Comparison of \({\varvec{\nu }}_{\varvec{\mu }}\)Ar multiplicity distributions observed by MicroBooNE to GENIE model predictions
Abstract
We measure a large set of observables in inclusive charged current muon neutrino scattering on argon with the MicroBooNE liquid argon time projection chamber operating at Fermilab. We evaluate three neutrino interaction models based on the widely used GENIE event generator using these observables. The measurement uses a data set consisting of neutrino interactions with a final state muon candidate fully contained within the MicroBooNE detector. These data were collected in 2016 with the Fermilab Booster Neutrino Beam, which has an average neutrino energy of \(800~\hbox {MeV}\), using an exposure corresponding to \( 5.0\times 10^{19}\) protonsontarget. The analysis employs fully automatic event selection and charged particle track reconstruction and uses a datadriven technique to separate neutrino interactions from cosmic ray background events. We find that GENIE models consistently describe the shapes of a large number of kinematic distributions for fixed observed multiplicity.
1 Introduction
A growing number of neutrino physics experiments use liquid argon as a neutrino interaction target nucleus in a time projection chamber [1]. Experiments that use or will use liquid argon time projection chamber (LArTPC) technology include those in the ShortBaseline Neutrino (SBN) program [2] at Fermilab, centered on searches for nonstandard neutrino oscillations, and the longbaseline DUNE experiment [3]. The SBN program consists of the MicroBooNE experiment [4], an upgraded ICARUS experiment [5], and the new SBND experiment [6]. The DUNE experiment seeks to establish the mass ordering of the three standard model neutrinos and the charge parity violation parameter phase \(\delta _{CP}\) in the PMNS neutrino mixing matrix [7].
All LArTPC neutrino oscillationrelated measurements require a precise understanding of neutrino scattering physics and the measured response of the LArTPC detector to final state particles. These depend on: (a) the neutrino flux seen by the experiment, (b) the neutrino scattering cross sections, (c) the interaction physics of scattering final state particles with argon, (d) transport and instrumentation effects of charge and light in the LArTPCs, and (e) software reconstruction algorithms. In practice item (a) is determined by a combination of hadron production cross section measurements and precise descriptions of neutrino beamline components. Item (b) is most commonly provided by the GENIE [8] neutrino event generation model for neutrinoargon scattering. Items (c)–(e) are incorporated into a detailed suite of GEANT4based [9] simulation and event reconstruction products called LArSoft [10].
GENIE has been built up from models of the most important physical scattering neutrinonucleon mechanisms for the SBN and DUNE energy regimes (0.5–5 GeV): quasielastic (QE) scattering \(\nu _{\ell }N\rightarrow \ell ^{}N^{ \prime },\nu _{\ell }N^{\prime }\), resonance production (RES) \(\nu _{\ell }N\rightarrow \ell ^{}R,\nu _{\ell }R^{\prime }\), and nonresonant multihadron production referred to as deep inelastic scattering (DIS): \(\nu _{\ell }N\rightarrow \ell ^{}X,\nu _{\ell }X^{\prime }\) [11, 12]. The underlying neutrinonucleon scattering processes receive significant modification from the nuclear environment, including the effects of Fermi motion of target nucleons, manynucleon effects, and final state interactions (FSI) [13]. While GENIE has received a fair amount of “tuning” (the process of finding a set of GENIE parameters chosen to optimize agreement with a particular data set) from previous electron and neutrino scattering measurements, considerable uncertainties remain in the modeling of both the underlying neutrinonucleon scattering and the nuclear environment [14].
Relatively few neutrino scattering measurements on argon exist [15, 16, 17, 18, 19, 20], especially for the recoil hadronic system. Most of these report lowstatistics exclusive final states. Nearly all existing neutrino scattering constraints on GENIE models derive measurements on scattering from carbon, which has \(30\%\) of argon’s atomic mass number and a \(22\%\) lower neutrontoproton ratio. We take a step in improving the empirical understanding of neutrino scattering from argon here by performing a large set of comparisons of observed inclusive properties of charged current scattering, measured at the MicroBooNE experiment in the Fermilab Booster Neutrino Beam (BNB) [21] (MicroBooNE and MiniBooNE share the same beam), to predictions from several variants of GENIE. These comparisons are generated by applying fully automated event reconstruction and signal selection tools to a subset of MicroBooNE’s first collected data. While this analysis must focus in large part on reducing cosmic ray backgrounds, sensitivity to GENIE model parameters remains.
In Sect. 2, we introduce the formalism that relates interaction models to our measurements. In Sect. 3, we describe the MicroBooNE detector and Booster Neutrino Beam. Section 4 describes the cosmic ray backgrounds in MicroBooNE. Section 5 summarizes the event selection procedure and the main software tools used in the analysis. Section 6 presents the procedure for discriminating BNB neutrino interactions from cosmic ray background events. Section 7 shows the results of a systematic uncertainty analysis. Section 8 presents the comparison of observed charged particle multiplicity distributions and charged track kinematic distributions for each multiplicity, to predictions from GENIE. Section 9 provides a discussion of the result, and Sect. 10 gives an overall conclusion.
2 Introduction to observed charged particle multiplicity and kinematic distributions
Neutrino interactions in the MicroBooNE detector produce charged particles that can be reconstructed as tracks in the liquid argon medium of the MicroBooNE LArTPC. These interactions can be characterized by a number of inclusive properties. The charged particle multiplicity, or number of primary charged particles, n, is a simple observable characterizing final states in highenergycollision processes, including neutrino interactions. We note that in MicroBooNE the observable charged particle multiplicity corresponds to that of charged particles exiting the target nucleus participating in the neutrino interaction.
The charged particle multiplicity distributions (CPMD) comprise the set of probabilities, \(P_{n}\), associated with producing n charged particles in an event, either in full phase space or in restricted phase space domains. In addition to the observed CPMD, kinematic properties of all charged particle tracks for each multiplicity can be examined. Determination of inclusive event properties such as the CPMD and of individual track kinematic properties at Fermilab BNB neutrino energies naturally fits into the modern strategy [11, 12] of presenting neutrino interaction measurements in the form of directly observable quantities.
Inclusive measurements expand the empirical knowledge of neutrinoargon scattering that will be required by the DUNE experiment and the Fermilab SBN program. As physical observables, the CPMD and other distributions can also be used to test models, or particular tunes of models such as GENIE. These models are typically constructed from a set of exclusive cross section channels, and tests of inclusive distributions can provide independent checks.
