) 1.37 45 NC 1 π0 Coherent 0.45 NC 1 π0 Non-Coherent 29.36 70 NC 1 π0 Coherent 0.35 NC 1 π0 Non-Coherent 29.54 0 0 0 0 NC 2+ π 0.23 CC νµ 1 π 7.33 NC 2+ π 0.51 CC νµ 1 π 6.27 BNB Other 19.47 CC ν /ν Intrinsic 4.62 BNB Other 16.90 CC ν /ν Intrinsic 0.24 Events 40 e e Events e e Dirt 0.55 Run 1 Cosmic Data 2.24 60 Dirt 3.10 Run 1 Cosmic Data 13.75 35 Flux & XS Systematics : 66.43 Run 1 On-Beam Data 57.00 Flux & XS Systematics : 72.73 Run 1 On-Beam Data 82.00 γ 50 γ 30 1 1p 0.41e20 POT 1 1p 0.41e20 POT MicroBooNE Preliminary MicroBooNE Preliminary 25 40

20 30 15 20 10 10 5

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 ν Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) Cosmic Only Cut Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) e Only Cut 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 ν Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) Cosmic Only Cut Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) e Only Cut (Data/MC: 0.86) (KS: 0.978) (χ2/nDOF : 4.99/6) (χ2 Pval: 0.546) (Data/MC: 1.13) (KS: 0.934) (χ2/nDOF : 3.84/6) (χ2 Pval: 0.698)

(a) After Pre-selection and Cosmic BDT >0.975 (b) After Pre-selection and νe BDT >0.571.

24 1x SM NC ∆ Radiative 0.55 x2 SM NC ∆ Radiative (LEE) 1.11 1x SM NC ∆ Radiative 0.42 x2 SM NC ∆ Radiative (LEE) 0.84 NC 1 π0 Coherent 0.08 NC 1 π0 Non-Coherent 10.55 22 NC 1 π0 Coherent 0.08 NC 1 π0 Non-Coherent 4.84 22 π0 ν π0 π0 ν π0 NC 2+ 0.00 CC µ 1 2.37 20 NC 2+ 0.00 CC µ 1 0.84 BNB Other 7.80 CC ν /ν Intrinsic 1.58 BNB Other 9.08 CC ν /ν Intrinsic 1.28 Events 20 e e Events e e Dirt 1.17 Run 1 Cosmic Data 4.48 18 Dirt 0.86 Run 1 Cosmic Data 4.16 18 Flux & XS Systematics : 29.68 Run 1 On-Beam Data 27.00 Flux & XS Systematics : 22.40 Run 1 On-Beam Data 20.00 16 16 1γ1p 0.41e20 POT 1γ1p 0.41e20 POT 14 14 MicroBooNE Preliminary MicroBooNE Preliminary 12 12 10 10 8 8 6 6 4 4 2 2

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) NCπ0 Only Cut Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) SSV Only Cut 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) NCπ0 Only Cut Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) SSV Only Cut (Data/MC: 0.91) (KS: 0.615) (χ2/nDOF : 8.24/6) (χ2 Pval: 0.221) (Data/MC: 0.89) (KS: 0.432) (χ2/nDOF : 11.30/6) (χ2 Pval: 0.079)

1x SM NC ∆ Radiative 0.56 x2 SM NC ∆ Radiative (LEE) 1.11 16 NC 1 π0 Coherent 0.02 NC 1 π0 Non-Coherent 15.74 0 0 NC 2+ π 0.11 CC νµ 1 π 1.27 BNB Other 2.27 CC ν /ν Intrinsic 0.42 Events 14 e e Dirt 0.00 Run 1 Cosmic Data 0.64 Flux & XS Systematics : 22.14 Run 1 On-Beam Data 19.00 12 1γ1p 0.41e20 POT 10 MicroBooNE Preliminary 8

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) BNB Other Only Cut 1.5 1 0.5

Data/Prediction 0 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) BNB Other Only Cut (Data/MC: 0.86) (KS: 0.891) (χ2/nDOF : 3.33/6) (χ2 Pval: 0.766)

(e) After Pre-selection and BNB Other BDT >0.963

Figure 14: 1γ1p predicted distributions and comparisons to Run 1 open data after pre-selection cuts and each optimized BDT cut applied as indicated on each sub-ﬁgure caption. Reasonable data to Monte Carlo agreement is observed for all distributions. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

18 0 Cosmic BDT BNB Other BDT NC π BDT νe BDT SSV BDT 1γ1p Selection Score cut: 0.975 0.963 0.467 0.571 0.522 Signal eﬃciency: 18.9% 15.5% 14.7% 17.9% 23.5% 1γ0p Selection Score cut: 0.988 0.893 0.429 - - Signal eﬃciency: 55.3% 69.6% 47.4% - -

Table 3: Summary of optimized BDT score cuts applied to each selection, 1γ1p and 1γ0p, and corresponding signal eﬃciencies.

The resulting distributions for both the 1γ1p and the 1γ0p selections are shown in Figs. 15 and 16, respectively. The resulting number of events, at ﬁnal selection stage, is provided in Tab. 12. The two data events passing ﬁnal selection, from the 1γ1p sample, are shown in Fig. 17 and two representative events from the 1γ0p selection are shown in Fig. 18. The distributions are provided for the currently unblinded data sample from Run 1, corresponding to a bit less than 5×1019 POT agyer data quality cuts. This corresponds to < 5% of the total collected data by MicroBooNE. The corresponding predicted distributions projected to the full available data set, corresponding to 12.25×1020 POT, are shown in the right panels of Figs. 15 and 16.

NC 1 π0 Coherent 0.00 NC 1 π0 Non-Coherent 1.77 0 0 NC 2+ π 0.00 CC νµ 1 π 0.04 BNB Other 0.17 CC ν /ν Intrinsic 0.00 2.5 e e Dirt 0.00 Run 1 Cosmic Data 0.00 Events 1x SM NC ∆ Radiative 0.31 x2 SM NC ∆ Radiative (LEE) 0.63 0 0 Flux & XS Systematics : 2.93 Run 1 On-Beam Data 2.00 40 NC 1 π Coherent 0.00 NC 1 π Non-Coherent 55.66 0 0 2 NC 2+ π 0.00 CC νµ 1 π 0.91 γ Events 1 1p 0.41e20 POT BNB Other 6.97 CC νe/νe Intrinsic 1.61 MicroBooNE Preliminary 35 Dirt 0.00 Run 1+3 Cosmic Data 0.00 1.5 1x SM NC Δ Radiative 10.30 x2 SM NC Δ Radiative (LEE) 20.60 30 Flux & XS Systematics : 96.05 1 25 1γ1p 12.25e20 POT MicroBooNE Simulation Preliminary 0.5 20

15 20 100 200 300 400 500 600 Corrected Calorimetric Shower Energy [MeV] 1.5 10 1 0.5 5

Data/Prediction 0 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Corrected Calorimetric Shower Energy [MeV] Corrected Calorimetric Shower Energy [MeV] (Data/MC: 0.68) (KS: 0.978) (χ2/nDOF : 5.17/12) (χ2 Pval: 0.952)

Figure 15: 1γ1p final selection with all cuts applied. On the left is the reconstructed shower energy for Run 1 open data showing 2 surviving data events in the selection, with an expectation of ∼ 3 Monte Carlo events. On the right is the same predicted distribution for the full MicroBooNE data set of 12.25×1020 POT. The shaded band corresponds to the combined flux, cross-section and statistical (due to finite statistics) uncertainty on the Monte Carlo. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

12 NC 1 π0 Coherent 0.61 NC 1 π0 Non-Coherent 4.41 0 0 NC 2+ π 0.17 CC νµ 1 π 0.70 ν ν BNB Other 1.31 CC e/ e Intrinsic 0.65 Dirt 0.42 Run 1 Cosmic Data 0.32 Events 10 1x SM NC ∆ Radiative 0.42 x2 SM NC ∆ Radiative (LEE) 0.84 Flux & XS Systematics : 9.84 Run 1On-Beam Data 7.00 NC 1 π0 Coherent 16.24 NC 1 π0 Non-Coherent 142.48 0 0 NC 2+ π 2.69 CC νµ 1 π 24.85 8 γ Events 1 0p 0.41e20 POT 120 BNB Other 47.26 CC νe/νe Intrinsic 20.66 MicroBooNE Preliminary Dirt 11.39 Run 1+3 Cosmic Data 19.80 6 1x SM NC Δ Radiative 12.25 x2 SM NC Δ Radiative (LEE) 24.50 100 Flux & XS Systematics : 322.11

4 1γ0p 12.25e20 POT 80 MicroBooNE Simulation 2 Preliminary 60

2 100 150 200 250 300 350 400 450 500 550 Corrected Calorimetric Shower Energy [MeV] 40 1.5 1 20 0.5

Data/Prediction 0 100 150 200 250 300 350 400 450 500 550 100 150 200 250 300 350 400 450 500 550 Corrected Calorimetric Shower Energy [MeV] Corrected Calorimetric Shower Energy [MeV] (Data/MC: 0.71) (KS: 1.000) (χ2/nDOF : 1.14/4) (χ2 Pval: 0.888)

Figure 16: 1γ0p final selection with all cuts applied. The top figure shows reconstructed shower energy for Run 1 open data showing 7 surviving data events in the selection, with an expectation of ∼ 9.8 Monte Carlo events. The bottom figure shows the predicted distribution for the full MicroBooNE data set of 12.25×1020 POT. The shaded band corresponds to the combined flux, cross-section and statistical (due to finite statistics) uncertainty on the Monte Carlo. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

20 Figure 17: The two data events passing the ﬁnal 1γ1p selection in the open Run 1 data sample. Left: The ﬁrst event showing clean conversion distance and no strong evidence of a secondary shower that would be suggestive of it being NC π0 in origin. Although based on our simulation it is most likely a NC π0, it highlights a data event that matches out signal extremely well. Right: Here, the highly ionizing track in the center is reconstructed as the proton, with the three electromagnetic showers at the bottom being reconstructed as a single photon candidate. The rightmost shower, as well as the multiple tracks on the left were reconstructed in a separate slice. This is an example of a π0 event that due to reconstruction failures is a clear background to the selection.

Figure 18: Two example data events passing the ﬁnal 1γ0p selection in the open Run 1 data sample. Both showers show a large dE/dx at the shower start, with the characteristic e+e− pair production ‘V’ shape.

21 3.3 Sideband Validation The single photon analysis is performed as a blind analysis, whereby the reconstruction, selection, and final fits are finalized with statistics-limited data sets, which provide negligible sensitivity to an enhanced rate of NC ∆ radiative decay events. After the analysis is finalized, and prior to signal unblinding, higher statistics “sideband boxes,” comprising events which are topologically similar to our 1γ signal but signal- blind, are studied. This allows us to confirm that our backgrounds are correctly predicted and reconstructed in our analysis. Three mutually exclusive 1γ1p sideband boxes have been defined in terms of inverse optimized BNB Other and NC π0 BDT cuts. The sideband “boxes” are defined to be exclusive of the signal-inclusive box (box A):

• Box B is deﬁned as events passing the optimized NC π0 BDT cut but failing the optimized BNB Other BDT cut.

• Box C is deﬁned as events failing both the optimized NC π0 BDT cut and the optimized BNB Other BDT cut.

• Box D is deﬁned as events failing the optimized NC π0 BDT cut but passing the optimized BNB Other BDT cut. Since NC π0 mis-identiﬁed events are the primary background, the boxes explicitly target at least one high-statistics sideband sample which is NC π0 pure, as well as others which target other backgrounds more holistically. The resulting distributions are shown in in Figs. 19 through 21 for the currently open 5×1019 POT data set from Run 1, showing reasonable data to Monte Carlo agreement (all p−values > 5%). In order to preserve blindness to electron-like interpretations of the MiniBooNE low energy excess, as analyses targeting such interpretations are currently ongoing by the MicroBooNE collaboration [12, 13], we utilize the νe rejection BDT as shown in Fig. 11 and pre-apply a cut removing 92.5% of intrinsic νe events for all sideband boxes. Processing of Run 1-3 data through sideband selection is ongoing to provide higher-statistics comparisons prior to signal unblinding.

1x SM NC ∆ Radiative 0.08 x2 SM NC ∆ Radiative (LEE) 0.16 14 NC 1 π0 Coherent 0.10 NC 1 π0 Non-Coherent 2.67 0 0 NC 2+ π 0.00 CC νµ 1 π 1.85 BNB Other 3.84 CC ν /ν Intrinsic 0.16 Events e e 12 Dirt 0.28 Run 1 Cosmic Data 1.92 Flux, XSec, & MC-Stats Errors : 11.06 Run 1 On-Beam Data 12.00 10 1γ1p 0.41e20 POT MicroBooNE Preliminary 8

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) B 1.5 1 0.5

Data/Prediction 0 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) B (Data/MC: 1.09) (KS: 0.995) (χ2/nDOF : 2.97/3) (χ2 Pval: 0.397)

NC 1 π0 Coherent 2.99 NC 1 π0 Non-Coherent 82.51 0 0 NC 2+ π 1.33 CC νµ 1 π 59.05

Events 350 BNB Other 176.57 CC νe/νe Intrinsic 5.01 Dirt 9.02 Run 1+3 Cosmic Data 80.89 300 1x SM NC Δ Radiative 2.60 x2 SM NC Δ Radiative (LEE) 5.19 Flux & XS Systematics : 425.16 250 1γ1p 12.25e20 POT MicroBooNE Simulation 200 Preliminary

150

100

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) B

Figure 19: The reconstructed ∆ invariant mass distribution for (far sideband) box B, deﬁned as passing the optimized NC π0 BDT cut but failing the optimized BNB Other BDT cut. Top: Run 1 open data, in comparison with MC prediction. Bottom: MC prediction for 12.25×1020 POT, corresponding to the full data set for Runs 1-5. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

80 1x SM NC ∆ Radiative 0.12 x2 SM NC ∆ Radiative (LEE) 0.24 NC 1 π0 Coherent 0.35 NC 1 π0 Non-Coherent 16.83 0 0 NC 2+ π 0.45 CC νµ 1 π 5.15 70 BNB Other 28.14 CC ν /ν Intrinsic 0.25 Events e e Dirt 4.70 Run 1 Cosmic Data 27.82 60 Flux, XSec, & MC-Stats Errors : 84.06 Run 1 On-Beam Data 83.00 1γ1p 0.41e20 POT 50 MicroBooNE Preliminary 40

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) C 1.5 1 0.5

Data/Prediction 0 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) C (Data/MC: 0.99) (KS: 0.441) (χ2/nDOF : 7.72/6) (χ2 Pval: 0.259)

2400 NC 1 π0 Coherent 9.04 NC 1 π0 Non-Coherent 513.68 0 0 NC 2+ π 11.97 CC νµ 1 π 151.36 Events 2200 ν ν BNB Other 882.79 CC e/ e Intrinsic 8.93 2000 Dirt 127.31 Run 1+3 Cosmic Data 831.42 1x SM NC ∆ Radiative 3.61 x2 SM NC ∆ Radiative (LEE) 7.21 1800 Flux & XS Systematics : 2547.32 1600 1γ1p 12.25E20 POT 1400 MicroBooNE Simulation 1200 Preliminary 1000 800 600 400 200

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) C

Figure 20: The reconstructed ∆ invariant mass distribution for (far sideband) box C, deﬁned as failing both the optimized NC π0 BDT cut and the optimized BNB Other BDT cut. Top: Run 1 open data, in comparison with MC prediction. Bottom: MC prediction for 12.25×1020 POT, corresponding to the full data set for Runs 1-5. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

9 1x SM NC ∆ Radiative 0.07 x2 SM NC ∆ Radiative (LEE) 0.13 NC 1 π0 Coherent 0.02 NC 1 π0 Non-Coherent 6.53 0 0 NC 2+ π 0.00 CC νµ 1 π 0.36 8 BNB Other 1.09 CC ν /ν Intrinsic 0.05 Events e e Dirt 0.00 Run 1 Cosmic Data 0.32 7 Flux, XSec, & MC-Stats Errors : 8.57 Run 1 On-Beam Data 10.00 6 1γ1p 0.41e20 POT MicroBooNE Preliminary 5

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) D 1.5 1 0.5

Data/Prediction 0 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) D (Data/MC: 1.17) (KS: 0.998) (χ2/nDOF : 5.18/6) (χ2 Pval: 0.520)

NC 1 π0 Coherent 0.79 NC 1 π0 Non-Coherent 198.79 0 0 NC 2+ π 2.61 CC νµ 1 π 14.54 Events 250 BNB Other 25.58 CC νe/νe Intrinsic 1.72 Dirt 0.00 Run 1+3 Cosmic Data 15.27 1x SM NC Δ Radiative 2.16 x2 SM NC Δ Radiative (LEE) 4.33 200 Flux & XS Systematics : 265.80

1γ1p 12.25e20 POT 150 MicroBooNE Simulation Preliminary

100

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (corrected) D

Figure 21: The reconstructed ∆ invariant mass distribution for (far sideband) box D, deﬁned as failing the optimized NC π0 BDT cut but passing the optimized BNB Other BDT cut. Top: Run 1 open data, in comparison with MC prediction. Bottom: MC prediction for 12.25×1020 POT, corresponding to the full data set for Runs 1-5. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

25 3.4 Validation of “Dirt” Backgrounds In early stages of the analysis, a particularly concerning background, which was large in the MiniBooNE search for νe CCQE-like events, has been “dirt” events. These are neutrino-beam-induced events which originate outside the active detector volume, but whose final state products make it through the active volume and are mis-reconstructed and mis-identified as single-photon events. As such, a targeted selection was developed to isolate a dirt-rich sample in MicroBooNE, and verify data to Monte Carlo agreement, thus building confidence that this type of background is accurately predicted and accounted for in the single photon analysis. The number of predicted dirt events, scaled to a data set corresponding to 12.25×1020 POT, is shown for each successive 1γ1p and 1γ0p selection stage (starting with topological selection and ending with final selection) in Figs. 22 and 23. The contribution to the 1γ1p final selected sample is negligible. However, as expected, it’s harder to reject dirt events in the 1γ0p selection, as shown by the non-negligible background in Fig. 23. This is because for the 1γ0p case there is no reconstructed track to provide information about the vertex position. The ability to accurately reconstruct the neutrino vertex using these tagged protons is an excellent demonstration of the power of topological reconstruction in a LArTPC.

