First measurement of neutrino oscillation parameters using neutrinos and antineutrinos by NOvA

The NOvA experiment has made a $4.4\sigma$-significant observation of $\bar\nu_{e}$ appearance in a 2 GeV $\bar\nu_{\mu}$ beam at a distance of 810 km. Using $12.33\times10^{20}$ protons on target delivered to the Fermilab NuMI neutrino beamline, the experiment recorded 27 $\bar\nu_{\mu} \rightarrow \bar\nu_{e}$ candidates with a background of 10.3 and 102 $\bar\nu_{\mu} \rightarrow \bar\nu_{\mu}$ candidates. This new antineutrino data is combined with neutrino data to measure the oscillation parameters $|\Delta m^2_{32}| = 2.48^{+0.11}_{-0.06}\times10^{-3}$ eV$^2/c^4$, $\sin^2 \theta_{23} = 0.56^{+0.04}_{-0.03}$ in the normal neutrino mass hierarchy and upper octant and excludes most values near $\delta_{\rm CP}=\pi/2$ for the inverted mass hierarchy by more than 3$\sigma$. The data favor the normal neutrino mass hierarchy by 1.9$\sigma$ and $\theta_{23}$ values in the upper octant by 1.6$\sigma$.

The NOvA experiment has made a 4.4σ-significant observation ofνe appearance in a 2 GeVνµ beam at a distance of 810 km. Using 12.33 × 10 20 protons on target delivered to the Fermilab NuMI neutrino beamline, the experiment recorded 27νµ →νe candidates with a background of 10.3 and 102νµ →νµ candidates. This new antineutrino data is combined with neutrino data to measure the oscillation parameters |∆m 2 32 | = 2.48 +0.11 −0.06 × 10 −3 eV 2 /c 4 , sin 2 θ23 = 0.56 +0.04 −0.03 in the normal neutrino mass hierarchy and upper octant and excludes most values near δCP = π/2 for the inverted mass hierarchy by more than 3σ. The data favor the normal neutrino mass hierarchy by 1.9σ and θ23 values in the upper octant by 1.6σ.
Within this framework, several questions remain unanswered. The angle θ 23 produces nearly maximal mixing but has large uncertainties. If maximal, it would introduce an unexplained µ−τ symmetry; should it differ from 45 • , its octant would determine whether ν τ or ν µ couples more strongly to ν 3 . Furthermore, while it is known that the two independent mass splittings differ by a factor of 30, the sign of the larger splitting is unknown. The ν 1 and ν 2 states that contribute most to the ν e state could be lighter ("normal hierarchy", NH) or heavier ("inverted hierarchy", IH) than the ν 3 state. This question has important implications for models of neutrino mass [11][12][13][14][15] and for the study of the Dirac vs. Majorana nature of the neutrino [16,17]. Additionally, neutrino mixing may be a source of CP violation if sin δ CP is non-zero.
The NOvA experiment measures oscillations by comparing the energy spectra of neutrino interactions in two detectors placed in the Fermilab NuMI beam [22] at distances of 1 km (Near Detector, ND) and 810 km (Far Detector, FD) from the production target. The 14 kton FD measures 15 m × 15 m × 60 m while the 290 ton ND consists of a 3.8 m × 3.8 m × 12.8 m main detector followed by a muon range stack. Both detectors use liquid scintillator [23] contained in PVC cells that are 6.6 cm × 3.9 cm (0.15 radiation lengths × 0.45 Molière radii) in cross section and span the height and width of the detectors in planes of alternating vertical and horizontal orientation. The ND is located 100 m underground. The FD oper-ates on the surface with modest shielding resulting in 130 kHz of cosmic-ray activity. The detectors are located 14.6 mrad off the beam axis where the neutrino energy spectrum peaks at 2 GeV. Magnetic focusing horns in the beamline charge-select neutrino parents giving 96% (83%) pure ν µ (ν µ ) event samples between 1 and 5 GeV. Most contamination is wrong-sign (ν in the ν beam, or vice versa) with < 1% ν e +ν e contamination.
This Letter reports data from an antineutrino beam run spanning from June 29, 2016 to February 26, 2019, with an exposure of 12.33×10 20 protons-on-target (POT) delivered during 317.0 s of beam-on time, combined with the previously reported [21] neutrino beam exposure of 8.85 × 10 20 POT and 438.2 s. During these periods, the proton source achieved a peak hourly-averaged power of 742 kW.