Our analysis requires at least one of the charged tracks to be consistent with a muon; hence the \(O_{n}\) are effectively observed CPMD for \(\nu _{\mu } \) charged current (\(\nu _{\mu }\) CC) interactions. The \(\nu _{\mu }\) NC, \(\nu _{e}\), \(\bar{\nu }_{e}\), and \(\bar{\nu }_{\mu }\) backgrounds, in total, are expected to be less than \(10\%\) of the final sample. The muon candidate is included in the charged particle multiplicity, and all events thus have \( n\ge 1\). For each multiplicity, we have available the kinematic properties of charged tracks. These can in principle be related to the 4vector components of each track; however, we choose distributions of directly observable quantities in the detector: visible track length and track angles.
The observed CPMD and inclusive observed kinematic distributions have several desirable attributes. The \(\sigma _{CC,n}\) are all large up to \(n\lesssim 4\) at these neutrino energies (see Sect. 3); therefore only modest event statistics are required. Only minimal kinematic properties of the final state are imposed (the track definition implies an effective minimum kinetic energy), and complexities associated with particle identification and photon reconstruction are avoided. At the same time, the observed quantities reveal much of the power of the LArTPC in identifying and characterizing complex neutrino interactions. The observed CPMD and associated kinematic distribution ratios will have reduced sensitivity to systematic normalization uncertainties associated with flux and efficiency compared to absolute cross section measurements.
A disadvantage of the use of observed CPMD and other kinematic quantities is their lack of portability. One must have access to the full MicroBooNE simulation suite to use the \(O_{n}\) to test other models.
3 The MicroBooNE detector and the booster neutrino beam
The MicroBooNE TPC (Fig. 2) has an active mass of about 85 tons (85 mg) of liquid argon. It is 10.4 meters long in the beam direction, 2.3 m tall, and 2.6 m in the electron drift direction. Electrons require 2.3 ms to drift across the full width of the TPC from cathode (at \(70\) kV) to anode (at \(\sim 0\) kV). Events are read out on three anode wire planes with 3 mm spacing between wires. Drifting electrons pass through the first two wire planes, which are oriented at \(\pm 60^\circ \) relative to vertical, producing bipolar induction signals. The third wire plane, the collection plane, has its wires oriented vertically and collects the charge of the drifting electrons in the form of a unipolar signal. The MicroBooNE readout electronics allow for measurement of both the time and charge created by drifting electrons on each wire. The amplified, shaped waveforms from 8256 wires from induction and collection planes are digitized at 2 MHz using 12bit ADCs. A data acquisition system readout window consisting of 9600 recorded samples (4.8 ms) for all wires is then noisefiltered and deconvolved utilizing offline software algorithms. Reconstruction algorithms are then used on these output waveforms to reconstruct the times and amplitudes of charge depositions (hits) on the wires from particleinduced ionization in the TPC bulk.
While all three anode planes are used for track reconstruction, the collection plane provides the best signaltonoise performance and charge resolution. The analysis presented here excludes regions of the detector that have nonfunctional collection plane channels (\(\sim 10\%\)). It also imposes requirements on the minimum number of collection plane hitscurrent pulses processed through noise filtering [22], deconvolution, and calibrationassociated with the reconstructed tracks. All charged particle track candidates are required to have at least 15 collection plane hits, and the longest muon track candidate is required to have at least 80 collection plane hits. Furthermore, as described in Sect. 5.2, we use two discriminants to extract the neutrino interaction and cosmic ray background contributions to our data sample that are based on collection plane hits.
A light collection system consisting of 32 8inch photomultiplier tubes (PMTs) with nanosecond timing resolution enables precise determination of the time of the neutrino interaction, which crucially aids in the reduction of cosmic ray backgrounds.
The BNB employs protons from the Fermilab Booster synchrotron impinging on a beryllium target. The proton beam comes in bunches of protons called “beam spills”, has a kinetic energy of 8 GeV, a repetition rate of up to 5 Hz, and is capable of producing \(5\times 10^{12}\) protonsperspill. Secondary pions and kaons decay producing neutrinos with an average energy of 800 MeV. MicroBooNE received \(3.6\times 10^{20}\) protonsontarget in its first year of running, from fall 2015 through summer 2016. This analysis uses a fraction of that data corresponding to \(5.0\times 10^{19}\) protonsontarget.
4 Cosmic ray backgrounds
The MicroBooNE detector lacks appreciable shielding from cosmic rays (CR) since the detector is at the earth’s surface and has little overburden. Most events that are recorded and processed through an online software trigger which requires that the total light recorded with the PMT system exceeds 6.5 photoelectrons (PE) during neutrino beam operations (“onbeam data”) contain no neutrino interactions. Triggered events with a neutrino interaction typically have the products of up to 20 cosmic rays coincident with the beam spill in the event readout window (4.8 ms) contributing to a recorded event along with the products of the neutrino collision. A large sample of events recorded under identical conditions as the onbeam data, minus the coincidence requirement with the beam, (“offbeamdata”) has been recorded for use in characterizing cosmic ray backgrounds. A straightforward onbeam minus offbeam background subtraction is difficult, as the offbeam data does not reproduce all correlated detector effects associated with onbeam events that contain a neutrino interaction with several overlaid cosmic rays. The situation is particularly complicated with events containing neutrino interactions with \(N_{obs,n} = 1\), which share the same topology with the most common singlemuon CR configuration. Monte Carlo simulations of the CR flux using the CORSIKA package [23] provide useful guidance; however, the ability of these simulations to describe the very rare CR topologies that closely match neutrino interactions is not well known.
For these reasons this analysis employs a method to separate neutrino interaction candidates from CR backgrounds that is driven by the data itself. Even though CR tracks should always appear to at least enter the detector, they can satisfy the experimental condition of being fully contained if a segment of the CR track falls outside the data acquisition readout time window, or if a segment of the track fails to be identified due to instrumentation or algorithmrelated inefficiencies. The separation of neutrino interaction candidates from CR backgrounds rests on the observation that a neutrino \(\nu _{\mu }\) CC interaction produces a final state \(\mu ^{}\) that slows down as it moves away from its production point at the neutrino interaction vertex due to ionization energy loss in the liquid argon. As it slows down, its rate of restricted energy loss [24], \(dE/dx_{R}\), increases, and deviations from a linear trajectory due to multiple Coulomb scattering (MCS) become more pronounced. A CR muon track can produce an apparent neutrino interaction vertex if it comes to rest in the detector or it is not fully reconstructed to the edge of the TPC, but the CR track will exhibit large \( dE/dx_{R} \) and MCS effects in the vicinity of this vertex. Furthermore, the vast majority of \(\nu _{\mu }\) CC muons travel in the neutrino beam direction (“upstream” to “downstream”), whereas CR muons move upstream or downstream with equal probability.
5 Event selection and classification
5.1 Data