26 Topological Selection Pre-Selection Cuts 70000 NC 1 π0 Coherent 61.68 NC 1 π0 Non-Coherent 2639.63 NC 1 π0 Coherent 26.91 NC 1 π0 Non-Coherent 1378.96 10000 OTPC NC 1 π0 663.79 NC 2+ π0 83.58 OTPC NC 1 π0 80.31 NC 2+ π0 29.16 Events Events π0 ν π0 π0 ν π0 60000 OTPC NC 2+ 60.48 CC µ 1 2018.51 OTPC NC 2+ 5.79 CC µ 1 449.54 0 0 OTPC CC νµ 1 π 18.46 BNB Other 15010.00 OTPC CC νµ 1 π 0.78 BNB Other 2238.26 ν ν ν ν OTPC BNB Other 9336.89 CC e/ e Intrinsic 404.13 8000 OTPC BNB Other 490.79 CC e/ e Intrinsic 232.93 50000 ν ν ν ν OTPC CC e/ e Intrinsic 405.09 Dirt 8173.37 OTPC CC e/ e Intrinsic 232.93 Dirt 436.42 Run 1+3 Cosmic Data 55918.83 1x SM NC ∆ Radiative 44.41 Run 1+3 Cosmic Data 3126.48 1x SM NC ∆ Radiative 28.09 x2 SM NC ∆ Radiative (LEE) 88.83 OTPC x3 SM NC ∆ Radiative 4.47 x2 SM NC ∆ Radiative (LEE) 56.18 OTPC x3 SM NC ∆ Radiative 0.57 40000 6000 MC Stats-Only Error, MC Events: 94932.16 MC Stats-Only Error, MC Events: 8814.11 1γ1p 12.25E20 POT 1γ1p 12.25E20 POT 30000 MicroBooNE Simulation MicroBooNE Simulation Preliminary 4000 Preliminary 20000

2000 10000

1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (Corrected) Implied Invariant Mass of Photon-Proton Pair [GeV] (Corrected)

Post-Cosmic BDT Post-BNB BDT

1800 NC 1 π0 Coherent 10.82 NC 1 π0 Non-Coherent 873.61 600 NC 1 π0 Coherent 0.79 NC 1 π0 Non-Coherent 468.14 OTPC NC 1 π0 8.13 NC 2+ π0 13.22 OTPC NC 1 π0 1.07 NC 2+ π0 8.33 Events Events 0 0 0 0 1600 OTPC NC 2+ π 0.00 CC νµ 1 π 216.26 OTPC NC 2+ π 0.00 CC νµ 1 π 39.80 0 0 OTPC CC νµ 1 π 0.10 BNB Other 624.69 500 OTPC CC νµ 1 π 0.00 BNB Other 58.00 1400 ν ν ν ν OTPC BNB Other 30.03 CC e/ e Intrinsic 150.99 OTPC BNB Other 4.65 CC e/ e Intrinsic 29.36 ν ν ν ν OTPC CC e/ e Intrinsic 150.99 Dirt 10.69 OTPC CC e/ e Intrinsic 29.36 Dirt 2.42 1200 Run 1+3 Cosmic Data 101.93 1x SM NC ∆ Radiative 22.68 400 Run 1+3 Cosmic Data 17.77 1x SM NC ∆ Radiative 17.43 x2 SM NC ∆ Radiative (LEE) 45.37 OTPC x3 SM NC ∆ Radiative 0.10 x2 SM NC ∆ Radiative (LEE) 34.86 OTPC x3 SM NC ∆ Radiative 0.02 1000 MC Stats-Only Error, MC Events: 2259.62 MC Stats-Only Error, MC Events: 711.99 1γ1p 12.25E20 POT 300 1γ1p 12.25E20 POT 800 MicroBooNE Simulation MicroBooNE Simulation Preliminary Preliminary 600 200

400 100 200

π0 ν Post-NC BDT Post- e BDT NC 1 π0 Coherent 0.00 NC 1 π0 Non-Coherent 235.92 350 NC 1 π0 Coherent 0.00 NC 1 π0 Non-Coherent 225.73 OTPC NC 1 π0 0.50 NC 2+ π0 4.81 OTPC NC 1 π0 0.50 NC 2+ π0 4.81 Events Events 350 π0 ν π0 π0 ν π0 OTPC NC 2+ 0.00 CC µ 1 18.01 300 OTPC NC 2+ 0.00 CC µ 1 16.49 0 0 OTPC CC νµ 1 π 0.00 BNB Other 32.96 OTPC CC νµ 1 π 0.00 BNB Other 29.33 300 ν ν ν ν OTPC BNB Other 2.33 CC e/ e Intrinsic 21.87 OTPC BNB Other 2.33 CC e/ e Intrinsic 4.47 ν ν ν ν OTPC CC e/ e Intrinsic 21.87 Dirt 2.42 250 OTPC CC e/ e Intrinsic 4.47 Dirt 2.42 250 Run 1+3 Cosmic Data 3.74 1x SM NC ∆ Radiative 14.49 Run 1+3 Cosmic Data 3.74 1x SM NC ∆ Radiative 14.01 x2 SM NC ∆ Radiative (LEE) 28.98 OTPC x3 SM NC ∆ Radiative 0.02 x2 SM NC ∆ Radiative (LEE) 28.01 OTPC x3 SM NC ∆ Radiative 0.02 200 MC Stats-Only Error, MC Events: 387.93 MC Stats-Only Error, MC Events: 336.33 200 1γ1p 12.25E20 POT 1γ1p 12.25E20 POT MicroBooNE Simulation 150 MicroBooNE Simulation 150 Preliminary Preliminary 100 100

50 50

Final Selection

NC 1 π0 Coherent 0.00 NC 1 π0 Non-Coherent 55.37 80 OTPC NC 1 π0 0.29 NC 2+ π0 0.00 Events 0 0 OTPC NC 2+ π 0.00 CC νµ 1 π 0.91 70 0 OTPC CC νµ 1 π 0.00 BNB Other 6.97 ν ν OTPC BNB Other 0.00 CC e/ e Intrinsic 1.61 60 ν ν OTPC CC e/ e Intrinsic 1.61 Dirt 0.00 Run 1+3 Cosmic Data 0.00 1x SM NC ∆ Radiative 10.30 50 x2 SM NC ∆ Radiative (LEE) 20.60 OTPC x3 SM NC ∆ Radiative 0.00 MC Stats-Only Error, MC Events: 97.66 40 1γ1p 12.25E20 POT MicroBooNE Simulation 30 Preliminary

1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 Implied Invariant Mass of Photon-Proton Pair [GeV] (Corrected)

Figure 22: The 1γ1p sample, starting with topological selection stage (top left), and as a function of subsequent selection stages, showing contribution from “dirt” events, in brown. From left to right, and top 0 to bottom: topological selection stage, preselection stage, cosmic BDT, BNB BDT, NC π BDT, BNB νe BDT, and SSV BDT (final selection) stage. OTPC signifies the true neutrino interaction took place outside of the active TPC volume, but inside of the cryostat, and is another source of “dirt” events. By final selection stage, the number of predicted dirt events in the final selected sample is small, but non-negligible. The distributions are scaled to 12.25×1020 POT, corresponding to MicroBooNE Runs 1-5. Shown are only Monte Carlo intrinsic statistical uncertainties. 27 Topological Selection Pre-Selection Cuts 20000 NC 1 π0 Coherent 79.73 NC 1 π0 Non-Coherent 1170.35 NC 1 π0 Coherent 77.31 NC 1 π0 Non-Coherent 1118.96 OTPC NC 1 π0 Coherent 509.91 NC 2+ π0 31.85 12000 OTPC NC 1 π0 Coherent 350.41 NC 2+ π0 28.70 Events 18000 Events 0 0 0 0 OTPC NC 2+ π 41.40 CC νµ 1 π 295.09 OTPC NC 2+ π 28.48 CC νµ 1 π 268.93 ν π0 ν π0 16000 OTPC CC µ 1 4.12 BNB Other 2242.96 OTPC CC µ 1 2.91 BNB Other 1897.23 ν ν 10000 ν ν OTPC BNB Other 2177.77 CC e/ e Intrinsic 169.40 OTPC BNB Other 1517.51 CC e/ e Intrinsic 161.69 ν ν ν ν 14000 OTPC CC e/ e Intrinsic 0.75 Dirt 2279.62 OTPC CC e/ e Intrinsic 0.11 Dirt 1500.58 Run 1+3 Cosmic Data 11981.64 1x SM NC ∆ Radiative 31.51 Run 1+3 Cosmic Data 8106.05 1x SM NC ∆ Radiative 30.68 8000 12000 x2 SM NC ∆ Radiative (LEE) 63.01 OTPC x3 SM NC ∆ Radiative 4.59 x2 SM NC ∆ Radiative (LEE) 61.35 OTPC x3 SM NC ∆ Radiative 3.20 MC Stats-Only Error, MC Events: 21083.70 MC Stats-Only Error, MC Events: 15154.09 10000 1γ0p 12.25E20 POT 6000 1γ0p 12.25E20 POT 8000 MicroBooNE Simulation MicroBooNE Simulation Preliminary Preliminary 6000 4000

4000 2000 2000

0 100 200 300 400 500 600 0 100 200 300 400 500 600 Corrected Calorimetric Shower Energy [MeV] Corrected Calorimetric Shower Energy [MeV]

Post-Cosmic BDT Post-BNB BDT

NC 1 π0 Coherent 57.65 NC 1 π0 Non-Coherent 376.03 NC 1 π0 Coherent 39.91 NC 1 π0 Non-Coherent 284.09 450 OTPC NC 1 π0 Coherent 42.60 NC 2+ π0 9.69 OTPC NC 1 π0 Coherent 25.01 NC 2+ π0 4.39 Events Events 350 OTPC NC 2+ π0 3.14 CC ν 1 π0 73.54 OTPC NC 2+ π0 2.69 CC ν 1 π0 47.57 400 µ µ 0 0 OTPC CC νµ 1 π 0.74 BNB Other 95.80 OTPC CC νµ 1 π 0.30 BNB Other 54.54 OTPC BNB Other 34.37 CC ν /ν Intrinsic 61.93 300 OTPC BNB Other 19.31 CC ν /ν Intrinsic 27.12 350 e e e e ν ν ν ν OTPC CC e/ e Intrinsic 0.00 Dirt 18.87 OTPC CC e/ e Intrinsic 0.00 Dirt 12.47 300 Run 1+3 Cosmic Data 52.84 1x SM NC ∆ Radiative 17.21 250 Run 1+3 Cosmic Data 41.07 1x SM NC ∆ Radiative 15.68 x2 SM NC ∆ Radiative (LEE) 34.43 OTPC x3 SM NC ∆ Radiative 0.55 x2 SM NC ∆ Radiative (LEE) 31.36 OTPC x3 SM NC ∆ Radiative 0.36 MC Stats-Only Error, MC Events: 879.40 MC Stats-Only Error, MC Events: 605.88 250 200 1γ0p 12.25E20 POT 1γ0p 12.25E20 POT 200 MicroBooNE Simulation 150 MicroBooNE Simulation Preliminary Preliminary 150 100 100 50 50

0 100 200 300 400 500 600 0 100 200 300 400 500 600 Corrected Calorimetric Shower Energy [MeV] Corrected Calorimetric Shower Energy [MeV]

Final Selection 240 NC 1 π0 Coherent 15.53 NC 1 π0 Non-Coherent 126.51 220 OTPC NC 1 π0 Coherent 16.68 NC 2+ π0 0.00 Events 0 0 OTPC NC 2+ π 2.69 CC νµ 1 π 24.64 200 0 OTPC CC νµ 1 π 0.20 BNB Other 34.79 ν ν 180 OTPC BNB Other 12.47 CC e/ e Intrinsic 20.66 OTPC CC ν /ν Intrinsic 0.00 Dirt 11.39 160 e e Run 1+3 Cosmic Data 19.80 1x SM NC ∆ Radiative 12.15 140 x2 SM NC ∆ Radiative (LEE) 24.31 OTPC x3 SM NC ∆ Radiative 0.29 MC Stats-Only Error, MC Events: 322.11 120 1γ0p 12.25E20 POT 100 MicroBooNE Simulation 80 Preliminary

0 100 200 300 400 500 600 Corrected Calorimetric Shower Energy [MeV]

Figure 23: The 1γ0p sample, starting with topological selection stage (top left), and as a function of subsequent selection stages, showing contribution from “dirt” events, in brown. From left to right, and top to bottom: topological selection stage, preselection stage, cosmic BDT, BNB BDT, and NC π0 BDT (final selection) stage. OTPC signifies the true neutrino interaction took place outside of the active TPC volume, but inside of the cryostat, and is another source of “dirt” events. By final selection stage, the number of predicted dirt events in the final selected sample is small but not negligible. The distributions are scaled to 12.25×1020 POT, corresponding to MicroBooNE Runs 1-5. Shown are only Monte Carlo intrinsic statistical uncertainties.

28 At topological selection stage, the total dirt contribution breakdown is as shown in Fig. 24. Dirt backgrounds to both 1γ1p and 1γ0p topological selections are dominated by cosmogenic background-contaminated reconstructed showers, shown in bright green. Dirt backgrounds to the 1γ1p topological selection are also dominated by electrons from muon decay. Those are removed at pre-selection cut stage with a shower energy cut. An example of a simulated dirt Monte Carlo event which passes ﬁnal 1γ1p selection is shown in Fig. 25.

2400 0 γ π0 π0 γ Shower from π 33.33 Other γ Shower 14.31 Shower Proton Track from 6.01 Other Events from 111.79 2200 10000 Events Events γ Shower from Other 23.96 e Shower from Muon Decay 85.96 2000 e Shower 4.96 Other Monte-Carlo Shower 27.70 e Shower from Other 6.09 Other Monte-Carlo Shower 84.30

1800 Cosmic Overlay Shower 102.37 All MC with Stats-Only Error 182.66 8000 Cosmic Overlay Shower 324.88 All MC with Stats-Only Error 642.98 1600 OTPC 1γ0p 0.40e20 POT OTPC 1γ1p 0.40e20 POT 1400 MicroBooNE Simulation Preliminary 6000 MicroBooNE Simulation Preliminary 1200

1000 4000 800

600

400 2000

200

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Reconstructed Shower Energy [GeV] Reconstructed Shower Energy [GeV]

Figure 24: True composition breakdown of 1γ0p (left) and 1γ1p (right) dirt events at topological selection level. Dirt backgrounds to both 1γ1p and 1γ0p topological selections are dominated by cosmogenic background- contaminated reconstructed showers, shown in bright green. Dirt backgrounds to the 1γ1p topological selection are also signiﬁcantly contributed from electrons from muon decay. Those are removed at pre-selection stage with a shower energy cut.

Figure 25: Argo [14] event display for a true dirt Monte Carlo event which passes ﬁnal 1γ1p selection. Right: full detector view, with the ionization charge deposition 3D spacepoints highlighted in blue; the light blue circles represent PMTs above certain activity. Left: zoom-in view near the TPC boundary, showing the interaction vertex outside the rectangular active TPC volume.

29 To verify the accuracy of the dirt background predictions, a targeted selection has been developed, which makes use of directional vectors to preferentially select events originating near the active TPC boundary, which point inward toward the detector, and/or opposite to the beam-forward direction. Speciﬁcally, the following variables are considered:

• Geometrical Variables:

1. Start point and orientation (θyz, φyx) of the reconstructed shower.

2. End points (both start and end point) and orientation (θyz, φyx) of the reconstructed track (ap- plicable to the 1γ1p topological selection, only).

• Vertex reconstruction: 1. Distance of the reconstructed shower start point to the reconstructed vertex. 2. Distance of the reconstructed track end points to the reconstructed vertex.

• Reconstructed visible energy: 1. The maximum reconstructed shower energy among three wire planes. 2. The reconstructed track kinetic energy assuming the track is a proton.

