High-Statistics Measurement of Neutrino Quasielasticlike Scattering at 6 GeV on a Hydrocarbon Target

M. F. Carneiro, D. Ruterbories, Z. Ahmad Dar, F. Akbar, D. A. Andrade, M. V. Ascencio, W. Badgett, A. Bashyal, A. Bercellie, M. Betancourt, K. Bonin, A. Bravar, H. Budd, G. Caceres, T. Cai, H. da Motta, G. A. Díaz, J. Felix, L. Fields , A. Filkins, R. Fine, A. M. Gago, A. Ghosh, R. Gran, D. Hahn, D. A. Harris, S. Henry, J. Hylen, S. Jena, D. Jena, C. Joe, B. King, J. Kleykamp, M. Kordosky, D. Last, T. Le, J. LeClerc, A. Lozano, X.-G. Lu, E. Maher, S. Manly, W. A. Mann, K. S. McFarland, C. L. McGivern, A. M. McGowan, B. Messerly, J. Miller, J. G. Morfín, M. Murphy, D. Naples, J. K. Nelson, C. Nguyen, A. Norrick, A. Olivier, V. Paolone, G. N. Perdue, P. Riehecky, H. Schellman, P. Schlabach, C. J. Solano Salinas, H. Su, M. Sultana, V. S. Syrotenko, D. Torretta, C. Wret, B. Yaeggy, K. Yonehara, and L. Zazueta Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA Centro Brasileiro de Pesquisas Físicas, Rua Doutor Xavier Sigaud 150, Urca, Rio de Janeiro, Rio de Janeiro, 22290-180, Brazil Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA AMU Campus, Aligarh, Uttar Pradesh 202001, India Campus León y Campus Guanajuato, Universidad de Guanajuato,

The charged-current quasielastic (CCQE) neutrino interaction (i.e., ν μ n → μ − p) is an important channel in the E ν range of a few GeV and is of value in searches for leptonic CP-symmetry violation [1][2][3][4][5][6]. Because there is little missing energy, this channel allows a good estimate of the incident neutrino energy. However, imperfect knowledge of nuclear effects remains a limiting factor for oscillation measurements [7]. These uncertainties are significant in current experiments [1][2][3][4] and will become more important with the statistics of DUNE [5] and Hyper-Kamiokande [6].
For free nucleons, quasielastic scattering is described by the standard theory of weak interactions combined with nucleon form factors [8]. Electron-nucleon scattering experiments [9] measure the electromagnetic form factors, but measurement of the axial-vector form factor F A , at fourmomentum transfer squared Q 2 ∼ 0.1 GeV 2 , can only be done via ν=ν nucleon scattering.
The axial-vector form factor is usually parametrized using the dipole form and has been measured at zero energy transfer through beta-decay experiments [10,11]. The vector (V), axial-vector (A), and VA interference terms of free-nucleon hadronic currents have been studied on free or quasifree nucleons on hydrogen and deuterium targets [12][13][14][15].
Neutrino oscillation experiments in the few-GeV range, however, use detectors constructed of carbon [3,16], oxygen [17], iron [18], or argon [5,19]. Nuclear effects are significant and must be modeled for these experiments to reach their full physics potential. Historically, a relativistic Fermi gas (RFG) [20] has been used to model the initialstate nucleon, but modifications are necessary to reproduce experimental data [3,16,21,22]. The local Fermi gas (LFG) is an extension to the RFG with a local density approximation [23,24]. Alternatively, spectral function (SF) techniques [25] use a mean field to replace the sum of individual interactions.
Long-range correlations between nucleons are modeled using a random-phase approximation (RPA) correction [26][27][28][29][30][31] to account for the screening effect that arises from the proximity of other nucleons in the nuclear potential well. The RPA correction reduces the interaction rate at low Q 2 while enhancing moderate Q 2 interactions.
A complete description of the experimental signature for quasielastic scattering must also account for the propagation through the nucleus of particles produced by any initial charged-current interaction. The charged lepton produced escapes the nucleus without interacting but final-state hadrons are likely to interact. Such final-state interactions (FSI) may produce new particles such as pions or mimic the CCQE signal through absorption of pions in resonance production. In both cases, the observed final state differs from the original interaction.
We use a topology-based signal definition where a muon, zero or more nucleons, and no mesons or heavy baryons are in the final state (CCQE-like). CCQE-like processes include pion production, where the pion is absorbed in the nucleus and 2p2h processes where more than one nucleon is produced. The history of CCQE measurements is extensive [21,22,[42][43][44][45][46][47][48][49][50][51][52][53][54], but the community has yet to converge on a full description of the nuclear effects since the measured final state is determined by a mixture of initial interaction dynamics and nuclear effects.