“Onbeam data”, taken only during periods when a beam spill from the BNB is actually sent. The onbeam data used in this analysis were recorded from February to April 2016 using data taken in runs in which the BNB and all detector systems functioned well. This sample comprises about \(15\%\) of the total neutrino data collected by MicroBooNE in its first running period (October 2015 to summer 2016),

“Offbeam data”, taken with the same software trigger settings as the onbeam data, but during periods when no beam was received. The offbeam data were collected from February to October 2016.
5.2 Simulation

Neutrino interactions simulated with a default GENIE model overlaid with CORSIKA CR events (“MC default”),

MC default augmented by the GENIE implementation of the Meson Exchange Current model [25] overlaid with CORSIKA CR events (“MC with MEC”),

MC default augmented by the GENIE implementation of the Transverse Enhancement Model [26] overlaid with CORSIKA CR events (“MC with TEM”).
The generator stage (production of a set of final state fourvectors for particles originating from the argon nucleus as a result of the \(\nu _\mu \)Ar interaction in GENIE) employs GENIE (version v2.8.6d for the MC default and v2.10.6 for the MC with MEC and TEM) with overlaid simulated CR backgrounds using CORSIKA version v7.4003 with a constant mass composition model (CMC) [33] at 226 m above sealevel elevation. Simulated secondary particle propagation utilizes GEANT version v4.9.6.p04d using a physics particle list \(QGSP\texttt {\underline{{ }}}BIC\) with custom physics list for optical photons, and the detector simulation employs LArSoft version v4.36.00. All GENIE samples were processed with the same GEANT and LArSoft versions for detector simulation and reconstruction. These samples thus allow for relative comparison of different GENIE models to the data.
5.3 Reconstruction
Event reconstruction makes use of anode plane waveforms from the TPC and light signals from the PMT system. Raw signals from the TPC, recorded on the wires, first pass through a noise filter [22] before hits are extracted from the observed waveforms on each wire. A set of reconstruction algorithms known as Pandora [34, 35] combine hits connected in space and time into twodimensional (2D) clusters for each of the three anode planes. Then a threedimensional (3D) vertex reconstruction is performed in which the energy deposition around the vertex and the knowledge of the beam direction is used to preferentially select vertex candidates with more deposited energy and with low z coordinates, respectively. 2D clusters in all three planes are then merged into 3D tracks and showers. The preferential direction for tracks and showers is also from the upstream to the downstream end of the detector. In this analysis, for each 3D track candidate, the start position is taken to be the 3D track end closest to the candidate neutrino vertex, if the track satisfies the requirement that the track start position is sufficiently close to the vertex. This analysis makes no use of shower objects, which are mainly associated with electrons and photons.
Passing rates for event selection criteria applied to onbeam data, offbeam data, and MC default samples. Numbers are absolute event counts. Quantities in parentheses give the relative passing rate with respect to the step before (first percentage) and the absolute passing rate with respect to the starting sample (second percentage)
Selection cuts  Onbeam data  Offbeam data  MC default  

Events  Passing rates  Events  Passing rates  Events  Passing rates  
Total events  547,616  2,954,586  188,880  
\(\nu _{\mu }\) events passing precuts  4049  (0.74%/0.74%)  14,213  (0.48%/0.48%)  7106  (3.8%/3.8%) 
Events passing dead region cut  3080  (76%/0.56%)  10,507  (74%/0.36%)  5632  (79%/2.9%) 
Long track starting \(46~\hbox {cm}\) below the TPC top surface  2438  (79%/0.44%)  7883  (75%/0.27%)  4795  (85%/2.6%) 
Long track to vertex distance \(< 3~\hbox {cm}\)  2435  (99%/0.44%)  7862  (99%/0.27%)  4781  (99%/2.5%) 
Events with \(\ge 80\) collection plane hits  1930  (79%/0.35%)  5279  (67%/0.17%)  4387  (92%/2.3%) 
Events passing wire gap cuts  1795  (93%/0.33%)  4954  (94%/0.16%)  4016  (92%/2.1%) 
Selected number of events from the onbeam data, offbeam data, and MC default samples and their corresponding acceptance rates on the multiplicity basis
Multiplicities  Onbeam data  Offbeam data  MC default  

Events  Event rate (%)  Events  Event rate (%)  Events  Event rate (%)  
Total events  1795  4954  4016  
\(\hbox {mult} = 1\)  1379  77  4113  83  2599  65 
\(\hbox {mult} = 2\)  389  22  828  17  1186  30 
\(\hbox {mult} = 3\)  26  1.4  12  0.2  210  5 
\(\hbox {mult} = 4\)  1  0.06  1  0.2  18  0.4 
\(\hbox {mult} = 5\)  0  0  0  0  3  0.07 
5.4 Event selection
Event selection starts by requiring an optical flash within the 1.6 \(\upmu \)s duration beam spill window and the summed light collected by the PMT to exceed 50 PE. Reconstructed vertices must be contained in the fiducial volume of the detector, defined as 10 cm from the border of the active volume in x, 10 cm from the border of the active volume in z , and 20 cm from the border of the active volume in y (see Fig. 2 for detector coordinates). At each candidate neutrino interaction vertex, a candidate muon track is identified as the longest of all tracks starting within 5 cm of the vertex. The candidate muon track is further required to be fully contained within the detector, where containment requires both ends of the track to lie within the same fiducial volume required for an event vertex, to have at least 75 cm 3D track length, and to have an event vertex located within 80 cm in z of the PMTreconstructed position of an optical flash. Considerable CR backgrounds remain after these preselection procedures, with signal/background \(\approx 1/1\).
Preselected events then pass through a second stage filter that imposes further quality conditions on track candidates. Start and end points of the candidate muon must lie in detector regions with functional collection plane wires. The candidate muon track must start 46 cm below the top surface of the TPC in order to suppress CR backgrounds, must start within 3 cm (reduced from 5 cm) of the selected vertex position, must have at least 80 hits in the collection wire plane, and must not have significant wire gaps in the start and end 20 collection planehit segments used in the pulseheight (PH) test (Sect. 5.5.1) and the multiple Coulomb scattering test (Sect. 5.5.2).
Events satisfying all of the above criteria constitute the final data sample. Table 1 lists the event passing rates for the onbeam data, offbeam data, and the MC default samples at different steps of the event selection. The passing rates in onbeam data are consistent with expectations for a mix of CRonly events, as provided by the offbeam data, and events containing a neutrino interaction in addition to cosmic rays, as provided by the MC.
The observed multiplicity of a selected event is defined to be the number of particles starting within 3 cm of the selected vertex that have at least 15 collection plane hits where the Pandora MicroBooNE track reconstruction algorithms perform optimally. There is no containment requirement for tracks other than the candidate muon track. Table 2 lists the number of selected events in each multiplicity bin with relative event rates for onbeam data, offbeam data, and MC default samples.
The minimum collection plane hit condition corresponds to a minimum range in liquid argon of 4.5 cm, and the requirement thus excludes charged particles below a particletypedependent kinetic energy threshold from entering our sample that ranges from 31 MeV for a \(\pi ^{\pm }\) to 69 MeV for a proton. No acceptance exists for particles with kinetic energies below these thresholds, which roughly increase as the secant of the track angle with respect to the neutrino beam direction.
The average efficiency for the Pandorabased track reconstruction used in this analysis is \( \left\langle \epsilon \right\rangle \approx 45\%\) at the 15 collection plane hit threshold. This relatively low value, with implicit kinetic energy thresholds, creates a common occurrence called “feeddown” wherein events produced with n tracks at the argon nucleus exit position are reconstructed with an observed multiplicity \( n^{\prime }<n\). For example, \(n=1\) is commonly observed because one of the two tracks in a quasielasticlike event fails to be reconstructed due to low acceptance or tracking efficiency.
The candidate muon containment requirement limits its energy to be \( \lesssim 1.2\) GeV depending on the muon scattering angle. This results in a sample biased towards relatively higher inelasticity, \(E_{H}/E_{\nu }\), with \( E_{H}\) being the energy transferred from the neutrino to the hadronic system in the collision.
Final categories from the onbeam data, offbeam data, and MC default samples. Numbers are absolute event counts. The percentages correspond to the fraction of events in each category
Categories  Onbeam data  Offbeam data  MC default  