The flux of neutrinos delivered to the detectors is calculated using a simulation of the production and transport of particles through the beamline components [22,24] and reweighted [25] to incorporate external measurements of hadron production and interactions [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. Neutrino interactions in the detector are simulated using the genie event generator [45]. The cross section model has been tuned to improve agreement with external measurements and ND data, reducing uncertainties in the extrapolation of measurements in the ND to the FD. As in Ref. [21], we set M A in the quasielastic dipole form factor to 1.04 GeV/c 2 [46] and use corrections to the chargedcurrent (CC) quasielastic cross section derived from the random phase approximation [47,48]. In this analysis, we also apply this effect to baryon resonance production as a placeholder for the unknown nuclear effect that produces a suppression observed at low four-momentum transfer in our and other measurements [49][50][51][52]. Additionally, we increase the rate of deep-inelastic scattering with hadronic mass W > 1.7 GeV/c 2 by 10% to match our observed rates of short track-length ν µ CC events. We model multi-nucleon ejection interactions following Ref. [53] and adjust the rates in bins of energy transfer, q 0 , and 3-momentum transfer, | q|, for ν µ andν µ separately to maximize agreement in the ND. The calculation of the ν e andν e rates uses these same models.
The energy depositions of final-state particles are simulated with geant4 [24] and input to a custom simulation of the production of, and the detector response to, scintillation and Cherenkov light [54]. The absolute energy scale of the detectors is calibrated to within ±5% using the minimum ionizing portion of cosmic-ray muon tracks that stop in the detectors.
Cells with activity above threshold (hits) are grouped based on their proximity in space and time to produce candidate neutrino events. Events are assigned a vertex, and clusters are formed from hits likely to be associated with particles produced there [55]. These clusters are categorized as electromagnetic or hadronic in origin using a convolutional neural network (CNN) [56]. Hits forming tracks are identified as muons by combining information on the track length, dE/dx, vertex activity, and scattering into a single particle identification (PID) score [57]. The same reconstruction algorithms are applied to events from data and simulation in both detectors.
The ν µ andν µ candidates are required to have a vertex inside the fiducial volume and no evidence of particles exiting the detector. The ν e andν e candidates are divided into a "core" sample which satisfies these containment requirements, and a "peripheral" sample which loosens these requirements for the most signal-like event topologies. A second CNN [58] serves as the primary PID, classifying event topologies as ν e CC, ν µ CC, ν τ CC, neutralcurrent (NC), or cosmic ray. The network is trained on simulated neutrino events and cosmic-ray data, separately for neutrino and antineutrino beam conditions. It has an improved architecture and higher rate of cosmic ray rejection over the previous network [21]. Events identified as ν µ CC are further required to contain at least one track classified as a muon.
Several requirements further reduce cosmic-ray backgrounds. For the ν µ CC sample, a boosted decision tree (BDT) algorithm based on vertex position and muon-like track properties is used. Events in the core ν e sample not aligned with the beam direction and that are near the top of the detector are rejected. Events characterized as detached bremsstrahlung showers from cosmic tracks are also removed, as are events whose topology is consistent with photons entering from the detector north side where there is less shielding. Events in the ν e peripheral sample are tested against a BDT classifier using event position and direction information to separate them from cosmicray topologies.
The selection of ν µ andν µ CC events is 31.2% (33.9%) efficient relative to true interactions in the fiducial volume, resulting in 98.6% (98.8%) pure samples at the FD during neutrino (antineutrino) beam operation. Both ν µ andν µ are counted as signal for the disappearance measurements. Selections against exiting particle tracks are the largest source of inefficiency. The efficiency for selecting signal ν e CC (ν e CC) events is 62% (67%). Purities for the signal ν e (ν e ) samples fall in the range 57-78% (55-77%) depending on the impact of oscillations on the signal and wrong-sign background levels. These efficiencies and purities differ from those quoted in Ref. [21] due to a reoptimization of the selection algorithms [59]. The wrong-sign component of the selected ν µ sample in the ND is calculated to be 2.8 ± 0.3% and 10.6 ± 1.1% for the neutrino and antineutrino beams. These fractions were found to be consistent with a data-driven estimate based on the rate of ν µ CC and NC interactions with associated detector activity indicative of neutron capture.
The incident neutrino energy is reconstructed from the measured energies of the final-state lepton and recoil hadronic system. The lepton energy is estimated from track length for muon candidates and from calorimetric energy for electron candidates. The hadronic energy is estimated from the sum of the calibrated hits not associated with the primary lepton. The neutrino energy resolution at the FD is 9.1% (8.1%) for ν µ CC (ν µ CC) events and 10.7% (8.8%) for ν e CC (ν e CC) events. The ν µ andν µ events with the lowest hadronic energy fraction give the best energy resolution and lowest backgrounds, yielding the most precise measurement of the oscillated spectral shape, so we analyzed the spectra separately in quartiles of this variable [21].
The energy spectra of the selected ν µ CC and ν e CC interactions in the ND during neutrino and antineutrino beam operations are shown in Fig. 1. The selected ND ν e sample consists entirely of background sources for the ν e appearance measurement, predominantly the intrinsic beam ν e component, along with misidentified ν µ CC and NC interactions. We analyze the ν e candidate energy spectra in two bins of ν e PID ("low" and "high") to isolate a highly pure sample of ν µ → ν e andν µ →ν e at the FD. In the ND, the high-PID sample is dominated by intrinsic beam ν e . A third bin containing the "peripheral" events is added for the FD.