In this Letter, we report a study of muon neutrino CCQElike interactions in the Neutrinos at Main Injector (NuMI) [55] "medium energy" beam. The data correspond to an exposure of 1.061 × 10 21 protons on target (POT), which combined with the higher flux per POT results in over a factor of 10 increase in statistics above our previous measurements [21,45,52,54]. The new configuration provides a broad neutrino flux peaked at 6 GeV. We present two-dimensional cross sections for CCQE-like scattering as a function of muon transverse (p ⊥ ) and longitudinal (p k ) momentum. We also report the differential cross section versus the square of the momentum transferred using a quasielastic interaction hypothesis, where Q 2 μ and the neutrino energy E ν is also determined using the quasielastic (QE) hypothesis (see [54]). This result extends the Q 2 QE range by a factor of 4 compared to previous measurements.
The NuMI beam line consists of a 120-GeV primary proton beam, a two-interaction-length graphite target, two parabolic focusing horns, and a 675-m decay pipe. For these data, taken between 2013 and 2017, the horn polarities are set to create a neutrino-dominated beam. The beam line is modeled with a Geant4-based [56,57] simulation (g4numi [58] version 6, built against Geant version v.9.4.p2). There are known discrepancies between Geant4 predictions of proton on carbon and other interactions relevant to NuMI flux predictions. MINERvA corrects the Geant4 flux predictions with hadron-production data [58]. In addition, measurements of neutrino-electron (ν − e) scatters, as described in [59], constrain the flux and reduces the normalization uncertainty on the integrated flux between 2 and 20 GeV from 7.8% to 3.9%.
We restrict this study to events originating in the central scintillator tracker region of the MINERvA detector [60]. The target mass consists of 88.5%, 8.2%, and 2.5% carbon, hydrogen, and oxygen, respectively, plus small amounts of heavier nuclei. The 5.3-ton tracker fiducial region is followed by an electromagnetic calorimeter made up of 20 scintillator planes interleaved with 0.2-cm thick lead sheets, followed by a hadronic calorimeter region of 20 scintillator planes interleaved with 2.54-cm thick iron slabs. PHYSICAL REVIEW LETTERS 124, 121801 (2020)

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The magnetized MINOS muon spectrometer [61] begins 2 m downstream and provides momentum and charge information for muons.
Neutrino interactions are simulated using the GENIE 2.12.6 event generator [62]. The GENIE default interaction model is adjusted to match MINERvA GENIE tune v1 (MnvGENIEv1). This model includes three modifications to the default GENIE model. First, the Valencia RPA correction [26,63], appropriate for a Fermi gas [27,31], is added as a function of energy and three-momentum transfer. Second, the prediction for multinucleon scattering given by the Valencia model [64][65][66] in GENIE 2.12.6 is added and modified with an empirical fit [67] based on previous MINERvA data. The modification, referred to as the "low-recoil fit," increases the integrated 2p2h rate by 49%. Finally, nonresonant pion production is reduced by 57% to agree with a fit to measurements of that process on deuterium [68].
The kinematics of each interaction are reconstructed using the measured muon momentum and angle with respect to the beam as described in [54]. To address the MINOS acceptance, only events with muons created within < 20°of the neutrino beam and above 1.5 GeV=c in momentum are accepted.
As a cross-check of its flux predictions, MINERvA also uses samples of neutrino-nucleus interactions with less than 800 MeV transferred to the hadronic system. Data and simulation comparisons show a discrepancy as a function of neutrino energy. To determine the source of this discrepancy, we fit the neutrino energy distributions in different spatial regions of the detector to templates that allow both the beam line parameters (i.e., focusing horn current and position) and the muon energy scale to float. Hadron-production and neutrino interaction uncertainties are evaluated to obtain the systematic uncertainty on the fit results. The data and simulation prediction before and after the muon energy scale shift are shown in the Supplemental Material [69]. The discrepancy is most consistent with a 3.6% muon energy scale shift, which is 1.8 times the a priori energy scale uncertainty. In this analysis, the reconstructed muon energy is shifted by 3.6%, with an uncertainty of 1.0% (the posterior uncertainty from the fit).
We retain two populations of events: a muon-only sample with no identified proton and a muon þ proton sample. These samples are analyzed separately since their background components have different sources. For both of these populations, there are three sidebands used to constrain three backgrounds, as described in [54].
As the signal definition for CCQE-like interactions includes no final-state mesons or heavy baryons, the energy loss profiles of tracks contained within MINERvA are required to be consistent with a proton hypothesis. For events with Q 2 QE > 0.6 GeV 2 the proton-interaction probability is high, so no energy loss cut is made in this region. This results in a small discontinuity in the transverse momentum distributions for the muon þ additional track samples. To reduce inelastic backgrounds, events with untracked energy above 0.5 GeV are removed. Events with Michel electrons (from the decay chain π AE → μ AE → e AE ) are also vetoed.
The first sideband consists of events having two or more clusters of energy detached from the primary vertex, but passing all other cuts. This sample, shown in Fig. 1 (left), helps constrain backgrounds from processes with π 0 's in the final state (FS) or events where a π þ charge exchanges. The second sideband consists of events passing all cuts but the Michel electron cut. This sample is primarily sensitive to backgrounds from charged pions, as shown in Fig. 1 (right). The third (and smallest) sideband comes from events with both a Michel electron and extra clusters, and it is sensitive to multipion events.