• Inner products of reconstructed object (track or shower) directional vectors, with the latter illustrated in Fig. 26. Directional vectors are deﬁned by the reconstructed shower cone or track, pointing from the shower cone or track start point to the end point. Inner products are then constructed from the normalized directional vectors and the following vectors that start from the reconstructed shower start point or reconstructed vertex (for track object) and end at diﬀerent physical points of the detector geometry as described below:

1. Radial Vector (RV or tRV, where “t” denotes a track-related variable) points to the center of the TPC. 2. Unit Radial vector is the same radial vector as above, but with its modulus normalized to 1. This is referred to as UR or tUR. 3. Vertical Vector Y (VY or tVY) points to the plane y = 0 and is parallel to the y-axis. 4. Horizontal Vector X (VX or tVX) points to the plane x = 128.2cm and is parallel to the x-axis. 5. Central axis Vector Z (VZ or tVZ) points to the central axis along the beam direction. 6. Vector TPC Tip (VTT or tVTT), points to the TPC downstream tip, where the tip is the center of the TPC wall that is furthest away from the beam origin (furthest downstream point from BNB target)

30 Figure 26: Examples of RV, VY, VX, VZ, and VTT are shown in this diagram for the case of two different showers reconstructed at different positions in the detector and with different orientations.

31 A combination of cuts based on the above variables is applied, after topological selection, to obtain a sample of events with an enhanced dirt fraction. The cuts have been optimized so as to minimize NC ∆ radiative events that enter the dirt-enhanced sample, exploiting powerful correlations among diﬀerent variables, which are diﬀerent for signal events and dirt events. Examples that illustrate this are provided in Fig. 27.

Figure 27: 2D histograms for true NC ∆ radiative signal (left) and true dirt (right) events, at 1γ0p topological selection stage, illustrating correlations between the VX and reconstructed shower energy variables, used to select a dirt-enhanced sample.

Figures 28 and 29 show 1γ1p and 1γ0p event distributions, respectively, before and after the optimized set of dirt-enhancing cuts are applied, both after topological selection stage. As shown in the ﬁgures, good data to Monte Carlo agreement is observed, including in regions of small reconstructed distance back to SCB, which is where dirt events contribute most dominantly. This provides conﬁdence that dirt events are well modeled in the Monte Carlo.

1800 x2 SM NC ∆ Radiative (LEE) 2.94 1x SM NC ∆ Radiative 1.47 x2 SM NC ∆ Radiative (LEE) 0.02 1x SM NC ∆ Radiative 0.01 BNB NC 1 π0 85.21 BNB CC 1 π0 67.80 BNB NC 1 π0 1.02 BNB CC 1 π0 0.21 1600 50

Events ν Events ν BNB Other 487.90 e Intrinsic 13.07 BNB Other 4.13 e Intrinsic 0.02 Dirt 642.98 Cosmic Data 1895.00 Dirt 25.39 Cosmic Data 56.08 1400 All MC with Stats-Only Error 3196.37 On-Beam Data 3264.00 All MC with Stats-Only Error 86.88 On-Beam Data 87.00 40 1200 1γ1p 0.40e20 POT 1γ1p 0.40e20 POT

1000 MicroBooNE Preliminary MicroBooNE Preliminary 30

800

20 600

400 10 200

0 20 40 60 80 100 120 0 20 40 60 80 100 120 Distance from Shower Start to SCB Distance from Shower Start to SCB 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Distance from Shower Start to SCB Distance from Shower Start to SCB (Data/MC: 1.02) (KS: 0.734) (χ2/nDOF : 10.43/8) (χ2 Pval: 0.236) (Data/MC: 1.00) (KS: 0.998) (χ2/nDOF : 8.39/8) (χ2 Pval: 0.397)

Figure 28: Distribution of 1γ1p topologically-selected events without (left) and with (right) dirt-enhancing cuts applied. Shown are only intrinsic Monte Carlo statistical uncertainties.

32 100 x2 SM NC ∆ Radiative (LEE) 2.10 1x SM NC ∆ Radiative 1.05 x2 SM NC ∆ Radiative (LEE) 0.01 1x SM NC ∆ Radiative 0.01 500 BNB NC 1 π0 42.44 BNB CC 1 π0 10.16 BNB NC 1 π0 1.21 BNB CC 1 π0 0.30

Events ν Events ν BNB Other 82.13 e Intrinsic 5.49 BNB Other 6.35 e Intrinsic 0.05 Dirt 182.66 Cosmic Data 451.08 80 Dirt 46.82 Cosmic Data 105.09 All MC with Stats-Only Error 777.11 On-Beam Data 784.00 All MC with Stats-Only Error 159.85 On-Beam Data 160.00 400 1γ0p 0.40e20 POT 1γ0p 0.40e20 POT 60 300 MicroBooNE Preliminary MicroBooNE Preliminary

40 200

100 20

0 20 40 60 80 100 120 0 20 40 60 80 100 120 Distance from Shower Start to SCB Distance from Shower Start to SCB 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Distance from Shower Start to SCB Distance from Shower Start to SCB (Data/MC: 1.01) (KS: 0.038) (χ2/nDOF : 15.68/8) (χ2 Pval: 0.047) (Data/MC: 1.00) (KS: 0.810) (χ2/nDOF : 7.57/8) (χ2 Pval: 0.476)

Figure 29: Distribution of 1γ0p topologically-selected events without (left) and with (right) dirt-enhancing cuts applied. Shown are only intrinsic Monte Carlo statistical uncertainties.

33 4 NC π0 Selection for In Situ Constraint

It is very clear from the results of the single shower selections that NC π0 are by far the most dominant background to the NC ∆ radiative decay search. In order to ensure that our simulation of these is reliable and validate the predictions of the NC π0 background to the 1γ selections, a dedicated 2γ1p and 2γ0p measurement has been performed, providing access to a high-purity, high-statistics sample of NC π0 events. In addition to this, the high-statistics NC π0 sample can constrain the exact rate of expected π0 events and allow us to perform a combined single-photon and NC π0 ﬁt in order to reduce the systematic uncertainty on the NC π0 background ﬂux and cross-section.

Through the dedicated 2γ1p and 2γ0p selections, described in the following subsections, we ﬁnd that the data is inconsistent with the GENIE central value prediction for NC π0 production, at the level of ∼ 20%, consistent with GENIE cross-section normalization uncertainty. This has led us to perform a data-driven correction to the coherent and non-coherent NC π0 rate normalizations, as described in Sec. 6.

4.1 Event Selection The first stage of selection for both the 2γ1p and 2γ0p selections consists of initial topological and low- level pre-selection cuts that are run over MicroBooNE data. This stage eliminates sufficient NC ∆ signal events so blindness is maintained. This is accomplished via the use of dedicated filters, providing a total of ∼ 5.8 × 1020 POT available for further study. The 2γ1p filter and pre-selection consists of six total cuts,

• The reconstructed event topology consists of two showers and one track.

• The conversion distances for both showers is greater than 1 cm. • The reconstructed neutrino vertex is at least 5 cm away from any TPC wall. • The reconstructed leading shower energy is > 30 MeV.

• The reconstructed subleading shower energy is > 20 MeV. • The 3D distance between the event vertex and the track starting point is < 10 cm. For events with a proton track, we expect the vertex to be within a few centimeters of the track start point.

As with the 2γ0p we no longer have a proton candidate track from which to calculate variables such as the conversion distance, the pre-selection cuts are instead deﬁned with a simpler subset of cuts, alongside the diﬀerent topology:

• The reconstructed event topology consists of two showers and zero tracks • The reconstructed leading shower energy is > 30 MeV.

• The reconstructed subleading shower energy is > 20 MeV. • The reconstructed neutrino vertex is at least 5 cm away from any TPC wall.

Data to Monte Carlo comparisons of the selections after these initial pre-selection cuts can be found in Fig. 30. We show the reconstructed invariant mass of the two photons, which for true NC π0 events should peak at the π0 mass of 135 MeV. As can be seen, even at this stage, the majority of events do contain a CC or NC π0. However, as we are speciﬁcally targeting NC π0 events, the remaining cosmic contaminated events, as well as the CC π0, need to be further rejected.

1x SM NC ∆ Radiative 2.07 x2 SM NC ∆ Radiative (LEE) 4.15 1x SM NC ∆ Radiative 2.72 x2 SM NC ∆ Radiative (LEE) 5.45 350 NC 1 π0 Coherent 9.61 NC 1 π0 Non-Coherent 735.19 NC 1 π0 Coherent 36.82 NC 1 π0 Non-Coherent 634.49 0 0 0 0 NC 2+ π 40.82 CC νµ 1 π 538.10 NC 2+ π 27.84 CC νµ 1 π 115.37 BNB Other 587.00 CC ν /ν Intrinsic 28.21 250 BNB Other 437.40 CC ν /ν Intrinsic 28.17 Events e e Events e e 300 Dirt 110.02 Run 1+2+3 Cosmic Data 1042.39 Dirt 133.21 Run 1+2+3 Cosmic Data 1135.76 Flux & XS Systematics : 3097.56 Run 1+2+3 On-Beam Data 2923.00 Flux & XS Systematics : 2557.23 Run 1+2+3 On-Beam Data 2402.00 250 200 2γ1p 5.84E20 POT 2γ0p 5.89E20 POT MicroBooNE Preliminary MicroBooNE Preliminary 200 150 150 100 100 50 50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Reconstructed π0 Invariant Mass [GeV] Reconstructed π0 Invariant Mass [GeV] 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Reconstructed π0 Invariant Mass [GeV] Reconstructed π0 Invariant Mass [GeV] (Data/MC: 0.94) (KS: 0.976) (χ2/nDOF : 25.97/34) (χ2 Pval: 0.836) (Data/MC: 0.94) (KS: 1.000) (χ2/nDOF : 22.06/34) (χ2 Pval: 0.943)

(a) 2γ1p Selection (b) 2γ0p Selection

Figure 30: The invariant mass of the reconstructed NC π0 sample for both the 2γ1p and 2γ0p selections, after pre-selection cuts. At this stage, while π0 (CC and NC combined) make up the largest single contribution of the 2γ1p, there is still a signiﬁcant amount of cosmic events that are selected. For 2γ0p, the situation is diﬀerent as the demand of no track like objects removes almost all CC π0 (which often has a long muon track), leaving the NC π0 as the largest BNB driven contribution. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

4.2 BDT Training In order to reject the remaining backgrounds, a boosted decision tree (BDT) is trained to select NC π0 events by utilizing a set of 10 calormetric and geometric variables in the 2γ1p π0 selection:

• Leading and subleading shower conversion distances. • Leading and subleading shower impact parameters. The impact parameter is the distance of closest approach between the back-projection of the reconstructed shower direction and the neutrino interaction candidate.

• Reconstructed leading shower energy (taken as the maximum value among the three wire planes). • Reconstructed track length.

• Reconstructed track angle θyz. • Distance from track end point to nearest TPC wall in 3D. • Track mean dE/dx over the whole track. • Ratio of track end-half dE/dx to track start-half dE/dx. This variable helps select stopping protons. See Fig. 31 for an example of the separation power of one of the more powerful BDT variables, the track mean dE/dx variable, for selecting highly ionizing protons over both cosmic and BNB νµ CC. The resulting BDT response can be seen in Fig. 32a, with the NC π0 piling up on the right (note that the small amount of signal on the left hand side tends to be cosmic contaminated events). A cut at 0.854 maximizes NC π0 eﬃciency times purity.

The analogous training variables for the 2γ0p NC π0 selection BDT must be somewhat modiﬁed as we no longer have a track like-object with which to reject cosmic muons and νµ CC events. The 10 variables utilized are:

0.45 π0 1x SM NC ∆ Radiative 2.07 x2 SM NC ∆ Radiative (LEE) 4.15 Signal NC BNB Background NC 1 π0 Coherent 9.61 NC 1 π0 Non-Coherent 735.19 1000 0 0 NC 2+ π 40.82 CC νµ 1 π 538.10 BNB Other 587.00 CC ν /ν Intrinsic 28.21 0.4 Events e e Dirt 110.02 Run 1+2+3 Cosmic Data 1042.39 γ 2 1p 800 Flux & XS Systematics : 3097.56 Run 1+2+3 On-Beam Data 2923.00 0.35 MicroBooNE Simulation - Preliminary 2γ1p 5.84E20 POT MicroBooNE Preliminary 0.3 600 Events [Area Normalized] 0.25 400

0.2 200

0.15 0 2 4 6 8 10 12 Reconstructed Track dE/dx [MeV/cm] 0.1 1.5 1 0.05 0.5

0 Data/Prediction 0 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 Reconstructed Track dE/dx [MeV/cm] Reconstructed Track dE/dx [MeV/cm] (Data/MC: 0.94) (KS: 0.698) (χ2/nDOF : 8.19/18) (χ2 Pval: 0.976) (a) MC-only Distributions (area normalized) (b) Data and MC Distributions

Figure 31: (a) Monte Carlo predicted distribution of reconstructed track (mean truncated) dE/dx, separated between signal and BNB backgrounds. (b) Data to Monte Carlo distribution comparison for the same variable. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

• Both shower conversion distances

• Both shower impact parameters. • Both shower energies (maximum among the three wire planes). • Both ratios of shower length to shower energy.

• Leading shower θyz. • Neutrino score of the slice containing the leading shower. with the resulting BDT response shown in Fig. 32. A cut at 0.95 maximizes the purity times eﬃciency of the selected NC π0 events.

∆ ∆ ∆ ∆ 1x SM NC Radiative 2.07 x2 SM NC Radiative (LEE) 4.15 4 1x SM NC Radiative 2.72 x2 SM NC Radiative (LEE) 5.45 NC 1 π0 Coherent 9.61 NC 1 π0 Non-Coherent 735.19 10 NC 1 π0 Coherent 36.82 NC 1 π0 Non-Coherent 634.49 0 0 0 0 NC 2+ π 40.82 CC νµ 1 π 538.10 NC 2+ π 27.84 CC νµ 1 π 115.37 BNB Other 587.00 CC ν /ν Intrinsic 28.21 BNB Other 437.40 CC ν /ν Intrinsic 28.17 Events e e Events e e Dirt 110.02 Run 1+2+3 Cosmic Data 1042.39 Dirt 133.21 Run 1+2+3 Cosmic Data 1135.76 Flux & XS Systematics : 3097.56 Run 1+2+3 On-Beam Data 2923.00 Flux & XS Systematics : 2557.23 Run 1+2+3 On-Beam Data 2402.00 103 3 2γ1p 5.84E20 POT 10 2γ0p 5.89E20 POT MicroBooNE Preliminary MicroBooNE Preliminary

102 102

10 10

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 BDT Response BDT Response 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 BDT Response BDT Response (Data/MC: 0.94) (KS: 0.360) (χ2/nDOF : 16.06/30) (χ2 Pval: 0.982) (Data/MC: 0.94) (KS: 1.000) (χ2/nDOF : 24.56/30) (χ2 Pval: 0.746)

(a) 2γ1p BDT response (b) 2γ0p BDT response

Figure 32: Data to Monte Carlo comparisons for the 2γ1p BDT response (left). To maximize efficiency times purity in the final selection, we place a cut on this distribution at 0.854. Shown on the right is the Data to Monte Carlo comparison for the 2γ0p BDT response, where to maximize efficiency times purity, we place a cut on this distribution at 0.950. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

37 4.3 Final Selection Figure 33a shows the final reconstructed π0 invariant mass of the 2γ1p selection. A Gaussian fit to the data points gives a mean of 137.6 ± 2.1 MeV with a width of 44.4 ± 1.8 MeV, summarized in Tab. 6. Figure 34a shows the π0 momentum, while the reconstructed cosine of the center-of-mass (CM) decay angle is shown in Fig. 34b. This is defined as the angle between the lab-frame π0 momentum direction and the single photon which has the smallest opening angle w.r.t the π0 boost direction as calculated in the center of mass (CM) frame. In theory, this quantity should give a flat distribution for signal events, but in reality we 0 see some tapering off at high cos(θcm), corresponding to more asymmetric π decays. This is expected, as we are likely to miss the subleading photon shower in highly asymmetric decays. Overall there is a ≈ 20% deficit in observed events in the final selection, which is relatively flat in the observed variables. Although large, this is mostly within the flux and cross-section uncertainties of the NC π0 production rate. It does, however, suggest that the GENIE central value for NC π0 production may be too high, motivating the possibility of fitting the rate to the observed data, as is discussed in Sec. 6.