PH, MCS  Events  Event rate (%)  Events  Event rate (%)  Events  Event rate (%) 
PASS, PASS  802  44  1252  25  2464  61 
PASS, FAIL  334  19  1013  20  704  18 
FAIL, PASS  304  17  1049  21  442  11 
FAIL, FAIL  355  20  1640  33  406  10 
5.5 Event classification
Selected events are next classified into four categories based on whether they pass or fail the PH test and the MCS test described in the following sections. These are the candidate muon track directionbased tests which are used to separate neutrino signal and CR background contributions in the sample. Table 3 lists the event selection rates for the onbeam data, offbeam data, and the MC default samples in each category. The final samples are called neutrinoenriched, mixed, or backgroundenriched subsamples depending on whether events pass both tests, pass either one of the two tests, or fail both tests, respectively.
5.5.1 Pulse height test
 Compute the truncated mean of the pulse heights deposited in 20 consecutive collection plane hits, \(\left\langle PH\right\rangle _{U}\), starting 10 hits away from the upstream end of the muon track that is taken as a proxy for the upstream restricted energy loss. The truncated mean is formed by taking the average of the 20 PH after removing individual PH that do not lie within the range of 20–200% of the average [36]:which can be determined iteratively with an initial approximation that \( \left\langle PH\right\rangle \) is the arithmetic average. Use of the truncated mean PH rather than the average PH minimizes effects of large energy loss fluctuations,$$\begin{aligned} \left\langle PH\right\rangle _{U}=\frac{\sum \nolimits _{n=11}^{n=30}PH_{n} \left( 0.2\left\langle PH\right\rangle<PH_{n}<2.0\left\langle PH\right\rangle \right) }{\sum \nolimits _{n=11}^{n=30}\left( 0.2\left\langle PH\right\rangle<PH_{n}<2.0\left\langle PH\right\rangle \right) }, \end{aligned}$$(4)

Form a similar quantity from 20 consecutive collection plane hits that end 10 collection plane hits away from the downstream end of the track, \(\left\langle PH\right\rangle _{D}\),

Form the test \(p=\left\langle PH\right\rangle _{U}<\left\langle PH\right\rangle _{D}\). Muons from \(\nu _{\mu }\) CC interactions will pass this test with a probability \(P\left( PH\right) \). Muons from CR background can be characterized by the probability that they fail this test, denoted as \(Q\left( PH\right) .\)
5.5.2 Multiple Coulomb scattering test

Form three 20 collection planehit long track segments at the upstream, downstream, and geometric center of the track. The upstream and downstream segments are displaced by 10 collection plane hits from the upstream and downstream ends of the track, respectively,

Perform a simple linear least squares fit of hit time vs. (wire) position using the 20 contiguous collection plane hits at the upstream end of the track. Denote the determined line as \(L_{U}\). Perform a similar fit using the 20 collection plane hits at the downstream end of the track. Denote the determined line as \( L_{D}.\) Finally perform one more similar fit from the 20 collection plane hits located about the geometric center of the track. Denote this line as \(L_{M}\),
 Compare the hit time predicted at the geometric center of the track, \( t_{C}\), by \(L_{M}\), which uses hits about the geometric center, to the time predicted at the geometric center of the track by the projection of \(L_{U}\) from the beginning of the track:$$\begin{aligned} \Delta t_{UM}=\left t_{C}\left( L_{U}\right) t_{C}\left( L_{M}\right) \right . \end{aligned}$$(5)
 Repeat the process except compare \(t_{C}\) from \(L_{M}\) to the time predicted at the geometric center of the track by the projection of \(L_{D}\) from the end of the track:$$\begin{aligned} \Delta t_{DM}=\left t_{C}\left( L_{D}\right) t_{C}\left( L_{M}\right) \right . \end{aligned}$$(6)

Form the test \(q=\Delta t_{UM}<\Delta t_{DM}\). Since MCS should become, on average, more pronounced along the downstream end of the track as the momentum decreases, this provides a second directional test on the muon track candidate. Muons from \(\nu _{\mu }\) CC interactions will pass this test with a probability \(P\left( MCS\right) \). Muons from CR background can be characterized by the probability that they fail this test, denoted as \(Q\left( MCS\right) \).
Figure 7 presents the MCS downstream to upstream ratio \( \Delta t_{DM}/\Delta t_{UM}\) distribution for neutrino events only from MC default (signal MC) and offbeam data (cosmic data) samples. We observe that MCS ratio for the signal dominates over the background for values greater than 1 and we use this value to define the MCS test used in this analysis.
6 Signal extraction
6.1 Datadriven signal + background model
Onbeam data consists of a mixture of neutrino interaction and CR background events. We designate a passing of the PH or MCS test by the symbol \(\nu \), and a failure of either of the two tests by the symbol CR, thus creating the categories “\(\nu \nu \)”, “\(\nu CR\)”, “\(CR\nu \)”, “CRCR”, which contain a corresponding number of events \(N_{\nu \nu }\), \(N_{\nu CR}\), \(N_{CR\nu }\), and \(N_{CRCR}\). The “\(\nu \nu \)” and “CRCR ” categories are expected to have relatively high neutrino or CR purity, respectively; while the “\(\nu CR\) ” and “\(CR\nu \)” have mixed purity.
As the MCS and PH conditions result from different physical processes (muonnucleus and muonelectron scattering, respectively), and the MCS and PH test are formed from different measurements (time and charge, respectively), the PH and MCS tests are nearly independent with \(P\left( MCSPH\right) \approx \) \(P\left( MCS\right) \) and \(Q\left( MCSPH\right) \approx \) \(Q\left( MCS\right) \). In the analysis we find evidence for weak, but nonnegligible, correlations between the tests, and use the conditional probabilities to take these into account.
6.2 Fitting procedure
The fitting procedure can be used to obtain estimates for \(\hat{N}_{\nu }\), \( \hat{N}_{CR}\), \(\hat{N}_{CR}^{\prime }\), \(P\left( PH\right) \), \(P\left( MCS\right) \), \(Q\left( PH\right) \), and \(Q\left( MCS\right) \) for each multiplicity. When the probability parameters \(P\left( PH\right) \), \( P\left( MCS\right) \), \(Q\left( PH\right) \), and \(Q\left( MCS\right) \) are consistent between multiplicities, we use all multiplicities together in their determination for improved statistical precision and vary only the three parameters \(\hat{N}_{\nu }\), \(\hat{N}_{CR}\), and \(\hat{N}_{CR}^{\prime }\) for each individual multiplicity.
6.3 Results with simulated events
Maximum likelihood fits were performed on all three GENIE simulation samples to extract the values of seven parameters \(\hat{N}_{\nu }\), \(\hat{N}_{CR}\), \( \hat{N}_{CR}^{\prime }\), P(PH), Q(PH), P(MCS), and Q(MCS)). Parameters \(\alpha _\nu \) and \(\alpha _{CR}\) and their uncertainties were extracted from MC and offbeam data samples and kept fixed for the subsequent fits. As expected, the PH and MCS probabilities show no statistically significant difference between the three GENIE models considered. Table 4 lists the values obtained from the fit for the abovementioned parameters in the default MC and the MicroBooNE data.
Fit parameter results and corresponding uncertainties for the default MC and data samples. The same offbeam data sample was used in both fits. All uncertainties are from the fit and are purely statistical
Parameters  Fit results  