To constrain the background predictions, simultaneous fits are made to the three sidebands as a function of muon transverse momentum, for the single-and multitrack topologies separately. Templates based on three simulated background distributions are fit to the data and the resulting three background normalizations for each topology are used to estimate the contamination from each source. The effect of the fit on the backgrounds versus muon transverse momentum is shown in the Supplemental Material [69]. Using the fit results, we subtract the predicted backgrounds from the data in each bin. The one-and multitrack signal samples have 670 022 and 648 518 events, respectively,  and are shown in Fig. 2 with the predicted backgrounds after the fit. After background subtraction, the data are unfolded, following the method of D'Agostini [70,71], via the implementation in RooUnfold [72] using four iterations. To minimize model dependence, the unfolded Q 2 QE is the one calculated with the true muon kinematics assuming a quasielastic hypothesis, not the generator-level momentum transfer squared. The unfolded sample is corrected for selection efficiency as predicted by the simulation. The selection has an average efficiency of 70% in bins inside the edges of the phase space. The efficiency is approximately 70% below 0.1 GeV 2 in Q 2 QE , reducing to 10% at 10 GeV 2 . The efficiency-corrected distributions are normalized by the integral of the predicted neutrino flux in the 0-120 GeV range and by the number of nucleons (3.23 × 10 30 in the fiducial region) to derive differential cross sections.
The cross section uncertainties for four representative p k bins are shown in Fig. 3. Uncertainties for remaining bins and for the Q 2 QE result are available in the Supplemental Material [69]. Muon reconstruction uncertainties, which include muon energy scale, resolution, and angle uncertainties, dominate in most bins. A description of the remaining uncertainty classes and how they are assessed can be found in [54]. Additionally, we add an uncertainty to account for the possibility of low-Q 2 suppression in pion events, evaluated by adding the low-Q 2 suppression described in [73] to our default model. The flux uncertainties are described in [59].
The double-differential cross section is presented in Fig. 4. Here, MnvGENIEv1 serves as a reference simulation to which the data are compared. The simulation is seen to reproduce the data at zeroth order, but discrepancies are apparent. Bins above the spectral peak in p T are underpredicted in the p k range 3.0-5.0 GeV. From 5.5 to 8.0 GeV, the distributions below the spectral peak are overpredicted; underprediction of event rate resumes  dramatically at p k above 9.0 GeV. The simulation shows that CCQE and 2p2h comprise the dominant spectral components and that discrepancies could be alleviated by modest adjustments, particularly for CCQE at higher p T . The single-differential cross section dσ=dQ 2 QE is presented in Fig. 5 (top). The falloff of the cross section for Q 2 > 1.0 GeV 2 is reproduced at moderate and high Q 2 by the MnvGENIEv1 reference simulation, indicating that dipole forms for the vector and axial-vector nucleon form factors remain appropriate. Figure 5 (bottom) shows the ratio of data and selected generators to the reference simulation.
Here the cross section turnover in the range from 0.3 to ∼3.0 GeV 2 proceeds more gradually than predicted; all generators underpredict the data throughout this region. These general features are similar to those observed for the electromagnetic form factors in electron-nucleon elastic scattering experiments (see Fig. 17 of [74]). The present Letter, by mapping neutrino quasielastic scattering into the multi-GeV Q 2 region, provides new information about the axial-vector part of the nucleon current that cannot be accessed by electron scattering. This new information will enable tests of nuclear models heretofore based solely on electron scattering [75,76]. Table I provides the χ 2 for model predictions of the p ⊥ − p k differential cross section measurement. The models differ in additional effects added to the default version of the GENIE generator. The variations denoted "þRPA" include the Valencia RPA model [26,63], while "þ2p2h" adds the Valencia prediction for the multinucleon scattering [64][65][66]. "þMINOS (MINERvA) π low-Q 2 QE sup." refers to an empirical resonant pion low-Q 2 QE suppression based on MINOS [18] (MINERvA [73]) data. "π tune" refers to a 57% reduction nonresonant pion production motivated by deuterium data [68].
In general, the χ 2 values for all of the models are poor, but the models with the smallest χ 2 are those that include RPA but not 2p2h. This is in contrast to previous MINERvA measurements [54] of this channel in the lower-energy NuMI tune, indicating that the expanded phase space of this dataset is illuminating regions of mismodeling that could not be seen in prior measurements. A χ 2 table for model predictions of the single-differential cross section versus Q 2 QE is available in the Supplemental Material [69]. This result is the first CCQE-like measurement at Q 2 QE above 4 GeV 2 and spans almost 4 orders of magnitude in Q 2 . The data in this high-Q 2 region diverge from most predictions that are based on generators used by current oscillation experiments, and there are no models that are even in approximate agreement over all ranges of Q 2 . The high-statistics, double-differential cross sections will be an important benchmark for model developers who tune models for future neutrino oscillation measurements.