1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 1x SM NC ∆ Radiative 0.51 x2 SM NC ∆ Radiative (LEE) 1.03 160 NC 1 π0 Coherent 1.31 NC 1 π0 Non-Coherent 504.86 NC 1 π0 Coherent 23.42 NC 1 π0 Non-Coherent 318.60 0 0 0 0 NC 2+ π 20.30 CC νµ 1 π 75.62 80 NC 2+ π 9.06 CC νµ 1 π 37.25 BNB Other 80.72 CC ν /ν Intrinsic 5.64 BNB Other 49.36 CC ν /ν Intrinsic 2.07 Events 140 e e Events e e Dirt 16.09 Run 1+2+3 Cosmic Data 97.11 70 Dirt 10.77 Run 1+2+3 Cosmic Data 81.36 Flux & XS Systematics : 804.43 Run 1+2+3 On-Beam Data 634.00 Flux & XS Systematics : 533.43 Run 1+2+3 On-Beam Data 496.00 120 2γ1p 5.84E20 POT 60 2γ0p 5.89E20 POT 100 MicroBooNE Preliminary 50 MicroBooNE Preliminary 80 40

60 30

40 20

20 10

20 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 20 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Reconstructed π0 Invariant Mass [GeV] Reconstructed π0 Invariant Mass [GeV] 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Reconstructed π0 Invariant Mass [GeV] Reconstructed π0 Invariant Mass [GeV] (Data/MC: 0.79) (KS: 0.995) (χ2/nDOF : 23.00/34) (χ2 Pval: 0.924) (Data/MC: 0.93) (KS: 0.901) (χ2/nDOF : 30.04/34) (χ2 Pval: 0.662)

(a) 2γ1p (b) 2γ0p

Figure 33: Reconstructed π0 mass distributions for (a) 2γ1p and (b) 2γ0p. The distributions show predictions scaled to 5.85×1020 POT, which correspond to the total POT for ﬁltered Runs 1-3, and corresponding data. These distributions correspond to the GENIE central value (CV) prediction, i.e. no normalization correction has been applied to the NC π0 production (see Sec. for details on the referenced correction). Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 100 NC 1 π0 Coherent 1.31 NC 1 π0 Non-Coherent 504.86 60 NC 1 π0 Coherent 1.31 NC 1 π0 Non-Coherent 504.86 0 0 0 0 NC 2+ π 20.30 CC νµ 1 π 75.62 NC 2+ π 20.30 CC νµ 1 π 75.62 BNB Other 80.72 CC ν /ν Intrinsic 5.64 BNB Other 80.72 CC ν /ν Intrinsic 5.64 Events e e Events e e Dirt 16.09 Run 1+2+3 Cosmic Data 97.11 50 Dirt 16.09 Run 1+2+3 Cosmic Data 97.11 80 Flux & XS Systematics : 804.43 Run 1+2+3 On-Beam Data 634.00 Flux & XS Systematics : 804.43 Run 1+2+3 On-Beam Data 634.00

2γ1p 5.84E20 POT 40 2γ1p 5.84E20 POT 60 MicroBooNE Preliminary MicroBooNE Preliminary 30 40 20

20 10

20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 π0 θ Reconstructed Momentum [GeV] Reconstructed cos( CM) 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 π0 θ Reconstructed Momentum [GeV] Reconstructed cos( CM) (Data/MC: 0.79) (KS: 0.961) (χ2/nDOF : 13.90/34) (χ2 Pval: 0.999) (Data/MC: 0.79) (KS: 0.942) (χ2/nDOF : 19.58/34) (χ2 Pval: 0.977)

0 (a) π Momentum (b) cos(θcm)

1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 NC 1 π0 Coherent 1.31 NC 1 π0 Non-Coherent 504.86 NC 1 π0 Coherent 1.31 NC 1 π0 Non-Coherent 504.86 0 0 0 0 160 NC 2+ π 20.30 CC νµ 1 π 75.62 160 NC 2+ π 20.30 CC νµ 1 π 75.62 BNB Other 80.72 CC ν /ν Intrinsic 5.64 BNB Other 80.72 CC ν /ν Intrinsic 5.64 Events e e Events e e 140 Dirt 16.09 Run 1+2+3 Cosmic Data 97.11 140 Dirt 16.09 Run 1+2+3 Cosmic Data 97.11 Flux & XS Systematics : 804.43 Run 1+2+3 On-Beam Data 634.00 Flux & XS Systematics : 804.43 Run 1+2+3 On-Beam Data 634.00 120 2γ1p 5.84E20 POT 120 2γ1p 5.84E20 POT 100 MicroBooNE Preliminary 100 MicroBooNE Preliminary

80 80

60 60

40 40

20 20

2 10 20 30 40 50 60 70 80 90 100 2 10 20 30 40 50 60 70 80 90 100 Primary Shower Conversion Distance [cm] Secondary Shower Conversion Distance [cm] 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Primary Shower Conversion Distance [cm] Secondary Shower Conversion Distance [cm] (Data/MC: 0.79) (KS: 0.994) (χ2/nDOF : 24.10/34) (χ2 Pval: 0.896) (Data/MC: 0.79) (KS: 0.999) (χ2/nDOF : 26.59/34) (χ2 Pval: 0.814)

400 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 NC 1 π0 Coherent 1.31 NC 1 π0 Non-Coherent 504.86 0 0 NC 2+ π 20.30 CC νµ 1 π 75.62 BNB Other 80.72 CC ν /ν Intrinsic 5.64 Events 350 e e Dirt 16.09 Run 1+2+3 Cosmic Data 97.11 Flux & XS Systematics : 804.43 Run 1+2+3 On-Beam Data 634.00 300 2γ1p 5.84E20 POT 250 MicroBooNE Preliminary 200

150

100

2−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 θ Implied cos( π0) 1.5 1 0.5

Data/Prediction 0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 θ Implied cos( π0) (Data/MC: 0.79) (KS: 1.000) (χ2/nDOF : 4.90/10) (χ2 Pval: 0.898)

(e) Implied cos θπ

Figure 34: Some select Data to Monte Carlo comparisons for the 2γ1p final selection. Uncertainties shown include all flux and cross-section systematics. Shape agreement is good across all variables, with an overall ∼20% discrepancy in data that is on the lower edge of the 1σ flux and cross-section systematic error band. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions. 39 Table 4 breaks down the signal events in the 2γ1p final selection in terms of interaction type. As expected, the majority of selected events are resonant. Deep inelastic scatterig (DIS) events comprise ∼10% of the selection, while quasi-elastic, coherent, and meson exchange current (MEC) events each account for ∼1% or less of the final selection. Finally, Figs. 37 and 36 show two example event display of a candidate NC π0 interaction that passes the final 2γ1p selection.

Resonant DIS QE Coherent MEC Pre-Selection 81.3% 16.3% 1.3% 1.31% 0.06% Final Selection 85.2% 13.2% 1.2% 0.28% 0.07%

Table 4: Breakdown of interaction types in the 2γ1p selection, both at the pre-selection stage and ﬁnal selection stage.

Final selection distributions for 2γ0p are shown in Fig 35. Unlike in the 2γ1p case, the data to Monte Carlo normalization difference is less than 10%, within flux and cross-section uncertainties. The 2γ0p selection is 64.1% pure and 41.6% efficient in NC π0 events, relative to the topological selection. A Gaussian fit to the data points in the invariant mass distribution gives a mean of 140.2 ± 2.8 MeV and a width of 49.9 ± 2.7 MeV, summarized in Tab. 5. A breakdown of interaction types at the pre-selection stage, and final selection stage can be seen in Tab. 5.

Resonant DIS QE Coherent MEC Pre-Selection 79.1% 14.9% 0.52% 5.5% 0.02% Final Selection 79.2% 13.5% 0.45% 6.8% 0.00%

Table 5: Breakdown of interaction types in the 2γ0p NC π0 selection, both at the pre-selection stage and ﬁnal selection stage.

Selection Fit Mean (MeV) Fit Width (MeV) Fit Resolution (%) 2γ1p 137.6 ± 2.1 44.4 ± 1.8 32.2 ± 5.7 2γ0p 140.2 ± 2.8 49.9 ± 2.7 35.6 ± 5.7

Table 6: Gaussian ﬁt parameters for the 2γ1p and 2γ0p Run 1-3 selections, using the 2γ1p and 2γ0p ﬁltered data sets.

1x SM NC ∆ Radiative 0.51 x2 SM NC ∆ Radiative (LEE) 1.03 1x SM NC ∆ Radiative 0.51 x2 SM NC ∆ Radiative (LEE) 1.03 NC 1 π0 Coherent 23.42 NC 1 π0 Non-Coherent 318.60 50 NC 1 π0 Coherent 23.42 NC 1 π0 Non-Coherent 318.60 0 0 0 0 60 NC 2+ π 9.06 CC νµ 1 π 37.25 NC 2+ π 9.06 CC νµ 1 π 37.25 BNB Other 49.36 CC ν /ν Intrinsic 2.07 BNB Other 49.36 CC ν /ν Intrinsic 2.07 Events e e Events e e Dirt 10.77 Run 1+2+3 Cosmic Data 81.36 Dirt 10.77 Run 1+2+3 Cosmic Data 81.36 40 50 Flux & XS Systematics : 533.43 Run 1+2+3 On-Beam Data 496.00 Flux & XS Systematics : 533.43 Run 1+2+3 On-Beam Data 496.00 2γ0p 5.89E20 POT 2γ0p 5.89E20 POT 40 MicroBooNE Preliminary 30 MicroBooNE Preliminary

30 20 20 10 10

200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 π0 θ Reconstructed Momentum [GeV] Reconstructed cos( CM) 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 π0 θ Reconstructed Momentum [GeV] Reconstructed cos( CM) (Data/MC: 0.93) (KS: 0.437) (χ2/nDOF : 31.16/34) (χ2 Pval: 0.608) (Data/MC: 0.93) (KS: 0.550) (χ2/nDOF : 31.78/34) (χ2 Pval: 0.577)

0 (a) π Momentum (b) cos(θcm)

1x SM NC ∆ Radiative 0.51 x2 SM NC ∆ Radiative (LEE) 1.03 1x SM NC ∆ Radiative 0.51 x2 SM NC ∆ Radiative (LEE) 1.03 60 NC 1 π0 Coherent 23.42 NC 1 π0 Non-Coherent 318.60 60 NC 1 π0 Coherent 23.42 NC 1 π0 Non-Coherent 318.60 0 0 0 0 NC 2+ π 9.06 CC νµ 1 π 37.25 NC 2+ π 9.06 CC νµ 1 π 37.25 BNB Other 49.36 CC ν /ν Intrinsic 2.07 BNB Other 49.36 CC ν /ν Intrinsic 2.07 Events e e Events e e 50 Dirt 10.77 Run 1+2+3 Cosmic Data 81.36 50 Dirt 10.77 Run 1+2+3 Cosmic Data 81.36 Flux & XS Systematics : 533.43 Run 1+2+3 On-Beam Data 496.00 Flux & XS Systematics : 533.43 Run 1+2+3 On-Beam Data 496.00

40 2γ0p 5.89E20 POT 40 2γ0p 5.89E20 POT MicroBooNE Preliminary MicroBooNE Preliminary 30 30

20 20

10 10

200 0.5 1 1.5 2 2.5 3 200 1 2 3 4 5 6 Angle Between Showers [rad] Leading Shower Kalman All-Plane Median dE/dx [Mev/cm] 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 Angle Between Showers [rad] Leading Shower Kalman All-Plane Median dE/dx [Mev/cm] (Data/MC: 0.93) (KS: 0.996) (χ2/nDOF : 16.25/34) (χ2 Pval: 0.996) (Data/MC: 0.93) (KS: 0.006) (χ2/nDOF : 40.55/34) (χ2 Pval: 0.204)

1x SM NC ∆ Radiative 0.51 x2 SM NC ∆ Radiative (LEE) 1.03 400 NC 1 π0 Coherent 23.42 NC 1 π0 Non-Coherent 318.60 0 0 NC 2+ π 9.06 CC νµ 1 π 37.25 BNB Other 49.36 CC ν /ν Intrinsic 2.07 Events 350 e e Dirt 10.77 Run 1+2+3 Cosmic Data 81.36 Flux & XS Systematics : 533.43 Run 1+2+3 On-Beam Data 496.00 300 2γ0p 5.89E20 POT 250 MicroBooNE Preliminary 200

150

100

2−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 θ cos( π0) 1.5 1 0.5

Data/Prediction 0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 θ cos( π0) (Data/MC: 0.93) (KS: 1.000) (χ2/nDOF : 2.74/10) (χ2 Pval: 0.987)

(e) cos θπ

Figure 35: Some select Data to Monte Carlo comparisons for the 2γ0p ﬁnal selection. Agreement is reasonable across all variables, within ﬂux and GENIE cross-section uncertainties. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions.

41 Figure 36: Event display for an NC π0 candidate event which survives the ﬁnal 2γ1p selection, recorded during Run 3 of MicroBooNE. Leading shower energy was reconstructed as 332 MeV with a subleading shower energy of 98 MeV, and a corresponding invariant mass of 158.2 MeV.

Run 6026 Subrun 30 Event 1546

Figure 37: Event display for an NC π0 candidate event which survives the ﬁnal 2γ1p selection, recorded during Run 1of MicroBooNE. The reconstructed invariant mass is 146.2 MeV.

42 5 Evaluation of Systematic Uncertainties

The systematic uncertainties taken into account in this analysis can be grouped into three categories: 1. Re-weightable BNB ﬂux uncertainties 2. Re-weightable neutrino cross-section and interaction GENIE uncertainties 3. Detector systematic uncertainties

Both the ﬂux and cross-section uncertainties are estimated using re-weighting in which the central value (CV) Monte Carlo events are assigned weights that scale and shift the events depending on some underlying systematic variation. We construct an individual covariance matrix M k corresponding to each one of the underlying sources of systematic uncertainty we are studying, k. To construct this matrix we consider a k large number (N, usually > 100) separate varied distributions Vn of the ﬁnal selected 1γ1p, 1γ0p, 2γ1p and 2γ0p spectra, where n = 1, .., N. The varied distributions are calculated each time by varying the underlying source of uncertainty k within its associated error band, and re-weighting the CV spectra according to a corresponding pre-parameterized shift. The deviations of those varied distributions relative to the central value prediction, P , are then mapped onto the covariance matrix, constructed from the distributions as follows: N 1 X M k = (P − V k ) × (P − V k ), (1) ij N i i,n j j,n n=1 where i, j are bin numbers. The total covariance matrix encompassing all these uncertainties is then the linear sum of the covariance matricies for all individual systematic variations, k, under investigation.

5.1 Flux and Cross-section Systematic Uncertainties We use “event reweighting” as the basis of evaluation of ﬂux and cross-section systematic uncertainties. The approach is to consider a given physics parameter P that goes into our simulation and create a random 0 or Gaussian ﬂuctuation xp such that changing this parameter changes P into P as follows:

0 P −→ P = P (1 + xp ∗ (δP/P )), (2)

where δP is the standard deviation of P [15]. P can be a configurable parameter or a function or any prediction. In the case of cross-section uncertainties, instead of re-simulating entire samples with this new parameter P 0, the GENIE response is predicted for each generated event and events are assigned a new weight based on whether the change increases or decreases their likelihood of occurring. Each variation knob has a calculator that estimates this (knob being the term referring to a variation parameter). The MicroBooNE flux [16] and GENIE [15] technical notes provide more details. This method has a limitation in that events cannot be weighted into existence, but sufficiently large in statistics simulated samples should negate this, and this method is optimal given limited allocated computing resources. The covariance matrices generated via reweighting make use of the final selections for 2γ1p, 2γ0p, 1γ1p, and 1γ0p, from previous sections. For systematics evaluation, 41 parameters of underlying neutrino interaction uncertainties in GENIE are studied together, alongside 13 systematic effects coming from the BNB flux modeling. The flux systematics included in the analysis are listed and described in Tab. 7. Two dominant systematics for the analysis are skin depth and π+ production. The skin-depth flux unisim refers to the effect of time varying electric currents penetrating into the horn conductor. In the case of π+ production, the majority of neutrino flux at MicroBooNE comes from π+ production in proton-Be target interactions. As this affects the majority of events in final selection, this source of uncertainty is necessarily an important one for all our signal and backgrounds. The effect of π+ production variations on the NC π0 non-coherent component of the 2γ and 1γ final selected samples is illustrated in Figs. 39 and 38, respectively.

43 Variation Label Description expskin FluxUnisim Skin Depth for electric currents penetrating conductor horncurrent FluxUnisim Horn Current in magnetic focusing horn kminus PrimaryHadronNormalization K− Production Normalization kplus PrimaryHadronFeynmanScaling K+ Sanford Wang Central Spline Variation kzero PrimaryHadronSanfordWang K0 Sanford Wang nucleoninexsec FluxUnisim Nucleon Total Inelastic Cross-section on Be nucleonqexsec FluxUnisim Nucleon Total Quasi-elastic Cross-section on Be nucleontotxsec FluxUnisim Nucleon Total cross-section on Be piminus PrimaryHadronSWCentralSplineVariation π− Sanford Wang Central Spline Variation pioninexsec FluxUnisim Pion Total Inelastic Cross-section on Be pionqexsec FluxUnisim Pion Total Quasi-elastic Cross-section on Be piontotxsec FluxUnisim Pion Total Cross-section on Be piplus PrimaryHadronSWCentralSplineVariation π+ Sanford Wang Central Spline Variation

Table 7: List of sources of ﬂux systematic uncertainties, evaluated using the reweighting method.

Figure 38: A variation plot illustrating the central Sanford Wang π+ flux uncertainty effect on the NCπ0 non-coherent background in the final 1γ1p (right) and 1γ0p (left) selection. The color scale represents the density of “multisims” or reweighted iterations that land in that particular bin thus giving a visual representation of the spread of prediction created by this underlying systematic uncertainty.

44 Figure 39: A variation plot illustrating the central Sanford Wang π+ flux uncertainty effect on the NCπ0 non-coherent signal in the final 2γ1p (right) and 2γ0p (left) selections. The color z scale represents the density of “multisims” or reweighted iterations that land in that particular bin thus giving a visual representation of the spread of prediction created by this underlying systematic uncertainty.