Default MC  Data  
Floating parameters  
\(\hat{N}_{\nu }\)  \(3405 \pm 159\)  \(1023 \pm 170\) 
\(\hat{N}_{CR}\)  \(611 \pm 150\)  \(782 \pm 169\) 
\(\hat{N}_{CR}^{\prime }\)  \(5002 \pm 71\)  \(5002 \pm 71\) 
P(PH)  \(0.848 \pm 0.018\)  \(0.766 \pm 0.050\) 
P(MCS)  \(0.770 \pm 0.0123\)  \(0.730 \pm 0.039\) 
Q(PH)  \(0.542 \pm 0.007\)  \(0.552 \pm 0.007\) 
Q(MCS)  \(0.537 \pm 0.007\)  \(0.534 \pm 0.007\) 
Fixed parameters  
\(\alpha _\nu \)  \(1.32 \pm 0.05\)  \(1.32 \pm 0.05\) 
\(\alpha _{CR}\)  \(1.36 \pm 0.04\)  \(1.36 \pm 0.04\) 
Fitted and true number of neutrino events for the MC default sample for different multiplicity bins. The last column shows good agreement between the fit results and true content for different bins
Multiplicities  Fit \(N_{\nu }\)  True \(N_{\nu }\)  Truefit \(\chi ^{2}/\hbox {ndf}\) 

1  \(2070 \pm 63\)  2152  1.7 
2  \(1112 \pm 44\)  1092  0.2 
3  \(210 \pm 14\)  208  0.0 
4  \(18 \pm 4\)  18  0.0 
5  \(3 \pm 2\)  3  0.0 
Statistical and systematic uncertainties estimates from data and MC
Uncertainty sources  Uncertainty estimates  

\(\hbox {mult}=1\) (%)  \(\hbox {mult}=2\) (%)  \(\hbox {mult}=3\) (%)  \(\hbox {mult}=4\) (%)  
Data statistics  4  10  20  99 
MC statistics  2  3  7  22 
Short track efficiency  7  11  25  33 
Long track efficiency  1  2  4  7 
Background model systematics  2  2  0  0 
Flux shape systematics  0  0.4  0.2  0.5 
Electron lifetime systematics  0.5  0.1  6  5 
7 Statistical and systematic uncertainty estimates
7.1 Statistical uncertainties
Statistical uncertainties are returned from the MINUIT package used in our fitting for both data and MC samples. These uncertainties include contributions from the CR background in our fitting procedure, and our procedure includes the CR background systematic uncertainty in a contribution to the total statistical uncertainty. Both data and MC statistics contribute substantially to the overall uncertainties in our data, as shown in Fig. 9.
7.2 Short track efficiency uncertainties
The dominant systematic uncertainty originates from the differences in the efficiency between data and simulation for reconstructing shortlength hadron tracks. The overall efficiencies of the Pandora reconstruction algorithms are a strong function of the number of hits of the tracks, with a plateau not being reached until of order of several hundred hits. The inclusive efficiencies for reconstructing protons or pions at the 15 collection plane hit threshold is estimated to be \(\left\langle \varepsilon \right\rangle =0.45\pm 0.05 \). The absolute efficiency value is not used in this analysis, but we use this estimate to conservatively assign a mean efficiency uncertainty of \( \delta =15\%\).
Relative change in observed multiplicity probabilities corresponding to a \(15\%\) uniform reduction in short charged particle tracking efficiencies for three GENIE models: default, MEC, and TEM. The missing entry for observed multiplicity 5 in TEM is due to no event being generated with that observed multiplicity
Observed multiplicity  \(\frac{\Delta P_{n}}{P_{n}}\) (%) Default  \(\frac{\Delta P_{n}}{P_{n}}\) MEC (%)  \(\frac{\Delta P_{n}}{P_{n}}\) TEM (%) 

1  \(+7\)  \(+7\)  \(+8\) 
2  \(\)11  \(\)12  \(\)12 
3  \(\)25  \(\)25  \(\)25 
4  \(\)33  \(\)36  \(\)39 
5  \(\)44  \(\)48  – 
We use this result to generate the expected observed CPMD in simulation that would emerge from lowering the tracking efficiency by the factor \(1\delta \) compared to the default simulated CPMD. The difference between the two distributions is then taken as the systematic uncertainty assigned to short track efficiency, with the assumption that the effect of increasing the default efficiency by a factor \(1+\delta \) would produce a symmetric change. Table 7 summarizes this study for the three GENIE models used. The observed multiplicity \(=1\) probability increases because of “feed down” of events from higher multiplicity, due to the lowered efficiency, mainly from observed multiplicity \(=2\). The other observed multiplicity probabilities decrease accordingly. The largest effects are in high multiplicity bins because the loss of events from lowering the efficiency by the factor \(\left( 1\delta \right) \) varies as \( \left( 1\delta \right) ^{N1}\) for multiplicity bin N. Monte Carlo simulations show that “fake tracks” that could move events to higher multiplicity are rare. We have observed no statistically significant differences in the shape distributions after adjusting the efficiency by the constant pertrack factor implied by the pull factor.
7.3 Long track efficiency uncertainties
To first order, the efficiency for reconstructing tracks with length > 75 cm is not expected to affect the observed multiplicity distribution, as it is common to all multiplicities and cancels in the ratio when forming observed multiplicity probabilities. At second order, however, a multiplicity dependence that changes the distribution of observed multiplicity without affecting the overall number of events is possible. A plausible model for this is that higher multiplicity in an event helps Pandora better define a vertex, and thus increases the chance that the event passes the \(\nu _{\mu }\) CC selection filter.
We estimate the size of this effect by comparing the efficiencies obtained with the Pandora package for simulated quasielastic final states in which both the proton and muon are reconstructed, to charged pion resonance final states in which the proton, pion, and muon are all reconstructed. From this study we conclude that the efficiency for finding the muon in final states where all charged particles are reconstructed could be up to \(3\%\) higher for charged pion resonance events (observed multiplicity 3) than quasielastic events (observed multiplicity 2). We then assume, for the purpose of uncertainty estimation, that this relative enhancement seen for higher observed multiplicity events in the MC is absent in the data.
Relative change in observed multiplicity probabilities corresponding to increasing the conditional probability for reconstructing the long track by \(3\%\) for each additional track found in the event, as suggested by Pandora studies of QE and charged pion resonance production for three GENIE models: default, MEC, and TEM. The missing entry for observed multiplicity 5 in TEM is due to no event being generated with that observed multiplicity
Observed multiplicity  \(\frac{\Delta P_{n}}{P_{n}}\) Default (%)  \(\frac{\Delta P_{n}}{P_{n}}\) MEC (%)  \(\frac{\Delta P_{n}}{P_{n}}\) TEM (%) 