The ν µ and ν e signal spectra at the FD are predicted for the neutrino and antineutrino beams separately and are based on the observed spectra of ν µ candidate events in the ND. The true neutrino energy spectrum at the ND is estimated using the measured event rates in bins of reconstructed energy and the energy distributions of simulated events found to populate those bins. This true spectrum is corrected for differences in flux and acceptance between the ND and FD, as well as differences in the ν µ and ν e cross sections; oscillations are then applied to yield predictions for the true ν µ and ν e spectra at the FD. These spectra are then transformed into reconstructed energy using the underlying energy distributions from simulated neutrino interactions in the FD.
The predicted background spectra at the FD are also primarily data-driven. Data collected out-of-time with the NuMI beam provide a measurement of the rate of cosmic-ray backgrounds in the ν µ and ν e samples. Neutrino backgrounds calculated to populate the FD ν e spectra are corrected based on the reconstructed ν e candidates at the ND. The procedure from Ref. [21] is followed to determine corrections for each background component in the neutrino-mode beam, while for the antineutrinomode beam a single scale factor is used. The remaining backgrounds, which include any misidentified neutrino events in the ν µ samples and misidentified ν τ interactions in the ν e samples, make up less than 2% of the FD candidates and are taken directly from simulation.
To evaluate the impact of systematic uncertainties we recompute the extrapolation from the ND to the FD varying the parameters used to model the neutrino fluxes, neutrino cross sections, and the detector response. The procedure accounts for changes in the composition of the ν e background, and for impact on the transformation to and from true and reconstructed energies due to variations in the model parameters. We parameterize each systematic variation and compute its effect in each analysis bin. These parameters are included in the oscillation fit constrained within their estimated uncertainties by penalty terms in the likelihood function.
TABLE I. Systematic uncertainties on the total predicted numbers of signal and beam-related background events at the best fit point (see Table IV TABLE II. Systematic and statistical uncertainties on the oscillation parameters sin 2 θ23, ∆m 2 32 , and δCP, evaluated at the best fit point (see Table IV). The oscillation parameters that best fit the FD data are determined through minimization of a Poisson negative log-likelihood, −2 ln L, considering three unconstrained parameters, ∆m 2 32 , sin 2 θ 23 , and δ CP , as well as 53 constrained parameters covering the other PMNS oscillation parameters and the sources of systematic uncertainty summarized in Tables I and II. The two-detector design and extrapolation procedure significantly reduce the effect of the 10-20% a priori uncertainties on the beam flux and cross sections. The principal remaining uncertainties are neutrino cross sections, the energy scale calibration, the detector response to neutrons, and differences between the ND and FD that cannot be corrected by extrapolation.
The selection criteria and techniques used in the analysis were developed on simulated data prior to inspection of the FD data distributions. Figure 1 shows the energy spectra of the ν µ CC,ν µ CC, ν e CC, andν e CC candidates recorded at the FD overlaid on their oscillated bestfit expectations. Table III summarizes [60] with neutrino beam on the top and antineutrino beam on the bottom. For the ND νµ CC spectra, backgrounds aside from wrong-sign are negligible and not shown. The νe CC spectra are split into a low and high purity sample, and the FD spectra shows counts in the "peripheral" sample. The dashed lines in the ND νe spectra show the totals before data-driven corrections. counts and estimated compositions of the selected samples. We recorded 102ν µ candidate events at the FD, reflecting a significant suppression from the unoscillated expectation of 476. We find 27ν µ →ν e candidate events with an estimated background of 10.3 +0.6 −0.5 , a 4.4 σ excess over the predicted background. This observation is the first evidence ofν e appearance in aν µ beam over a long baseline. These new antineutrino data are analyzed together with 113 ν µ and 58 ν µ → ν e candidates from the previous data set. Table IV shows the overall best-fit parameters, as well as the best fits for each choice of θ 23 octant and hierarchy. The best-fit point is found for the normal hierarchy with θ 23 in the upper octant where −2 ln L = 157.1 for Confidence intervals for the oscillation parameters are determined using the unified approach [65], as detailed in Ref. [66]. Figure 2 compares the 90% confidence level contours in ∆m 2 32 and sin 2 θ 23 with those of other other experiments [19,20,62,63]. Figure 3 shows the allowed regions in sin 2 θ 23 and δ CP . These results exclude most values near δ CP = π/2 in the inverted mass hierarchy by more than 3σ; specifically the intervals between −0.04 to 0.97π in the lower θ 23 octant and 0.04 to 0.91π in the upper octant. The data prefer the normal hierarchy  2 32 and sin 2 θ23, with best-fit point shown as a black marker [61], overlaid on contours from other experiments [19,20,62,63].
with a significance of 1.9σ (p = 0.057, CL s = 0.091 [67]) and the upper θ 23 octant with a significance of 1.6σ (p = 0.11), profiling over all other parameter choices.
We are grateful to Stephen Parke (FNAL) for useful discussions. This document was prepared by the NOvA collaboration using the resources of the