45 Cross-section systematics are evaluated using the GENIE reweight package. There are a total of 34 systematics that are defined by a continuous parameter which we study together under the umbrella term “genie all” to assess their effect in our analysis. The “genie all” set of variations runs a suite of variations for a number of GENIE systematic knobs simultaneously, accounting for all correlations between the different variations. Table 15 in Appendix A summarizes the sources of (input) GENIE systematic uncertainties. Because “genie all” accounts for correlations between individual knobs, it is more appropriately used for the calculation of final uncertainties and production of covariance matrices, instead of looking at each variation individually. It is run with 400 total multisims. Nonetheless, it is instructive to study each variation in isolation as well for the purpose of better understanding which underlying systematic uncertainties are the largest for our various selections. The effect of cross-section variations from “genie all” is illustrated in Fig. 40 and Fig. 41, for the NCπ0 non-coherent component of the 2γ and 1γ final selection stages, respectively.

Figure 40: A variation plot illustrating the “genie all” uncertainties’ eﬀect on the NCπ0 non-coherent component in the ﬁnal 1γ selections. The color z scale represents the density of “multisims” or reweighted iterations that land in that particular bin thus giving a visual representation of the spread of prediction created by this set of underlying systematic uncertainties.

46 Figure 41: A variation plot illustrating the “genie all” uncertainties’ eﬀect on the NCπ0 non coherent component in the ﬁnal 2γ selections. The color z scale represents the density of “multisims” or reweighted iterations that land in that particular bin thus giving a visual representation of the spread of prediction created by this set of underlying systematic uncertainties.

47 Alongside “genie all”, there are an additional seven other cross-section modelling uncertainties whose underlying physics is not defined by continuous parameters, but are more in line with switching between two binary interaction models, and the representative uncertainty is then given by the absolute difference between two extreme ranges (these are referred to as the “min/max” variations. An example of this is “Theta Delta2Npi” knob, which varies the pion angular distribution for ∆ → Nπ events between the default Rein-Sehgal model and an isotropic distribution, with the full difference being the uncertainty. The fractional covariance and correlation matrices constructed for all four samples (2γ1p, 2γ0p, 1γ1p, and 1γ0p) for “genie all” are shown in Figs. 42 and 43, respectively.

Figure 42: The fractional covariance matrix for “genie all” cross-section systematic uncertainties, constructed for the four ﬁnal selected samples side by side. The “genie all” covariance matrix more properly accounts for correlations among diﬀerent systematic knobs. The single-photon samples are each binned in 5 and 3 bins of shower energy, for 1γ0p and 1γ1p, respectively, and the NC π0 samples are each binned in 8 bins of NC π0 momentum.

48 Figure 43: The correlation matrix for “genie all” cross-section systematic uncertainties, constructed for the four ﬁnal selected samples side by side. The “genie all” correlation matrix properly accounts for correlations among diﬀerent systematic knobs. The single-photon samples are each binned in 5 and 3 bins of shower energy, for 1γ0p and 1γ1p, respectively, and the NC π0 samples are each binned in 8 bins of NC π0 momentum.

49 Final covariance and correlation matrices are generated using the combination of “genie all”; the 7 min/max interaction systematics; flux variations attributed to magnetic focusing horn modeling, BNB proton-target interaction and secondary production and interaction uncertainties. These are used to assess overall uncertainty on our predictions and will ultimately be used for our NC π0 constraint analysis (see Sec. 6), and final fits. The correlation matrix and fractional covariance matrix for all four final selected samples are provided in Figs. 44 and 45 respectively, constructed using the method described before. The plotted variables and binning were chosen to optimize the constraint analysis described in Sec. 6.

Figure 44: The correlation matrix for combined cross-section and ﬂux systematics. The single-photon samples are each binned in 5 and 3 bins of shower energy, for 1γ0p and 1γ1p, respectively, and the NC π0 samples are each binned in 8 bins of NC π0 momentum.

50 Figure 45: The fractional covariance matrix for combined cross-section and ﬂux systematics. The single- photon samples are each binned in 5 and 3 bins of shower energy, for 1γ0p and 1γ1p, respectively, and the NC π0 samples are each binned in 8 bins of NC π0 momentum.

51 An estimation of the level of constraint on the uncertainty of the ﬁnal 1γ1p signal measurement can be evaluated using the method described in Ref. [17], by considering the NC π0 sideband (2γ1p) measurement, in a way analogous to how one can constrain νe backgrounds using observed νµ events in the MiniBooNE or MicroBooNE experiments. The procedure is as follows: one begins with the total covariance matrix containing statistical and systematic uncertainties (and correlations) for both the 1γ samples (signal and background) and the 2γ signal −1 and background samples:Mij. The matrix is inverted, yielding Mij . Given an assumed statistical error on 0 data p data the measured NC π (2γ1p and 20p) rates, per bin i, given by σi = Ni , and assuming that the number data MC of observed data events is equivalent to that of the Monte Carlo, Ni = Ni , we then add the inverted −1 new −1 MC statistical error to the diagonal of the 2γ portion of the inverted matrix, i.e. (Mij ) = Mij + δij/Ni . After this step, the matrix is re-inverted and this leads to new uncertainties on 1γ samples, which are reduced, relative to the original. Those uncertainties are referred to as “constrained” uncertainties. The level of constraint (i.e. the level of uncertainty reduction) grows with increased 2γ1p and 20p statistics. Systematic uncertainties of 25% in the 1γ channels are reduced to under 8% after the 2γ constraint is applied. Further details can be found in Tabs. 8 and 9 which show uncertainties on the total predicted 1γ1p and 1γ0p samples broken down by each individual systematic uncertainty. This allows us to probe which underlying uncertainties are being constrained and which are not being aided by the 2γ sideband. The level of constraint evaluated using this method suggests one should expect a promising reduction of the systematic uncertainty on the background components of 1γ1p and 1γ0p samples, which are highly correlated with the 2γ1p and 2γ0p samples. In all tables, the 2γ1p and 2γ0p are used to constrain the 1γ samples simultaneously in unison, which is of particular importance as the 1p selections are largely insensitive to NC π0 coherent events.

Variation Name Unconstrained Constrained Reduction Unconstrained Constrained Reduction Error 1γ1p Error 1γ1p Factor 1γ1p Error 1γ0p Error 1γ0p Factor 1γ0p expskin FluxUnisim 4.93% 3.41% 1.45 4.01% 2.77% 1.45 horncurrent FluxUnisim 0.69% 0.68% 1.01 0.54% 0.53% 1.01 π+ SW CV Spline Var 4.51% 3.23% 1.40 3.86% 2.76% 1.40 π− SW CV Spline Var - - 1.00 0.16% 0.16% 1.00 K+ FeynmanScaling 0.46% 0.46% 1.00 0.55% 0.55% 1.00 K0 SanfordWang 0.16% 0.16% 1.00 0.27% 0.27% 1.00 K− Normalization ------nucleoninexsec FluxUnisim 0.83% 0.82% 1.02 0.77% 0.76% 1.02 nucleonqexsec FluxUnisim 2.49% 2.17% 1.14 2.37% 2.07% 1.14 nucleontotxsec FluxUnisim 0.73% 0.72% 1.01 0.66% 0.65% 1.01 pioninexsec FluxUnisim 1.25% 1.20% 1.04 1.06% 1.02% 1.04 pionqexsec FluxUnisim 0.84% 0.83% 1.02 0.74% 0.73% 1.02 piontotxsec FluxUnisim 0.88% 0.86% 1.02 0.78% 0.76% 1.02

Table 8: Unconstrained and constrained ﬂux uncertainties, broken down by systematic uncertainty source, for the 1γ1p and 1γ0p total background predictions. A - value indicates no uncertainty.

52 Variation Name Unconstrained Constrained Reduction Unconstrained Constrained Reduction Error 1γ1p Error 1γ1p Factor 1γ1p Error 1γ0p Error 1γ0p Factor 1γ0p genie all 22.64% 7.21% 3.14 13.82% 4.48% 3.09 AGKYpT1pi 0.43% 0.43% 1.00 0.36% 0.36% 1.00 AGKYxF1pi 0.34% 0.34% 1.00 0.18% 0.18% 1.01 AhtBY 0.00% 0.00% 1.00 0.23% 0.23% 1.00 BhtBY UBGenie 0.01% 0.01% 1.00 0.23% 0.23% 1.00 CV1uBY 0.03% 0.03% 1.00 0.23% 0.23% 1.00 CV2uBY UBGenie 0.03% 0.03% 1.00 0.23% 0.23% 1.00 CoulombCCQE 0.03% 0.03% 1.00 0.22% 0.22% 1.00 EtaNCEL 0.02% 0.02% 1.00 0.21% 0.21% 1.00 FrAbs N UBGenie 4.91% 3.21% 1.53 4.61% 3.02% 1.53 FrAbs pi 5.12% 3.26% 1.57 3.33% 2.13% 1.57 FrCEx N 9.58% 6.69% 1.43 1.58% 1.10% 1.43 FrCEx pi 9.32% 4.36% 2.14 4.18% 1.96% 2.13 FrInel N UBGenie 1.11% 0.74% 1.50 5.39% 3.60% 1.50 FrInel pi 3.14% 2.78% 1.13 0.30% 0.28% 1.07 FracDelta CCMEC 0.05% 0.05% 1.00 0.32% 0.32% 1.00 FracPN CCMEC 0.03% 0.03% 1.00 0.22% 0.22% 1.00 MFP N 2.47% 2.19% 1.13 1.94% 1.72% 1.13 MFP pi 1.73% 1.65% 1.05 0.97% 0.93% 1.05 MaCCQE 0.09% 0.09% 1.00 0.34% 0.34% 1.00 MaCCRES 0.66% 0.60% 1.10 2.41% 2.20% 1.10 MaNCEL 0.42% 0.41% 1.02 0.28% 0.28% 1.01 MaNCRES 18.94% 5.45% 3.48 10.44% 3.01% 3.47 MvCCRES 0.68% 0.63% 1.08 2.18% 2.02% 1.08 MvNCRES 8.06% 4.77% 1.69 4.41% 2.61% 1.69 NonRESBGvbarnCC1pi - - - 0.21% 0.21% 1.00 NonRESBGvbarnCC2pi - - - 0.21% 0.21% 1.00 NonRESBGvbarnNC1pi 0.16% 0.16% 1.00 0.21% 0.21% 1.00 NonRESBGvbarnNC2pi - - - 0.21% 0.21% 1.00 NonRESBGvbarpCC1pi - - - 0.21% 0.21% 1.00 NonRESBGvbarpCC2pi - - - 0.21% 0.21% 1.00 NonRESBGvbarpNC1pi - - - 0.27% 0.27% 1.00 NonRESBGvbarpNC2pi - - - 0.21% 0.21% 1.00 NonRESBGvnCC1pi - - - 0.97% 0.96% 1.01 NonRESBGvnCC2pi 0.13% 0.13% 1.00 0.78% 0.78% 1.00 NonRESBGvnNC1pi UBGenie 3.01% 2.51% 1.20 2.92% 2.44% 1.20 NonRESBGvnNC2pi UBGenie - - - 0.30% 0.30% 1.00 NonRESBGvpCC1pi 0.35% 0.35% 1.00 0.21% 0.21% 1.00 NonRESBGvpCC2pi 0.13% 0.13% 1.00 0.35% 0.35% 1.00 NonRESBGvpNC1pi 1.04% 1.02% 1.02 0.40% 0.40% 1.01 NonRESBGvpNC2pi 0.55% 0.52% 1.04 0.79% 0.76% 1.04 Min/Max Variations NormCCCOH - - - 0.20% 0.20% 1.00 NormNCCOH - - - 3.90% 3.48% 1.12 RPA CCQE 0.04% 0.04% 1.00 1.29% 1.29% 1.00 Theta Delta2Npi 7.83% 4.91% 1.59 0.98% 0.62% 1.57 VecFFCCQEshape 0.06% 0.06% 1.00 0.24% 0.24% 1.00 AxFFCCQEshape 0.01% 0.01% 1.00 0.30% 0.30% 1.00 DecayAngMEC 0.02% 0.02% 1.00 0.62% 0.62% 1.00

Table 9: Unconstrained and constrained cross section uncertainties, broken down by systematic uncertainty source, for the 2γ1p and 2γ0p total background predictions. Note that only “genie all” and the 7 Min/Max variations are used to build the final covariance matrices, with the individual variations that make up “genie all” being shown for illustrative effects to inform53 which underlying physics is driving the size of the total uncertainty. The MA NC Resonant variation is highlighted as it is one of the primary uncertainties on the NC π0 backgrounds and is reduced by a factor of 3.5. 5.2 Detector Systematic Uncertainties Detector systematic uncertainties are assessed as described in detail in Ref. [18]. For the latest Mi- croBooNE Monte Carlo simulation, an innovative method [19], called wire-modification (or waveform- modification), was adopted to produce detector variation samples for a number of sources of detector systematic uncertainties [18]. This method characterizes the detector’s response in terms of the charge (Qhit) and width (σhit) of Gaussian hits of reconstructed ionization charge deposits as a function of time and TPC wire (see Fig. 46). By measuring the values of Qhit and σhit for relevant variables of both data and Monte (data/MC) (data/MC) Carlo, the continuous ratio functions RQ and Rσ can be obtained, which are used to produce varied Monte Carlo samples.

Figure 46: Schematic of a hit [19]. The blue region represents ﬁtting the hit with a Gaussian function, where Qhit and σhit are integrated area (charge) and standard deviation from the Gaussian ﬁt, respectively. The X axis is a time-tick, a unit of time analogous to time of readout.

The majority of detector systematic effects are either related to the TPC wire response or PMT light yield systematics, with a small amount of additional systematics that do not fall into these categories. For each category, there are several sub-categories. For example, within the wire response systematics, there is one named “wire-modification X” (WireX) which includes all detector effects that affect the variables associated with the detector drift coordinate. Similarly, there are “wire-modification YZ” (WireYZ), “wire- modification track angles θXZ and θYZ ” (AngleXZ and AngleYZ), and “wire-modification dE/dx” (dEdx) in this category which correspond to all detector effects that affect the variables associated with detector YZ (Y is vertical plane and Z is beam direction) coordinate plane, the track angles, and the charge deposited per unit length (dE/dx), respectively. For the Light Yield category, there are samples for 25% light yield reduction (LY), light yield attenuation (LYAtt) and light yield Rayleigh scattering length (LYRay). The other detector effects include space charge effects (SCE) and recombination effects (Recom2). For the single- photon analysis, five different final state Monte Carlo sub-samples are used to evaluate the uncertainties on the signal and background. These sub-samples are: NC ∆ Radiative Decay (signal), NC π0 (including 1π0 0 0 Coherent and 1π Non-Coherent), BNB intrinsic νe andν ¯e CC, νµ CC 1π , and other BNB backgrounds. The analysis process is exactly the same as that of single-photon selections and NC π0 selections described in the previous sections but applied to detector variation samples. Figures 47 and 48 show area normalized shape comparisons of reconstructed shower energy spectra (1γ1p selection) and reconstructed π0 momentum spectra (2γ1p selection) at the final selection stage, corresponding to the different variation.

54 (a) Sub-sample: NC ∆ Radiative (b) Sub-sample: NC 1π0 (Non-Coherent)

0 (c) Sub-sample: νµ CC 1π (d) Sub-sample: νe and ν¯e CC

Figure 47: Area-normalized shape comparisons of shower energy spectra for CV and for all detector systematics variations, shown for each sub-sample in the 1γ1p selected sample, at ﬁnal selection stage. The lower part of each plot is the ratio of various detector systematic eﬀects to the CV.

55 (a) Sub-sample: NC ∆ Radiative (b) Sub-sample: NC 1π0 (Non-Coherent)

0 (c) Sub-sample: νµ CC 1π (d) Sub-sample: νe and ν¯e CC

(e) Sub-sample: BNB Other

Figure 48: Area-normalized shape comparisons of π0 momentum spectrum between CV and detector systematics for 2γ1p at ﬁnal cut stage. The lower part of each plot is the ratio of various detector systematic eﬀects to the CV.

56 Table 10 summarizes the percent uncertainties assessed on each sub-sample at final selection stage. As can be seen in the table, the detector variations again have little effect for the NC ∆ signal. They have up to ∼3.5% variations for NC π0 induced backgrounds which form the largest background for this channel. The “BNB Other” sample comprises an almost-negligible background, but there are still residual events yielding 0 large uncertainties in a few detector variation samples. For CC π and intrinsic νe CC backgrounds, even though the variations are relatively large in percentage, because these backgrounds are relatively small, the contributing absolute systematic uncertainty is comparable to that of NC π0. Table 11 summarizes the percent uncertainties assessed on each sub-sample at final selection stage. Figure 49 shows the total effects from the detector systematics on the reconstructed shower spectrum (1γ1p) and reconstructed π0 momentum spectrum (2γ1p).