1  \(\)1  \(\)1  \(\)1 
2  \(+2\)  \(+2\)  \(+2\) 
3  \(+4\)  \(+4\)  \(+2\) 
4  \(+7\)  \(+7\)  \(+7\) 
5  \(+9\)  \(+9\)  – 
7.4 Background model uncertainties
In the signal extraction fitting procedure, two conditional parameters (\( \alpha _{\nu }\) and \(\alpha _{CR}\)) were extracted from the Monte Carlo simulation and offbeam data. To calculate the systematic uncertainties on these parameters, their values were varied by \(\pm 1\sigma \) of their statistical uncertainty. Those values were propagated in the observed charged particle multiplicity distribution. We also extracted the \(\alpha _{\nu }\) and \(\alpha _{CR}\) values separately from the GENIE default, GENIE + TEM, and GENIE + MEC models. The effect from this systematic variation were found to be very small.
7.5 Flux shape uncertainties
7.6 Electron lifetime uncertainties
The measured charge from muoninduced ionization can vary within the detector volume due to the finite probability for drifting electrons to be captured by electronegative contaminants in the liquid argon. This capture probability can be parameterized by an electron lifetime \(\tau \). We perform our analysis on simulation with two lifetimes that safely bound those measured during detector operating conditions, \(\tau = 6~\hbox {ms}\) and \(\tau =\infty ~\hbox {ms}\). The resulting distribution of percentage uncertainty as a function of multiplicity in Fig. 9 shows that the electron lifetime uncertainties minimally affect the multiplicity.
7.7 Other sources of uncertainty considered
A systematic comparison was performed on all kinematic quantities entering this analysis between offbeam CR data and the CR events simulated with CORSIKA. No statistically significant discrepancies were observed between event selection pass rates applied to offbeam data and MC simulation.
A check of possible timedependent detector response systematics was also performed by dividing the data into two samples and performing the analysis separately for each sample. Differences between the two samples are consistent within statistical fluctuations.
Fitted number of neutrino events for the data sample in different multiplicity bins. The uncertainties correspond to the statistical uncertainty estimates obtained from the fit. The percentages correspond to the fraction of events in each category
Multiplicities  Fitted \(N_{\nu }\)  Event fraction (%) 

1  \(732 \pm 53\)  72 
2  \(260 \pm 29\)  26 
3  \(26 \pm 5\)  2.6 
4  \(1 \pm 1\)  0.10 
5  \(0 \pm 0\)  0 
8 Results
8.1 Observed charged particle multiplicity distribution
Following the implementation of the signal extraction procedure and verification through closure test on MC events, we execute the same maximum likelihood fit on data. Table 4 lists the values of the fit parameters obtained for the data; and Table 9 lists the number of neutrino events in different multiplicity bins for the data. While our method does not require this to be the case, we note that the fitted PH and MCS test probabilities P(PH), Q(PH), P(MCS), and Q(MCS) agree in data and simulation within statistical uncertainties. This provides evidence that the simulation correctly describes the muon PH and MCS tests used in the analysis.
Area normalized, binbybin fitted multiplicity distributions from three different GENIE predictions overlaid on data are presented in Fig. 11 where data error bars include statistical uncertainties obtained from the fit and the MC error bands include MC statistical and systematic uncertainties that are listed in Table 6 added in quadrature.
8.2 Observed kinematic distributions
In short, we assume that the observed distribution of events consists of a mix of neutrino events plus CR events. The proportions of the mix in each category are fixed by the output of our fit, which, by construction, constrains the normalization of the model to equal that of the data. We emphasize that only the PH and MCS tests have been used to extract the neutrino interaction signal sample; no information from any quantity \(X_{ij}\) is used.
8.3 Checks on distributions lacking dynamical significance
As an example, we show the observed distributions for the selected vertex y position for the candidate muon track from the full selected sample in Fig. 12. For this and all subsequent distributions, the onbeam data events are indicated by plotted points with statistical error bars. The model prediction is shown by a colored band (red for GENIE default, green for GENIE+TEM, and blue for GENIE + MEC) with the width of the band indicating the correlated statistical plus efficiency systematic uncertainty from using common \(N_{\nu ,n},N_{CR,n}\) values for all bins of all distributions of a given multiplicity bin n. The CR contribution to a distribution in a given category is shown by the shaded cyan region. For example, Fig. 12 compares the onbeam data to GENIE default MC sample and also shows the CR background.
The signalenriched \(\left( PASS,PASS\right) \) category for vertex y has the nearly flat distribution expected for a neutrino event sample with a small CR background. Note that in our selection, we only allow candidate muon tracks initial y position \(<70\) cm. This cut rejects many cosmic rays that produce a downward trajectory in the final selected sample. The remaining background is dominated by cosmic rays with an apparent upward trajectory. This can be seen in the backgroundenriched sample \(\left( FAIL,FAIL\right) \) in the vertex y distribution where a peak at negative y values corresponds to “upwardsgoing” CR.
Figure 13 shows the distribution of azimuthal angle \(\phi \), defined in the plane perpendicular to the beam direction, of the muon candidate track for the full selected sample. The CRdominated \(\left( FAIL,FAIL\right) \) category shows the expected peaking at \(\phi =\pm \pi /2\) from the mainly verticallyoriented CR. The asymmetry in the peak’s structure is due to the requirement on vertex y position described previously in Sect. 5.4. By contrast the signalenriched \(\left( PASS,PASS\right) \) category has the nearly flat distribution expected for a neutrino event sample with a small CR background.
Similar levels of agreement exist between data and simulation for distributions of the event vertex x and z positions, for the \(\left( x,y,z\right) \) position of the end point of the muon track candidate, and for the azimuthal angles of individual tracks in multiplicity 2 and 3 topologies. We thus conclude that the simulation and reconstruction chain augmented by our method for estimated CR backgrounds satisfactorily describes features of the data that have no dependence on the neutrino interaction model.
8.4 Dynamically significant distributions
\(\chi ^{2}\) test results for dynamically significant variables for all three GENIE models. Only the uncorrelated statistical uncertainties from data are used in forming the \(\chi ^{2}\). Contributions from systematic uncertainties are not included. The last five listed distributions are not included in the total \(\chi ^{2}/DOF\) since these quantities can be expressed in terms of others
Distributions  \(\chi ^{2}/DOF\)  