Sub-sample WireX WireYZ AngleXZ AngleYZ dEdx LY LYAtt LYRay SCE Recom2 Sum NC ∆ 0.9 0.2 0.9 0.2 3.5 0.5 1.8 0.9 1.0 1.4 3.0 NC 1π0 Not Coh 3.5 2.2 1.5 1.7 0.2 1.5 1.7 1.0 1.4 2.9 6.2 NC 1π0 Coh 100 50 50 50 50 0.0 50 0.0 50 100 180 NC Multi-π0 ------0 CC νµ 1π 33.3 25.0 36.1 11.1 11.1 11.1 12.5 11.1 42.9 0.0 73.5 Intrinsic νe/¯νe CC 28.3 6.7 3.8 0.8 1.9 1.2 2.6 0.2 33.7 12.3 46.4 BNB Other - 0.0 0.0 0.0 0.0 - - - 0.0 0.0 0.0

Table 10: Percent (%) shifts in number of events for each 1γ1p sub-sample, for each systematic variation, defined as (N var − N CV )/N CV × 100%, at final selection stage. As noted before, the first two samples, NC ∆ and NC π0 Non-Coherent are both the primary components and also the only two high statistics detector variation samples that would be most robust to statistical variations. The combined (summed in quadrature) detector normalization uncertainties are given in the final column. For the purposes of this sum, the wire modified dEdx is not included; this is because both wire modified dEdx and the “Recombination 2” systematics cover the same underlying physics and including both would be double counting. “Recombination2” was chosen as it had the largest impact on our primary background, the NC π0.

(a) 1γ1p selection ﬁnal stage. (b) 2γ1p selection ﬁnal stage.

Figure 49: Final selected 1γ1p and 2γ1p distributions projected to Run 1-5 statistics of 12.25×1020 POT, shown with detector systematic uncertainties.

57 Sub-sample WireX WireYZ AngleXZ AngleYZ dEdx LY LYAtt LYRay SCE Recom2 Sum NC ∆ 5.2 0.6 0.9 4.6 4.9 2.2 0.7 0.3 6.4 12.2 15.6 NC 1π0 Not Coh 1.8 0.9 1.0 0.4 1.6 0.0 0.6 0.4 1.1 2.2 3.4 NC 1π0 Coh 8.8 3.0 14.3 2.9 20.0 0.0 2.9 3.0 16.1 17.6 29.8 NC Multi-π0 50 50 100 50 0.0 0.0 0.0 0.0 0.0 50 141 0 CC νµ 1π 3.8 1.9 5.8 7.6 0.3 4.6 6.9 0.3 1.7 8.2 15.8 Intrinsic νe/¯νe CC 4.3 6.5 10.5 0.6 4.5 2.1 4.1 2.2 1.0 23.8 27.0 BNB Other 2.9 31.9 7.3 14.5 39.1 0.0 7.8 0.0 18.8 45.9 61.7

Table 11: Percent (%) shifts in number of events for each 2γ1p sub-sample, for each systematic variation, defined as (N var − N CV )/N CV × 100%, at final selection stage. The combined (summed in quadrature) detector normalization uncertainties are given in the final column. For the purposes of this sum, the wire modified dEdx is not included, this is because both wire modified dE/dx and the “Recombination 2” systematics cover the same underlying physics and including both would be double counting. “Recombination 2” was chosen as it had the largest impact on our primary background, the NC π0.

58 6 Final Sensitivities and Preliminary Results 6.1 Fit Method The final 1γ1p, 1γ0p, 2γ1p, and 2γ0p selected distributions obtained following the methodology presented in Secs. 3 and 4, summarized in Fig. 50, along with their statistical and systematic uncertainties and systematic correlations, are used in a final fit to excess NC ∆ → Nγ events.

200 1x SM NC ∆ Radiative 12.25 x2 SM NC ∆ Radiative (LEE) 24.50 120 1x SM NC ∆ Radiative 10.30 x2 SM NC ∆ Radiative (LEE) 20.60 NC 1 π0 Coherent 16.24 NC 1 π0 Non-Coherent 142.48 NC 1 π0 Coherent 0.00 NC 1 π0 Non-Coherent 55.66

Events 0 0 Events 0 0 180 NC 2+ π 2.69 CC νµ 1 π 24.85 NC 2+ π 0.00 CC νµ 1 π 0.91 BNB Other 47.26 CC ν /ν Intrinsic 20.66 BNB Other 6.97 CC ν /ν Intrinsic 1.61 e e 100 e e 160 Dirt 11.39 Cosmic Data 19.80 Dirt 0.00 Cosmic Data 0.00 Flux, XS & Detector Systematics : 322.11 Flux, XS & Detector Systematics : 96.05 140 γ 80 γ 120 1 0p 12.25E20 POT 1 1p 12.25E20 POT MicroBooNE Simulation MicroBooNE Simulation 100 Preliminary 60 Preliminary

80 40 60

40 20 20

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 Reconstructed Shower Energy [GeV] Reconstructed Shower Energy [GeV]

600 1x SM NC ∆ Radiative 1.07 x2 SM NC ∆ Radiative (LEE) 2.14 600 1x SM NC ∆ Radiative 1.93 x2 SM NC ∆ Radiative (LEE) 3.87 NC 1 π0 Coherent 48.69 NC 1 π0 Non-Coherent 662.28 NC 1 π0 Coherent 2.75 NC 1 π0 Non-Coherent 1058.09

Events 0 0 Events 0 0 NC 2+ π 18.84 CC νµ 1 π 77.43 NC 2+ π 42.54 CC νµ 1 π 158.49 BNB Other 102.60 CC ν /ν Intrinsic 4.31 BNB Other 169.18 CC ν /ν Intrinsic 11.83 500 e e 500 e e Dirt 22.38 Run 1+2+3 Cosmic Data 169.12 Dirt 33.73 Run 1+2+3 Cosmic Data 203.53 Flux, XS & Detector Systematics : 1108.85 Flux, XS & Detector Systematics : 1685.93 400 400 2γ0p 12.25E20 POT 2γ1p 12.25E20 POT MicroBooNE Simulation MicroBooNE Simulation 300 Preliminary 300 Preliminary

200 200

100 100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Reconstructed π0 Momentum [GeV] Reconstructed π0 Momentum [GeV]

Figure 50: Final selection distributions for 1-shower (top), 2-shower (bottom), 0-proton (left) and 1-proton (right) topologies. The distributions show predictions scaled to 12.25×1020 POT, which corresponds to the total POT for Runs 1-5. These distributions correspond to the GENIE central value (CV) prediction, i.e. no normalization correction has been applied to the coherent and non-coherent NC π0 rates.

59 Prior to the fit, the 2γ selections are used to extract normalization correction factors to the GENIE- predicted NC π0 coherent and non-coherent rates. The extraction of these correction factors is carried out via a side-by-side fit to 2γ1p and 2γ0p data and Monte Carlo distributions, each provided in terms of three (3) bins of reconstructed cosine of the π0 angle relative to the neutrino beam direction. During the fit, 0 the normalizations of the coherent and non-coherent NC π components (Ncoh and Nnon−coh) in the 2γ1p and 2γ0p distributions are allowed to vary, and their best fit parameters are determined by minimizing the following χ2:

−1 X 3 χ2 = (MC − D ) δ + M syst (MC − D ), (3) scaled,i i 1/D + 2/MC ij ij scaled,j j i,j i i

where D refers to data, MCscaled refers to the total Monte Carlo prediction appropriately scaled by Ncoh and Nnon−coh factors, and Msyst represents a systematic covariance matrix iteratively updated to the best fit prediction, MC. This χ2 is the Combined Neyman-Pearson (CNP) χ2 [20], which is an approximation of the Poisson-likelihood built from a linear combination of the Neyman and Pearson χ2’s which leads to a significantly smaller bias on the best-fit model parameters compared to those using either the individual Neyman’s or Pearson’s chi-square. The fit accounts for statistical and full systematic uncertainties, including systematic correlations between the two distributions, except GENIE normalization uncertainties on the coherent and non-coherent components of the NC π0 prediction, and associated correlations, which are purposefully removed from the fit. The resulting allowed parameter space is shown in Fig. 51.

Figure 51: 1, 2, and 3σ C.L. contours obtained from the 3-bin NC π0 fit of the normalization of the coherent and non-coherent components of NC π0 production in the 2γ1p and 2γ0p samples, using data collected in the first Runs 1-3 of MicroBooNE data. Included in the fit are flux, cross-section, and detector systematic uncertainties and correlations, as well as statistical uncertainties.

We have verified that, once the resulting correction factors from the fit, Ncoh = 1.4 and Nnon−coh = 0.8, are applied to the 2γ1p and 2γ0p final selections, the agreement between data and Monte Carlo generally improves in all kinematic variables. This is illustrated in Figs. 52 and 53, for several kinematic variables. The predicted signal and background events corresponding to 12.25×1020 POT are tabulated in Tabs. 12 and 13, without and with the coherent and non-coherent NC π0 corrections applied. For the full data set of 12.25×1020 POT, corresponding to data collected by MicroBooNE during Runs 1-5, a statistical significance of 2.8σ (3.0σ) is expected for an excess of NC Delta Radiative events amounting to 2× SM contribution above the SM (corrected) prediction; such excess, if observed, would be consistent with an NC ∆ interpretation of the MiniBooNE observed low-energy excess.

1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 100 NC 1 π0 Coherent 1.83 NC 1 π0 Non-Coherent 403.89 60 NC 1 π0 Coherent 1.83 NC 1 π0 Non-Coherent 403.89 0 0 0 0 NC 2+ π 20.30 CC νµ 1 π 75.62 NC 2+ π 20.30 CC νµ 1 π 75.62 BNB Other 80.72 CC ν /ν Intrinsic 5.64 BNB Other 80.72 CC ν /ν Intrinsic 5.64 Events e e Events e e Dirt 16.09 Run 1+2+3 Cosmic Data 97.11 50 Dirt 16.09 Run 1+2+3 Cosmic Data 97.11 80 Flux & XS Systematics : 703.98 Run 1+2+3 On-Beam Data 634.00 Flux & XS Systematics : 703.98 Run 1+2+3 On-Beam Data 634.00

2γ1p 5.84E20 POT 40 2γ1p 5.84E20 POT 60 MicroBooNE Preliminary MicroBooNE Preliminary 30 40 20

20 10

20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 π0 θ Reconstructed Momentum [GeV] Reconstructed cos( CM) 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 π0 θ Reconstructed Momentum [GeV] Reconstructed cos( CM) (Data/MC: 0.90) (KS: 0.962) (χ2/nDOF : 15.65/34) (χ2 Pval: 0.997) (Data/MC: 0.90) (KS: 0.951) (χ2/nDOF : 23.33/34) (χ2 Pval: 0.916)

0 (a) π Momentum (b) cos(θcm)

1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 NC 1 π0 Coherent 1.83 NC 1 π0 Non-Coherent 403.89 NC 1 π0 Coherent 1.83 NC 1 π0 Non-Coherent 403.89 0 0 0 0 160 NC 2+ π 20.30 CC νµ 1 π 75.62 160 NC 2+ π 20.30 CC νµ 1 π 75.62 BNB Other 80.72 CC ν /ν Intrinsic 5.64 BNB Other 80.72 CC ν /ν Intrinsic 5.64 Events e e Events e e 140 Dirt 16.09 Run 1+2+3 Cosmic Data 97.11 140 Dirt 16.09 Run 1+2+3 Cosmic Data 97.11 Flux & XS Systematics : 703.98 Run 1+2+3 On-Beam Data 634.00 Flux & XS Systematics : 703.98 Run 1+2+3 On-Beam Data 634.00 120 2γ1p 5.84E20 POT 120 2γ1p 5.84E20 POT 100 MicroBooNE Preliminary 100 MicroBooNE Preliminary

80 80

60 60

40 40

20 20

2 10 20 30 40 50 60 70 80 90 100 2 10 20 30 40 50 60 70 80 90 100 Primary Shower Conversion Distance [cm] Secondary Shower Conversion Distance [cm] 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Primary Shower Conversion Distance [cm] Secondary Shower Conversion Distance [cm] (Data/MC: 0.90) (KS: 0.990) (χ2/nDOF : 28.36/34) (χ2 Pval: 0.740) (Data/MC: 0.90) (KS: 1.000) (χ2/nDOF : 30.30/34) (χ2 Pval: 0.650)

350 1x SM NC ∆ Radiative 0.92 x2 SM NC ∆ Radiative (LEE) 1.84 NC 1 π0 Coherent 1.83 NC 1 π0 Non-Coherent 403.89 0 0 NC 2+ π 20.30 CC νµ 1 π 75.62 BNB Other 80.72 CC ν /ν Intrinsic 5.64 Events 300 e e Dirt 16.09 Run 1+2+3 Cosmic Data 97.11 Flux & XS Systematics : 703.98 Run 1+2+3 On-Beam Data 634.00 250 2γ1p 5.84E20 POT 200 MicroBooNE Preliminary

150

100

2−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 θ Implied cos( π0) 1.5 1 0.5

Data/Prediction 0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 θ Implied cos( π0) (Data/MC: 0.90) (KS: 1.000) (χ2/nDOF : 5.23/10) (χ2 Pval: 0.875)

(e) cos θπ

Figure 52: Some select Data to Monte Carlo comparisons for the 2γ1p ﬁnal selection, after correction of the coherent and non-coherent NC π0 normalization. Uncertainties shown include ﬂux and cross-section systematics. To be compared with Fig. 34, which does not have the correction applied. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions. 61

1x SM NC ∆ Radiative 0.51 x2 SM NC ∆ Radiative (LEE) 1.03 1x SM NC ∆ Radiative 0.51 x2 SM NC ∆ Radiative (LEE) 1.03 NC 1 π0 Coherent 32.79 NC 1 π0 Non-Coherent 254.88 50 NC 1 π0 Coherent 32.79 NC 1 π0 Non-Coherent 254.88 0 0 0 0 60 NC 2+ π 9.06 CC νµ 1 π 37.25 NC 2+ π 9.06 CC νµ 1 π 37.25 BNB Other 49.36 CC ν /ν Intrinsic 2.07 BNB Other 49.36 CC ν /ν Intrinsic 2.07 Events e e Events e e Dirt 10.77 Run 1+2+3 Cosmic Data 81.36 Dirt 10.77 Run 1+2+3 Cosmic Data 81.36 40 50 Flux & XS Systematics : 479.08 Run 1+2+3 On-Beam Data 496.00 Flux & XS Systematics : 479.08 Run 1+2+3 On-Beam Data 496.00 2γ0p 5.89E20 POT 2γ0p 5.89E20 POT 40 MicroBooNE Preliminary 30 MicroBooNE Preliminary

30 20 20 10 10

200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 π0 θ Reconstructed Momentum [GeV] Reconstructed cos( CM) 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 π0 θ Reconstructed Momentum [GeV] Reconstructed cos( CM) (Data/MC: 1.04) (KS: 0.518) (χ2/nDOF : 35.66/34) (χ2 Pval: 0.390) (Data/MC: 1.04) (KS: 0.532) (χ2/nDOF : 35.97/34) (χ2 Pval: 0.376)

0 (a) π Momentum (b) cos(θcm)

1x SM NC ∆ Radiative 0.51 x2 SM NC ∆ Radiative (LEE) 1.03 1x SM NC ∆ Radiative 0.51 x2 SM NC ∆ Radiative (LEE) 1.03 60 NC 1 π0 Coherent 32.79 NC 1 π0 Non-Coherent 254.88 60 NC 1 π0 Coherent 32.79 NC 1 π0 Non-Coherent 254.88 0 0 0 0 NC 2+ π 9.06 CC νµ 1 π 37.25 NC 2+ π 9.06 CC νµ 1 π 37.25 BNB Other 49.36 CC ν /ν Intrinsic 2.07 BNB Other 49.36 CC ν /ν Intrinsic 2.07 Events e e Events e e 50 Dirt 10.77 Run 1+2+3 Cosmic Data 81.36 50 Dirt 10.77 Run 1+2+3 Cosmic Data 81.36 Flux & XS Systematics : 479.08 Run 1+2+3 On-Beam Data 496.00 Flux & XS Systematics : 479.08 Run 1+2+3 On-Beam Data 496.00

40 2γ0p 5.89E20 POT 40 2γ0p 5.89E20 POT MicroBooNE Preliminary MicroBooNE Preliminary 30 30

20 20

10 10

200 0.5 1 1.5 2 2.5 3 200 1 2 3 4 5 6 Angle Between Showers [rad] Leading Shower Kalman All-Plane Median dE/dx [Mev/cm] 1.5 1.5 1 1 0.5 0.5

Data/Prediction 0 Data/Prediction 0 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 Angle Between Showers [rad] Leading Shower Kalman All-Plane Median dE/dx [Mev/cm] (Data/MC: 1.04) (KS: 0.989) (χ2/nDOF : 18.06/34) (χ2 Pval: 0.989) (Data/MC: 1.04) (KS: 0.008) (χ2/nDOF : 46.39/34) (χ2 Pval: 0.076)

1x SM NC ∆ Radiative 0.51 x2 SM NC ∆ Radiative (LEE) 1.03 NC 1 π0 Coherent 32.79 NC 1 π0 Non-Coherent 254.88 350 0 0 NC 2+ π 9.06 CC νµ 1 π 37.25 BNB Other 49.36 CC ν /ν Intrinsic 2.07 Events e e 300 Dirt 10.77 Run 1+2+3 Cosmic Data 81.36 Flux & XS Systematics : 479.08 Run 1+2+3 On-Beam Data 496.00 250 2γ0p 5.89E20 POT MicroBooNE Preliminary 200

150

100

2−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 θ cos( π0) 1.5 1 0.5

Data/Prediction 0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 θ cos( π0) (Data/MC: 1.04) (KS: 1.000) (χ2/nDOF : 3.02/10) (χ2 Pval: 0.981)

(e) cos θπ

Figure 53: Some select Data to Monte Carlo comparisons for the 2γ0p final selection, after correction of the coherent and non-coherent NC π0 normalization. Uncertainties shown include all flux and cross- section systematics. To be compared with Fig. 35, which does not have the correction applied. Note: detector systematic uncertainties have been evaluated but are omitted in these distributions. 62 The application of the resulting correction factors from the fit, Ncoh = 1.4 and Nnon−coh = 0.8, to GENIE-predicted central values in the single-photon analysis yields the corrected distributions shown in the following subsection (specifically, in Fig. 54). Sensitivity projections are also provided in the following subsection, with and without this correction applied.

∆ ∆ ∆ ∆ 180 1x SM NC Radiative 12.25 x2 SM NC Radiative (LEE) 24.50 120 1x SM NC Radiative 10.30 x2 SM NC Radiative (LEE) 20.60 NC 1 π0 Coherent 22.73 NC 1 π0 Non-Coherent 113.99 NC 1 π0 Coherent 0.00 NC 1 π0 Non-Coherent 44.53 Events NC 2+ π0 2.69 CC ν 1 π0 24.85 Events NC 2+ π0 0.00 CC ν 1 π0 0.91 160 µ µ BNB Other 47.26 CC ν /ν Intrinsic 20.66 BNB Other 6.97 CC ν /ν Intrinsic 1.61 e e 100 e e Dirt 11.39 Cosmic Data 19.80 Dirt 0.00 Cosmic Data 0.00 140 Flux, XS & Detector Systematics : 300.11 Flux, XS & Detector Systematics : 84.92

120 80 1γ0p 12.25E20 POT 1γ1p 12.25E20 POT 100 MicroBooNE Simulation MicroBooNE Simulation Preliminary 60 Preliminary 80

60 40

40 20 20

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 Reconstructed Shower Energy [GeV] Reconstructed Shower Energy [GeV]

600 1x SM NC ∆ Radiative 1.07 x2 SM NC ∆ Radiative (LEE) 2.14 600 1x SM NC ∆ Radiative 1.93 x2 SM NC ∆ Radiative (LEE) 3.87 NC 1 π0 Coherent 68.17 NC 1 π0 Non-Coherent 529.82 NC 1 π0 Coherent 3.84 NC 1 π0 Non-Coherent 846.47

Events 0 0 Events 0 0 NC 2+ π 18.84 CC νµ 1 π 77.43 NC 2+ π 42.54 CC νµ 1 π 158.49 BNB Other 102.60 CC ν /ν Intrinsic 4.31 BNB Other 169.18 CC ν /ν Intrinsic 11.83 500 e e 500 e e Dirt 22.38 Run 1+2+3 Cosmic Data 169.12 Dirt 33.73 Run 1+2+3 Cosmic Data 203.53 Flux, XS & Detector Systematics : 995.87 Flux, XS & Detector Systematics : 1475.41 400 400 2γ0p 12.25E20 POT 2γ1p 12.25E20 POT MicroBooNE Simulation MicroBooNE Simulation 300 Preliminary 300 Preliminary

200 200

100 100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Reconstructed π0 Momentum [GeV] Reconstructed π0 Momentum [GeV]

Figure 54: Final selection distributions for 1-shower (top), 2-shower (bottom), 0-proton (left) and 1-proton (right) topologies. The distributions show predictions scaled to 12.25×1020 POT, which corresponds to the total POT for Runs 1-5. These distributions correspond to the corrected GENIE prediction, i.e. normalization 0 corrections of Ncoh = 1.4 and Nnon−coh = 0.8 have been applied to the coherent and non-coherent NC π fractions, respectively.

63 To assess sensitivity either to a hypothesized signal consistent with the MiniBooNE observed low-energy excess, or to any enhancement x∆ to the SM predicted NC ∆ → Nγ cross-section, a full ﬁt is performed simultaneously to the 1γ and 2γ selections. The data and Monte Carlo predictions are ﬁt as a function of reconstructed shower energy in the case of the 1γ selections and reconstructed π0 momentum in the case of the 2γ selections, minimizing the following χ2:

2 syst stat −1 χ = (MCscaled,i − Di)(Mij + Mij ) (MCscaled,j − Dj) (4)

where

stat 3 Mij = δij . (5) 1/Di + 2/MCi

Here, MCscaled is the Monte Carlo predicted spectrum modulated according to three fit parameters: x∆, 0 Ncoh, and Nnon−coh. For a sensitivity estimate, D is typically the null spectrum with NC π coherent and non-coherent components corresponding to either the GENIE central value or the corrected central value according to Ncoh,bf and Nnon−coh,bf ; MC is the central value spectrum corresponding to either the GENIE central value or the corrected central value; M syst is the full systematics covariance matrix evaluated at the best fit point, which includes flux, cross-section, and detector uncertainties and correlations; M stat is the CNP statistical covariance matrix evaluated at the best fit point, arrived at after an iterative fit, following the method in [21]. The final fractional covariance and correlation matrices corresponding to the GENIE CV (uncorrected) predictions are shown in Figs. 55 and 56, respectively. The order of fitted channels (left to right) correspond to 1γ1p (3 bins from 0 to 600 MeV), 1γ0p (6 bins from 100 to 700 MeV), 2γ1p (12 bins from 0 to 900 MeV) and 1γ0p (12 bins from 0 to 900 MeV). Those matrices include “genie all”, flux, and detector systematics the selections are subject to. They correspond to the collapsed background plus no signal prediction (i.e. the NC ∆ radiative rate is set to its 1×SM value) central values for 1γ and 2γ selections.

Collapsed fractional covariance matrix

0.4 30 0.35 Reco Bin j

25 0.3

0.25 20 0.2

15 0.15

0.1 10 0.05

5 0

−0.05 0 0 5 10 15 20 25 30 Reco Bin i

Figure 55: Final collapsed fractional covariance matrix for the 1γ1p, 1γ0p, 2γ1p and 2γ0p samples used in the final fits, with full flux, cross section and detector systematics included.

64 Collapsed correlation matrix 1

30 0.8 Reco Bin j 0.6 25 0.4

20 0.2

0 15 −0.2

10 −0.4

−0.6 5 −0.8

0 −1 0 5 10 15 20 25 30 Reco Bin i

Figure 56: Final collapsed correlation matrix for the 1γ1p, 1γ0p, 2γ1p and 2γ0p samples used in the final fits, with full flux, cross section and detector systematics included. Correlation factors between the most relevant bins in the 2γ1p and 1γ1p samples are in the range of 50-90%, allowing for a strong constraint of the NC π0 backgrounds via the simultaneous 1γ and 2γ fit method.

65 6.2 Projected Sensitivity to NC ∆ → Nγ The sensitivities to an enhanced NC ∆ → Nγ rate are shown in Figs. 60 (uncorrected NC π0 rates) and 61 (corrected NC π0 rates), left, for 12.25×1020 POT, which corresponds to the full set of MicroBooNE collected data, from Runs 1-5. The current sensitivity projections for the presently analyzed data from Runs 1-3 are shown in the same figures, on the right. As shown in the figures, which are Feldman-Cousins- corrected [22] using 10,000 fake experiments drawn from the underlying systematic and statistical covariance matrix, MicroBooNE will be able to measure an excess consistent with the MiniBooNE low energy excess interpretation as an underestimate of the NC ∆ → Nγ by a factor of 3 at well above 99% confidence level, with its full data set of 12.25×1020 POT. Fake data studies of sensitivities for two-hypothesis testing are provided in Fig. 57. Those are evaluated using 250,000 fake experiments, allowing accurate extrapolation to significance levels of up to 4σ. As shown by the median sensitivity in these figures, the MiniBooNE low-energy excess (LEE) interpreted as NC ∆ → Nγ events can be rejected by MicroBooNE in favor of the SM prediction at 2.1σ, assuming a measurement consistent with the SM prediction. For these studies we have focused on three scenarios, the LEE (x∆ = 3), the No-∆ (x∆ = 0) and the SM (x∆ = 1) hypothesis. In particular, the figures highlight the following:

• The median signiﬁcance of rejecting the No-∆ hypothesis (x∆ = 0) in favor of LEE hypothesis (x∆ = 3), assuming LEE is true is 3.6σ (68% of experiments range: 2.4σ → 4.6σ)

• The median signiﬁcance of rejecting SM hypothesis (x∆ = 1) in favor of LEE hypothesis (x∆ = 3), assuming LEE is true is 2.3σ (68% of experiments range: 1.2σ → 3.3σ)

• The median signiﬁcance of rejecting LEE hypothesis (x∆ = 3) in favor of the No-∆ hypothesis (x∆ = 0), assuming the No-∆ is true is 3.2σ (68% of experiments range: 2.2σ → 4.3σ)

• The median significance of rejecting LEE hypothesis (x∆ = 3) in favor of SM hypothesis (x∆ = 1), assuming SM is true is 2.1σ (68% of experiments range: 1.2σ → 3.1σ) It is worth noting that by fitting to 1γ and 2γ samples simultaneously, systematic uncertainties on the 1γ selections are effectively reduced, as illustrated in Tab. 14, Fig. 58 and Fig. 59. This demonstrates the importance of the NC π0 selection to the analysis, and showcases how powerful is the ability of the MicroBooNE LArTPC to provide measurements for a wide variety of exclusive interaction final states.

Sub-sample 1γ1p Selection 1γ0p Selection 2γ1p Selection 2γ0p Selection NC 1π0 Coherent 0.00 16.24 2.75 48.69 NC 1π0 Non-coherent 55.66 142.48 1058.09 662.28 NC ≥ 2π0 0.00 2.69 42.54 18.84 0 CC νµ 1π 0.91 24.85 158.49 77.43 BNB Other 6.97 47.26 169.18 102.60 CC νe/ν¯e Intrinsic 1.61 20.66 11.83 4.31 Dirt 0.00 11.39 33.73 22.38 Cosmic Data 0.00 19.80 203.53 169.12 1×SM NC ∆ Radiative 10.30 12.25 1.93 1.07 Total (1×SM) Prediction 75.45 297.61 1682.07 1106.71 2×SM NC ∆ Radiative 20.60 24.50 N/A N/A

Table 12: Event breakdown of ﬁnal selections for the 1γ1p, 1γ0p, 2γ1p, 2γ0p samples, for 12.25×1020 POT, without coherent and non-coherent NC π0 correction.

66 V12_Master_run5_v3_FULL5_NULL_V_LEECNP_Chi V12_Master_run5_v3_FULL6_LEE_V_NULLCNP_Chi

MicroBooNE +2 +1 Median -1 -2 MicroBooNE +2 +1 Median -1 -2 σ σ PDF PDF σ σ σ σ Simulation σ LEE (x3) Simulation σ No-Δ (x0) 0.07 0.07 Preliminary Preliminary No-Δ(x0) LEE (x3) 0.06 0.06

0.05 +2σ 0.05 +2σ 1-β(0.977) α(0.088 | 1.4σ) 1-β(0.977) α(0.102 | 1.3σ)

0.04 +1σ 0.04 +1σ 1-β(0.841) α(0.013 | 2.2σ) 1-β(0.841) α(0.008 | 2.4σ)

Median Median 0.03 0.03 1-β(0.500) α(10-3.12 | 3.2σ) 1-β(0.500) α(10-3.72 | 3.6σ)

-1σ -1σ 0.02 -4.82 0.02 -5.70 1-β(0.159) α(10 | 4.2σ) 1-β(0.159) α(10 | 4.6σ)

-2σ -2σ 0.01 0.01 1-β(0.023) α(10-inf | inf ) 1-β(0.023) α(10-inf | inf )

0 0 −80 −60 −40 −20 0 20 40 60 80 −50 0 50 100 150 Δ χ2 = χ2 - χ2 Δ χ2 = χ2 - χ2 V12_Master_run5_v3_FULL_LEE_V_SMCNP_ChiLEE (x3) No-Δ(x0) V12_Master_run5_v3_FULL_SM_V_LEECNP_ChiNo-Δ (x0) LEE (x3)

MicroBooNE +2 +1 Median -1 -2 MicroBooNE +2 +1 Median -1 -2 σ σ PDF PDF σ σ σ σ

Simulation σ σ 0.12 SM (x1) 0.12 Simulation LEE (x3) Preliminary Preliminary LEE (x3) SM (x1) 0.1 0.1

+2σ +2σ 0.08 1-β(0.977) α(0.468 | 0.1σ) 0.08 1-β(0.977) α(0.411 | 0.2σ)

+1σ +1σ 1-β(0.841) α(0.124 | 1.2σ) 1-β(0.841) α(0.125 | 1.2σ) 0.06 0.06 Median Median 1-β(0.500) α(0.012 | 2.3σ) 1-β(0.500) α(0.019 | 2.1σ) 0.04 0.04 -1σ -1σ 1-β(0.159) α(10-3.24 | 3.3σ) 1-β(0.159) α(0.001 | 3.1σ)

0.02 -2σ 0.02 -2σ 1-β(0.023) α(10-inf | inf ) 1-β(0.023) α(10-4.40 | 3.9σ)

0 0 −20 0 20 40 60 −40 −30 −20 −10 0 10 20 30 40 Δ χ2 = χ2 - χ2 Δ χ2 = χ2 - χ2 SM (x1) LEE (x3) LEE (x3) SM (x1)

Figure 57: Two-hypothesis test frequentist studies for a variety of hypotheses of ∆ radiative rates including the SM rate (×1 expected), the LEE rate (×3 expected) and the No-∆ rate (×0 expected, i.e. no ∆ radiative decay), for the full MicroBooNE Run 1-5 data set corresponding to 12.25×1020 POT.

Sub-sample 1γ1p Selection 1γ0p Selection 2γ1p Selection 2γ0p Selection NC 1π0 Coherent 0.00 22.73 3.84 68.17 NC 1π0 Non-coherent 44.53 113.99 846.47 529.82 NC ≥ 2π0 0.00 2.69 42.54 18.84 0 CC νµ 1π 0.91 24.85 158.49 77.43 BNB Other 6.97 47.26 169.18 102.60 CC νe/ν¯e Intrinsic 1.61 20.66 11.83 4.31 Dirt 0.00 11.39 33.73 22.38 Cosmic Data 0.00 19.80 203.53 169.12 1×SM NC ∆ Radiative 10.30 12.25 1.93 1.07 Total (1×SM) Prediction 75.45 297.61 1682.07 1106.71 2×SM NC ∆ Radiative 20.60 24.50 N/A N/A

Table 13: Event breakdown of ﬁnal selections for the 1γ1p, 1γ0p, 2γ1p, 2γ0p samples, for 12.25×1020 POT, 0 with coherent and non-coherent NC π corrections applied (corresponding to Ncoh = 1.4, Nnon−coh = 0.8).

67 Sample (bin) σunconstrained (%) σconstrained (%) Reduction Factor 1γ0p (100-200 MeV) 28.7 26.0 1.10 1γ0p (200-300 MeV) 20.6 12.3 1.68 1γ0p (300-400 MeV) 21.6 11.6 1.91 1γ0p (400-500 MeV) 18.9 9.40 2.01 1γ0p (500-600 MeV) 23.4 13.7 1.71 1γ0p (600-700 MeV) 22.2 14.5 1.54 1γ1p (0-200 MeV) 25.6 9.41 2.73 1γ1p (200-400 MeV) 25.5 8.26 3.09 1γ1p (400-600 MeV) 30.0 13.5 2.22

Table 14: The total (ﬂux, cross-section, and detector) constrained fractional uncertainties, and factor- reduction, for each bin of the 1γ1p and 1γ0p selections, assuming full Run1-5 12.25×1020 POT. Note: The total uncertainty ignores photonuclear absorption uncertainty, which is eﬀectively negligible.

200 120 1x SM NC Δ Radiative 10.30 x2 SM NC Δ Radiative (LEE) 20.60 1x SM NC Δ Radiative 12.25 x2 SM NC Δ Radiative (LEE) 24.50 NC 1 π0 Coherent 0.00 NC 1 π0 Non-Coherent 55.66 NC 1 π0 Coherent 16.24 NC 1 π0 Non-Coherent 142.48 Events 0 0 Events 180 0 0 NC 2+ π 0.00 CC νµ 1 π 0.91 NC 2+ π 2.69 CC νµ 1 π 24.85 100 BNB Other 6.97 CC νe/νe Intrinsic 1.61 BNB Other 47.26 CC νe/νe Intrinsic 20.66 Dirt 0.00 Cosmic Data 0.00 160 Dirt 11.39 Cosmic Data 19.80 Constrained Systematics : 96.05 Constrained Systematics : 322.11 140 80 1γ1p 12.25E20 POT 120 1γ0p 12.25E20 POT MicroBooNE Simulation MicroBooNE Simulation Preliminary 60 Preliminary 100

80 40 60

40 20 20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Reconstructed Shower Energy [GeV] Reconstructed Shower Energy [GeV]

Figure 58: Final selection distributions for the 1γ1p (left) and 1γ0p (right) topologies. The distributions show predictions scaled to 12.25×1020 POT, as in Fig. 50, but with the eﬀective anticipated systematic uncertainty reduction after applying the 2γ1p and 2γ0p constraint reﬂected in the reduced uncertainty bands.