GENIE default  \(\hbox {GENIE}+\hbox {MEC}\)  \(\hbox {GENIE}+\hbox {TEM}\)  
\(L_{11}\)  19/14  22/14  13/14 
\(L_{21}\)  4.0/9  4.6/9  7.3/9 
\(L_{22}\)  10/7  8.4/7  16/7 
\(L_{31}\)  4.5/6  3.4/6  5.5/6 
\(L_{32}\)  5.8/5  3.9/6  6.5/6 
\(L_{33}\)  0.1/3  0.7/3  0.5/3 
\(\cos \theta _{11}\)  23/19  20/19  15/19 
\(\cos \theta _{21}\)  14/14  24/14  22/14 
\(\cos \theta _{22}\)  16/20  15/20  16/20 
\(\cos \theta _{31}\)  6.0/7  4.2/7  9.2/7 
\(\cos \theta _{32}\)  25/13  20/13  15/13 
\(\cos \theta _{33}\)  15/11  13/11  17/11 
\(\sin \Theta _{11}\)  24/20  21/20  25/20 
\(\sin \Theta _{21}\)  6.4/7  3.6/7  6.3/7 
\(\sin \Theta _{22}\)  2.4/7  3.4/7  2.4/6 
\(\sin \Theta _{31}\)  4.3/5  6.0/5  9.1/5 
\(\sin \Theta _{32}\)  2.1/4  2.5/4  1.6/4 
\(\sin \Theta _{33}\)  8.5/6  7.0/5  9.5/6 
\(\phi _{22}\phi _{21}\)  13/15  12/15  14/15 
\(\phi _{32}\phi _{31}\)  10/13  9.2/13  10/14 
\(\phi _{33}\phi _{31}\)  15/12  13/12  8.7/11 
\(\phi _{32}\phi _{33}\)  11/14  11/14  11/14 
\(\cos \Omega _{221}\)  19/20  13/20  13/20 
\(\cos \Omega _{321}\)  14/13  13/13  17/13 
\(\cos \Omega _{331}\)  21/14  16/14  12/14 
\(\cos \Omega _{323}\)  12/15  18/15  19/15 
Total \(\chi ^{2}/DOF\)  228.1/216  216.9/216  229.6/216 
For onetrack events, three variables exist. We use the observed length \( L_{11}\) as a proxy for kinetic energy, and the cosine of the scattering angle with respect to the neutrino beam direction \(\cos \theta _{11}\). The azimuthal angle \(\phi _{11}\) has no dynamical significance and must be uniformly distributed due to the cylindrical symmetry of the neutrino beam.
Figure 14 shows the distributions of \(L_{11}\), \(\cos \theta _{11}\), and \(\sin \Theta _{11}\), from the neutrinoenriched sample compared to the GENIE default model. Figure 15 presents the \(L_{11}\) distribution for the GENIE + MEC and GENIE + TEM models. This is the distribution where the agreement between data and GENIE + TEM model, compared to the agreement between data and the other two models, is largest. Figure 16 presents the \(\cos \theta _{11}\) distribution for GENIE + MEC and GENIE + TEM models. This is the distribution where the agreement between data and the GENIE default compares least favorably than to the GENIE+MEC and GENIE+TEM models.
For brevity in the following, except where noted, we only show comparisons of data to predictions from the GENIE default model. Comparisons to GENIE + TEM and GENIE + MEC show qualitatively similar levels of agreement. Differences for specific distributions can be examined in terms of the \( \chi ^{2}\) test statistic values in Table 10.
The opening angle serves a useful role in identifying spurious twotrack events that result from the tracking algorithm “breaking” a single track into two tracks, most commonly in cosmic ray events. Broken tracks produce values of \(\cos \Omega _{221}\) very close to \(1\). Figures 17 and 18 show the distributions of (\(L_{21}\) and \(L_{22}\)) and (\(\cos \theta _{21}\) and \(\cos \theta _{22}\)) from the neutrinoenriched sample, compared to the GENIE default model. Figure 19 presents the distributions of \(\cos \theta _{21}\) using GENIE + MEC and GENIE + TEM models. This is the distribution where the agreement between data and GENIE default model, compared to the agreement between data and the other two models, is largest. Figures 20 and 21 show the distributions of (\(\sin \Theta _{21}\) and \(\sin \Theta _{22}\)) and (\(\phi _{22}\phi _{21}\) and \(\cos \Omega _{221}\)) from the neutrinoenriched sample, compared to the GENIE default model. We have performed a test where we remove all events in the first bin of Fig. 21; we see no changes in the level of agreement between data or model in other kinematic distribution comparisons, and no statistically significant shifts in the observed multiplicity distributions.
8.5 \(\chi ^{2}\) tests for kinematic distributions
We summarize here salient features of Table 10 as follows: all three models consistently describe the data, with summed \(\chi ^{2}\) per degreeoffreedom (\(\chi ^{2}/DOF\)) of 228.1 / 216, 216.9 / 216, and 229.6 / 216, respectively, and corresponding p values of \( P_{\chi ^{2}}=27\%\), \(47\%\), and \(25\%\) for GENIE default, MEC, and TEM, respectively. The total \(\chi ^{2}\) after including all dynamic and nondynamic variable distributions is 714 / 652. No tune of GENIE is superior to any other with any meaningful statistical significance for the distributions we have considered. The acceptable values of \(\chi ^{2}\) are consistent with the hypothesis that the combination of a GENIE event generator, the MicroBooNE BNB flux model, and the MicroBooNE GEANTbased detector simulation satisfactorily describe the properties of neutrino events examined in this analysis in a shape comparison. All elements of the MicroBooNE analysis chain thus appear to be performing satisfactorily; and no evidence exists for missing systematic effects that would produce datamodel discrepancies outside the present level of statistics.
Aggregating Table 10 different ways uncovers no significant discrepancies. The \(\chi ^{2}\) tests on leading track \( \cos \theta \) and \(\sin \Theta \) yield satisfactory results for all multiplicities. Combined \(\chi ^{2}/DOF\) for all distributions associated with a particular multiplicity likewise exhibit adequate agreement. The most poorly described single distribution is that for the length of the muon candidate in multiplicity 1 events. The \(P_{\chi ^{2}}\), while acceptable, are \(16\%\) and \(8\%\) for the GENIE default and GENIE + MEC, respectively. The GENIE+TEM model has \(P_{\chi ^{2}}=53\%\).
The \(\chi ^{2}\) values for different distributions in a given multiplicity are calculated using the same events, which gives rise to concerns about correlations between different distributions. We have performed studies that verify that the \(\chi ^{2}\) values would be highly correlated if the model and data disagreed by an overall normalization, but that otherwise the \( \chi ^{2}\) tests on different distributions exhibit independent behavior, even when the same events are used. The \(P_{\chi ^{2}}\) values for different distributions do not cluster near 0 or 1, which is consistent with the view that the projections display approximately independent statistical behavior.
In summary, all GENIE models successfully describe, through \(\chi ^{2}\) tests, the shapes of a complete set of dynamically significant kinematic variables for observed charged particle multiplicity distributions 1, 2, and 3. The statistical powerthe highest precision afforded by the available statistics with which the predictions can be testedof these tests from the overall data statistics available corresponds to approximately \(4\%\), \(7\%\), and \(20\%\) for multiplicity 1, 2, and 3, respectively.
8.6 \(\chi ^{2}\) tests for multiplicity distribution
While we find satisfactory agreement between GENIE models and kinematic distribution shapes using \(\chi ^{2}\) tests that incorporate only statistical uncertainties, the situation differs for the overall multiplicity distribution. Here, we find statistical \(\chi _{M}^{2}/\)DOF\(=30/4\), 22 / 4, and 28 / 4 for the default, MEC, and TEM GENIE models, respectively. However, in the case of multiplicity, a significant systematic uncertainty exists for tracking efficiency that must be taken into account before any conclusion can be drawn.
9 Discussion
9.1 GENIE predictions for observed multiplicity
At BNB energies, the nominal GENIE expectations for charged particle multiplicities at the neutrino interaction point are \(\approx \left( 80\%\right) \) \(n=2\) (from quasielastic scattering, \(\nu _{\mu }n\rightarrow \mu ^{}p\), neutral pion resonant production \(\nu _{\mu }n\rightarrow \mu ^{}R^{+}\rightarrow \mu ^{}p\pi ^{0}\), and coherent pion production \( \nu _{\mu }\mathrm {Ar}\rightarrow \mu ^{}\pi ^{+}\mathrm {Ar}\)); \(\approx \left( 20\%\right) \) \(n=3\) (resonant charged pion production \(\nu _{\mu }p\rightarrow \mu ^{}R^{++}\rightarrow \mu ^{}p\pi ^{+}\)); and \(\approx \left( 1\%\right) \) \(n\ge 4\) (from multiparticle production processes referred to as DIS). However, final state interactions (FSI) of hadrons produced in neutrino scattering with the argon nucleus can subtract or add charged particles that emerge from within the nucleus. These multiplicities are further modified by the selection criteria.

Multiplicity \(>3\), mainly predicted to be “DIS events” in which at least three short tracks are reconstructed. “DIS” is the usual term for multiparticle final states not identified with any particular resonance formation.

Multiplicity \(=3\), mainly predicted to be \(\mu ^{}p\pi ^{+}\) events from \(\Delta \) resonance production in which all three tracks are reconstructed. “Feed down” from higher multiplicity would be small due to the relatively small DIS cross section at MicroBooNE energies.

Multiplicity \(=2\), mainly predicted to be QE \(\mu ^{}p\) events and resonant \(\mu ^{}p\pi ^{0}\) events in which the proton is reconstructed, with a subleading contribution from “feed down” of resonant charged pion production events where one track fails to be reconstructed.

Multiplicity \(=1\), mainly predicted to be “feed down” from QE \(\mu ^{}p\) and \(\mu ^{}p\pi ^{0}\) events in which the proton is not reconstructed, with contributions from other higher multiplicity topologies in which more than one track fails to be reconstructed.
MicroBooNE also observes more onetrack events than GENIE predicts, as shown in Fig. 11. This corroborates ArgoNeuT’s observation that approximately 35\(\%\) of neutrino interactions on argon targets with no pions detected in the final state also contained no observable proton [42].
While our observed multiplicity distribution disagrees with GENIE expectations and shows consistency with a number of other experiments, we cannot, as noted in Sect. 8.6 definitively exclude an alternate explanation of the discrepancy in terms of a tracking efficiency error at this time.
Our kinetic energy thresholds limit acceptance in such a way that protons produced in FSI may not significantly contribute to the observed CPMD. Furthermore, our analysis requires a forwardgoing long contained track as a muon candidate, which restricts the final state phase space. Also, our analysis makes use of fully automated reconstruction. Therefore, results of this analysis should not be directly compared to the low energy proton multiplicity measurement reported by ArgoNeuT [18].
9.2 GENIE predictions for kinematic distributions
Figure 29 shows the predictions for reconstructed \(L_{11}\), \(\cos \theta _{11}\) , and \(\sin \Theta _{11}\) from the neutrinoenriched sample, using the GENIE default model. The muon track candidate is only mildly affected by the details of the recoiling hadronic system, and thus QE, RES, and DIS production produce similar shape contributions to \(L_{11}\), \(\cos \theta _{11}\), and \( \sin \Theta _{11}\).
Figures 30, 31, 32, and 33 present the distributions of reconstructed (\(L_{21}\) and \(L_{22}\)), (\(\cos \theta _{21}\) and \(\cos \theta _{22}\)), (\(\sin \Theta _{21}\) and \(\sin \Theta _{22}\)), and (\(\phi _{22}\phi _{21}\) and \(\cos \Omega _{221}\)) respectively from the neutrinoenriched sample, using the GENIE default model. There is again minimal difference between QE, resonance, and DIS channels in track length, \(\cos \theta \), or \( \sin \Theta \) for the leading track. However, the QE channel produces contributions to the distributions in \(\cos \theta _{21}\) and \(\cos \theta _{22}\) that are considerably less forwardpeaked than the resonance channel contributions. Distributions of these quantities in the data appear to be consistent with this picture. We also note that the \(\sin \Theta _{22}\) distribution receives a contribution from QE scattering peaked at small values, consistent with expectations for a proton, and a broader distribution more similar to that of the leading muon track candidate that is consistent with the hypothesis that a charged pion can be reconstructed as the second track in resonance contributions.
Striking differences between QE and RES contributions exist in the \( \phi _{22}\phi _{21}\) distribution between QE and resonance contributions in the Fig. 33. The QE contributions demonstrate the clear \(\phi _{22}\phi _{21}=\pm \pi \) peak expected for \(2\rightarrow 2\) scattering. The gap between the \(\pm \pi \) peaks is dominated by contributions from resonance feeddown.
Figures 34, 35, 36, 37, 38, and 39 present the reconstructed distributions of (\(L_{31}\), \(L_{32}\) , and \(L_{33}\)), (\(\cos \theta _{31}\), \(\cos \theta _{32}\), and \(\cos \theta _{33}\) ), (\(\sin \Theta _{31}\), \(\sin \Theta _{32}\), and \(\sin \Theta _{33}\)), (\( \phi _{32}\phi _{31}\) and \(\cos \Omega _{321}\)), (\(\phi _{33}\phi _{31}\) and \( \cos \Omega _{331}\)), (\(\phi _{32}\phi _{33}\) and \(\cos \Omega _{323}\)), respectively from the neutrinoenriched sample, using the GENIE default model. The threetrack sample in GENIE is dominated by resonance contributions, and the data sample, although of limited statistics, has a CR background consistent with zero. We can thus compare in detail GENIE predictions for kinematic shape distributions to data. GENIE’s predictions agree with observations.
10 Summary
We have completed an analysis that compares observed chargedparticle multiplicities and observed kinematic distributions of charged particles for fixed multiplicities in a restricted final state phase space for neutrino scattering events in argon to predictions from three GENIE tunes processed through the MicroBooNE simulation and reconstruction chain. Our analysis takes into account statistical uncertainties in a rigorous manner, and estimates the impact of the largest expected systematic uncertainties. We observe that all elements of the MicroBooNE measurement chaindetector performance, data acquisition, event reconstruction, Monte Carlo event generator, detector simulation, and flux modelingperform well.
With particletypedependent kinetic energy thresholds of 31 MeV for \(\pi ^\pm \) and 69 MeV for protons, we find all three GENIE tunes consistently describe data in the shapes of 26 different kinematic distributions at fixed multiplicities. GENIE appears to overpredict the number of threetrack events in data that would be expected from resonant pion production, and to underpredict the number of onetrack events; however, we cannot rule out a higher than expected tracking efficiency uncertainty as an alternative explanation for these observations. Our study thus empirically supports the use of GENIE in describing singleprocess (quasielastic, resonance) neutrino scattering on argon, but not the predictions for the relative contributions of different processes to the overall cross section. We find no significant differences at this stage in the experiment between the default GENIE tune or tunes that add MEC or TEM. Use of any of the three GENIE tunes for future MicroBooNE analyses, or for physics studies of inclusive final states performed for the SBN and DUNE experiments, receives empirical validation from this work.
As part of this analysis, we have developed a datadriven cosmic ray background estimation method based on the energy loss profile and multiple Coulomb scattering behavior of muons. Within the available Monte Carlo statistics, we have shown that this method provides an unbiased estimate of the number of neutrino events in a prefiltered sample, and, given current statistical precision, it is independent of the signaltobackground level, final state charged particle multiplicity, and other kinematic properties of the final state particles. This method can be applied to a broad range of charged current process measurements.
Significant improvements to MicroBooNE neutrino interaction property measurements are anticipated in the future through incorporation of nearly an orderofmagnitude more statistics, more fully developed reconstruction toolsincluding momentum reconstruction, particle identification, and lower kinetic energy thresholds for trackingand the availability of a recently installed external cosmicray tagger to the detector.
Notes
Acknowledgements
This material is based upon work supported by the following: the U.S. Department of Energy, Office of Science, Offices of High Energy Physics and Nuclear Physics; the U.S. National Science Foundation; the Swiss National Science Foundation; the Science and Technology Facilities Council of the United Kingdom; and The Royal Society (United Kingdom). Additional support for the laser calibration system and cosmic ray tagger was provided by the Albert Einstein Center for Fundamental Physics. Fermilab is operated by Fermi Research Alliance, LLC under Contract No. DEAC0207CH11359 with the United States Department of Energy.
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