∆ ∆ ∆ ∆ 120 1x SM NC Radiative 10.30 x2 SM NC Radiative (LEE) 20.60 180 1x SM NC Radiative 12.25 x2 SM NC Radiative (LEE) 24.50 NC 1 π0 Coherent 0.00 NC 1 π0 Non-Coherent 44.53 NC 1 π0 Coherent 22.73 NC 1 π0 Non-Coherent 113.99 Events NC 2+ π0 0.00 CC ν 1 π0 0.91 Events NC 2+ π0 2.69 CC ν 1 π0 24.85 µ 160 µ BNB Other 6.97 CC ν /ν Intrinsic 1.61 BNB Other 47.26 CC ν /ν Intrinsic 20.66 100 e e e e Dirt 0.00 Cosmic Data 0.00 Dirt 11.39 Cosmic Data 19.80 140 Constrained Systematics : 84.92 Constrained Systematics : 300.11

80 120 1γ1p 12.25E20 POT 1γ0p 12.25E20 POT MicroBooNE Simulation 100 MicroBooNE Simulation 60 Preliminary Preliminary 80

40 60

40 20 20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Reconstructed Shower Energy [GeV] Reconstructed Shower Energy [GeV]

Figure 59: Final selection distributions for the 1γ1p (left) and 1γ0p (right) topologies. The distributions show predictions scaled to 12.25×1020 POT, as in Fig. 50, but with the NC 1 π0 Coherent and NC 1 π0 Non-Coherent corrections applied (corresponding to Ncoh = 1.4, Nnon−coh = 0.8) and eﬀective anticipated systematic uncertainty reduction after applying the 2γ1p and 2γ0p constraint reﬂected in the reduced uncertainty bands.

68 To further improve the sensitivity studies from looking at simple 2-hypothesis tests, we elevate the ∆ radiative scale factor (x∆) to a continuous parameter and follow the Feldman-Cousins method to construct classical conﬁdence intervals as a function of observed ∆ radiative scale factor (x∆). The results of this are shown in Fig. 60 for both the full MicroBooNE dataset of Runs 1-5 (12.5×1020 POT) and Fig. 60 for a ﬁrst partial result with Runs 1-3 (6.9×1020 POT).

Feldman Cousins Corrected Confidence Belt Feldman Cousins Corrected Confidence Belt

) ) 7 Δ Δ Classical Confidence Confidence 7 Interval Level of 6 Interval

6 99% 99% 5 Radiative Rate (x Radiative Rate (x

Δ 5 Δ 95% 95% 4 True True 4 90% 3 90% 3

68% 2 68% 2

MicroBooNE MicroBooNE 1 1 Simulation Simulation Preliminary Preliminary 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Measured Δ Radiative Rate (x ) Measured Δ Radiative Rate (x ) Δ Δ

Figure 60: Feldman-Cousins calculated classical confidence belt for a combined 1γ1p, 1γ0p, 2γ1p and 2γ0p fit with full flux, cross-section and detector systematic uncertainties, fitting only for x∆ with the non- coherent and coherent π0 rates fixed at the GENIE CV. The left plot shows the confidence belts assuming the full MicroBooNE dataset of Runs 1-5 POT (12.25×1020 POT), whereas the right plot shows the results for a partial data set of Runs 1-3 (6.9×1020 POT). To construct a classical confidence interval of a given confidence (e.g. 90%) one draws a vertical line up from the assumed observed best-fit ∆ radiative decay rate, with the intersection of this line and the appropriate contour giving the confidence interval.

69 Feldman Cousins Corrected Confidence Belt Feldman Cousins Corrected Confidence Belt

) 7 ) 7 Δ Δ Classical Classical Confidence Confidence Level of Level of 6 Interval 6 Interval

99% 99% 5 5 Radiative Rate (x Radiative Rate (x Δ Δ

95% 95% 4 4 True True

3 90% 3 90%

2 68% 2 68%

MicroBooNE MicroBooNE 1 Simulation 1 Simulation Preliminary Preliminary 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Measured Δ Radiative Rate (x ) Measured Δ Radiative Rate (x ) Δ Δ

Figure 61: Feldman-Cousins calculated classical confidence belt for a combined 1γ1p, 1γ0p, 2γ1p and 2γ0p fit with full flux, cross-section and detector systematic uncertainties, fitting only for x∆ with the non- 0 coherent and coherent π rates fixed at the values obtained in the 2γ angular fit, corresponding to Ncoh = 1.4, Nnon−coh = 0.8. The left plot shows the confidence belts assuming the full MicroBooNE data set of Runs 1-5 POT (12.25×1020 POT), whereas the right plot shows the results for a partial data set of Runs 1-3 (6.9×1020 POT). To construct a classical confidence interval of a given confidence (e.g. 90%) one draws a vertical line up from the assumed observed best-fit ∆ radiative decay rate, with the intersection of this line and the appropriate contour giving the confidence interval.

70 A subset of the information shown in Fig. 60, for hypothetical data measurements ofx ˆ∆ = 0 andx ˆ∆ = 1 is highlighted in Fig. 62 where the allowed regions on x∆ have been mapped to the underlying GENIE cross-section on argon in units of σ (10−42cm2/nucleon). Both of these produce one-sided intervals bounding the cross-section from above.

BNB Flux at µBooNE (a.u) x3 SM rate (MiniBooNE LEE) BNB Flux at µBooNE (a.u) x3 SM rate (MiniBooNE LEE)

40 GENIE σ (G18_10a_02_11a) Expected 90% C.L 40 GENIE σ (G18_10a_02_11a) Expected 90% C.L /nucleon) /nucleon)

2 Flux Averaged GENIE <σ> Runs 1-3 (6.9e20 POT) 2 Flux Averaged GENIE <σ> Runs 1-3 (6.9e20 POT) 35 E.Wang et al. 1311.2151 35 E.Wang et al. 1311.2151 cm Runs 1-5 (12.3e20 POT) cm Runs 1-5 (12.3e20 POT) Mean Nucleon, CA 1σ spread Mean Nucleon, CA 1σ spread 5 5 -42 -42

(10 30 (10 30 σ σ

25 25

20 20

15 15

10 10

MicroBooNE MicroBooNE 5 Simulation 5 Simulation Preliminary Preliminary

0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Eν [GeV] Eν [GeV]

Figure 62: The expected classical 90% confidence intervals assuming observation of data consistent with no ∆ radiative decay (xˆ∆ = 0, left) and consistent with the GENIE CV prediction (xˆ∆ = 1, right). The GENIE v3 cross-section prediction is shown in red, alongside a leading theoretical calculation of the full single photon emission rate on argon in green [23], showing excellent agreement with GENIE. The all-flavor BNB neutrino flux is shown as the hashed gray histogram, as well as the total flux averaged GENIE cross section as the single point in magenta. The width of the horizontal errors bars represents 68% of the flux- times-cross-section distribution. The bound is placed on this flux-averaged cross section as, due to the neutral current nature of the process, we are not sensitive to parent neutrino energy at the level required to extract an energy dependent cross-section. Highlighted in yellow is the 3× the flux-averaged GENIE cross-section— the approximate enhancement to the ∆ radiative decay rate in order for it to be the sole explanation of the MiniBooNE LEE. The NC π0 rate is kept at the GENIE CV prediction.

7 Summary and Conclusions

We have presented the MicroBooNE search for excess neutrino-induced NC single-photon events, which has been optimized speciﬁcally for a signal topology consistent with NC ∆ resonance production followed by ∆ radiative decay. This search is being carried out by MicroBooNE in order to directly constrain the SM-predicted rate of the neutrino-induced NC ∆ → Nγ process on argon, at neutrino energies below 1 GeV, as well as to directly test the NC ∆ radiative decay interpretation of the previously observed and still unexplained MiniBooNE “low energy excess”. Through four exclusive, targeted single-photon and NC π0 selections, the MicroBooNE single-photon analysis is projected to yield world-leading constraints to the SM-predicted NC ∆ → Nγ cross section on argon, as shown in Fig. 62. It is also projected to provide a 2.1σ (statistical and systematics) test of the interpretation of the observed MiniBooNE low energy excess as an underestimate of NC single-photon production that is generally consistent with the NC ∆ → Nγ signature; this projected sensitivity is the

71 median significance of rejecting the low energy excess hypothesis in favor of the SM hypothesis, assuming the SM is true, for Runs 1-5. At the same time, the analysis has produced the world’s highest-statistics measurement of NC π0 interactions on argon in the exclusive 2γ1p and 2γ0p final state topologies. This is allowing information that is relevant to the single-photon search to be meaningfully extracted, such as corrections to the GENIE-predicted coherent and non-coherent NC π0 event rates. The analysis demonstrates the challenge of low-energy shower reconstruction in LArTPCs, but at the same time highlights the wealth of topological and calorimetric information that can be successfully extracted from recorded LArTPC data. Preliminary data to Monte Carlo comparisons with statistics-limited and blinded 1γ data sets show reasonable data to Monte Carlo agreement, within fully assessed systematic uncertainties, including flux, cross-section, and detector systematics. Further improvements to the MicroBooNE single-photon low energy excess search are possible with (ongoing) improvements in reconstruction, which are needed in order to enhance signal efficiency at the topological selection stage. Inclusion of information recorded by MicroBooNE’s cosmic ray tagger (CRT), a veto detector enveloping the MicroBooNE LArTPC that was intended to provide further rejection of detector-crossing cosmic ray muons and brought online at the end of Run 2, may also be considered to provide further cosmic rejection while preserving signal efficiency.

72 References

[1] A. A. Aguilar-Arevalo et al., “Unexplained Excess of Electron-Like Events From a 1-GeV Neutrino Beam,” Phys. Rev. Lett., vol. 102, p. 101802, 2009. [2] K. Abe et al., “Search for neutral-current induced single photon production at the ND280 near detector in T2K,” J. Phys., vol. G46, no. 8, p. 08LT01, 2019. [3] M. Collaboration, “MicroBooNE low-energy excess signal prediction from unfolding,” MicroBooNE Public Note 1043. [4] G. S. Karagiorgi, Searches for New Physics at MiniBooNE: Sterile Neutrinos and Mixing Freedom. PhD thesis, 2010. [5] R. Acciarri et al., “Design and Construction of the MicroBooNE Detector,” JINST, vol. 12, no. 02, p. P02017, 2017. [6] J. Conrad, B. Jones, Z. Moss, T. Strauss, and M. Toups, “The Photomultiplier Tube Calibration System of the MicroBooNE Experiment,” JINST, vol. 10, no. 06, p. T06001, 2015. [7] R. Acciarri et al., “Noise Characterization and Filtering in the MicroBooNE Liquid Argon TPC,” JINST, vol. 12, no. 08, p. P08003, 2017.

[8] M. Collaboration, “The microboone search for single photon events,” MicroBooNE Public Note 1041. [9] R. G. Murrells, The Search for Low Energy Single Photons in MicroBooNE. PhD thesis. [10] R. Acciarri, C. Adams, R. An, J. Anthony, J. Asaadi, M. Auger, L. Bagby, S. Balasubramanian, B. Baller, C. Barnes, et al., “The pandora multi-algorithm approach to automated pattern recognition of cosmic-ray muon and neutrino events in the microboone detector,” The European Physical Journal C, vol. 78, no. 1, p. 82, 2018. [11] X. Ji, “Space charge boundary of position dependence.” MicroBooNE DocDB: 26423, 2019. [12] M. Collaboration, “Event selection in the microboone deep learning based low energy excess analysis using two-body scattering criteria,” MicroBooNE Public Note 1086. [13] M. Collaboration, “Search for electron neutrinos in multiple topologies with the microboone experiment,” MicroBooNE Public Note 1085. [14] N. Tagg, “Argo event display.” ”https://argo-microboone.fnal.gov/”.

[15] C. Andreopoulos, “Genie physics & users manual v3 prelim.” https://genie- docdb.pp.rl.ac.uk/DocDB/0000/000002/006/man.pdf, 2019. [16] J. Zennamo and Z. Pavlovic, “Microboone ﬂux and ﬂux uncertainties.” MicroBooNE DocDB: 8622, 2017.

[17] M. H. Shaevitz, “Constraining the νe background uncertainties with the observed νµ events.” BooNE Technical Note: 221, 2007. [18] M. S. W. Group, “Mcc9 detector systematic uncertainties.” MicroBooNE DocDB: 27009, 2020. [19] L. Yates, “Detector systematics with waveform modiﬁcation.” MicroBooNE DocDB: 26195, 2019. [20] X. Ji, W. Gu, X. Qian, H. Wei, and C. Zhang, “Combined Neyman–Pearson chi-square: An improved approximation to the Poisson-likelihood chi-square,” Nucl. Instrum. Meth. A, vol. 961, p. 163677, 2020.

73 [21] A. Aguilar-Arevalo, C. Anderson, S. Brice, B. Brown, L. Bugel, J. Conrad, R. Dharmapalan, Z. Djurcic, B. Fleming, R. Ford, et al., “Event excess in the miniboone search for νµ → νe oscillations,” Physical Review Letters, vol. 105, no. 18, p. 181801, 2010. [22] G. J. Feldman and R. D. Cousins, “A Uniﬁed approach to the classical statistical analysis of small signals,” Phys. Rev. D, vol. 57, pp. 3873–3889, 1998.

[23] E. Wang, L. Alvarez-Ruso, and J. Nieves, “Photon emission in neutral current interactions at interme- diate energies,” Phys. Rev. C, vol. 89, no. 1, p. 015503, 2014.

74 A Appendix I: GENIE Cross section Systematics

75 Variation Label Description All UBGenie All multisim mode GENIE variables combined AGKYpT1pi UBGenie Pion transverse momentum for Nπ states in AGKY AGKYxF1pi UBGenie Pion Feynman x for Nπ states in AGKY AhtBY UBGenie A HT higher twist param in BY model scaling variable ξw ±25 % BhtBY UBGenie B HT higher twist param in BY model scaling variable ξw CV1uBY UBGenie C V 1u u valence GRV98 PDF correction param in BY model CV2uBY UBGenie C V 2u u valence GRV98 PDF correction param in BY model CoulombCCQE UBGenie Changes angular distribution of nucleon cluster EtaNCEL UBGenie Strange axial form factor η for NC elastic FrAbs N UBGenie Nucleon absorption probability. FrAbs pi UBGenie pi absorption probability FrCEx N UBGenie Fractional cross section for nucleon charge exchange FrCEx pi UBGenie Fractional cross section for π charge exchange FrInel N UBGenie Nucleon charge exchange probability FrInel pi UBGenie π charge exchange probability FracDelta CCMEC UBGenie Nucleon pi-minus production probability FracPN CCMEC UBGenie π-production probability MFP N UBGenie Nucleon mean free path (total rescattering probability) MFP pi UBGenie π mean free path (total rescattering probability) MaCCQE UBGenie Axial Mass for CCQE MaCCRES UBGenie Axial mass for CC resoce neutrino production MaNCEL UBGenie Axial mass for NC elastic MaNCRES UBGenie Axial mass for NC resoce neutrino production MvCCRES UBGenie Vector mass for CC resoce neutrino production MvNCRES UBGenie Vector mass for NC resoce neutrino production NonRESBGvbarnCC1pi UBGenie Non-Res background normalizationν ¯ neutron CC1π scattering NonRESBGvbarnCC2pi UBGenie Non-Res background normalizationν ¯ neutron CC2π scattering NonRESBGvbarnNC1pi UBGenie Non-Res background normalizationν ¯ neutron NC1π scattering NonRESBGvbarnNC2pi UBGenie Non-Res background normalizationν ¯ neutron NC2π scattering NonRESBGvbarpCC1pi UBGenie Non-Res background normalizationν ¯ proton CC1π scattering NonRESBGvbarpCC2pi UBGenie Non-Res background normalizationν ¯ proton CC2π scattering NonRESBGvbarpNC1pi UBGenie Non-Res background normalizationν ¯ proton NC1π scattering NonRESBGvbarpNC2pi UBGenie Non-Res background normalizationν ¯ proton NC2π scattering NonRESBGvnCC1pi UBGenie Non-Res background normalization ν neutron CC1π scattering NonRESBGvnCC2pi UBGenie Non-Res background normalization ν neutron CC2π scattering NonRESBGvnNC1pi UBGenie Non-Res background normalization ν neutron NC1π scattering NonRESBGvnNC2pi UBGenie Non-Res background normalization ν neutron NC2π scattering NonRESBGvpCC1pi UBGenie Non-Res background normalization ν proton CC1π scattering NonRESBGvpCC2pi UBGenie Non-Res background normalization ν proton CC2π scattering NonRESBGvpNC1pi UBGenie Non-Res background normalization ν proton NC1π scattering NonRESBGvpNC2pi UBGenie Non-Res background normalization ν proton NC2π scattering Min/Max Mode Variations NormCCCOH UBGenie Normilization for CC Coherent Processes (in developement) NormNCCOH UBGenie Normilization for NC Coherent Processes (in developement) RPA CCQE UBGenie Strength of RPA correction for central tune Theta Delta2Npi UBGenie Variation of angle of pion with respect to detector z axis TunedCentralValue UBGenie Tunes CCQE model based on central value MC VecFFCCQEshape UBGenie VecFFCCQEshape UBGenie DecayAngMEC UBGenie Changes angular distribution of nucleon cluster AxFFCCQEshape UBGenie Varies CCQE axial form factor model between dipole (CV) and z-expansion.

Table 15: Description of GENIE cross-section reweightable systematics. Note that Min/Max variations are not included in Genie ALL