Updated MiniBooNE Neutrino Oscillation Results with Increased Data and New Background Studies

The MiniBooNE experiment at Fermilab reports a total excess of $638.0 \pm 132.8$ electron-like events ($4.8 \sigma$) from a data sample corresponding to $18.75 \times 10^{20}$ protons-on-target in neutrino mode, which is a 46% increase in the data sample with respect to previously published results, and $11.27 \times 10^{20}$ protons-on-target in antineutrino mode. The additional statistics allow several studies to address questions on the source of the excess. First, we provide two-dimensional plots in visible energy and cosine of the angle of the outgoing lepton, which can provide valuable input to models for the event excess. Second, we test whether the excess may arise from photons that enter the detector from external events or photons exiting the detector from $\pi^0$ decays in two model independent ways. Beam timing information shows that almost all of the excess is in time with neutrinos that interact in the detector. The radius distribution shows that the excess is distributed throughout the volume, while tighter cuts on the fiducal volume increase the significance of the excess. We conclude that models of the event excess based on entering and exiting photons are disfavored.


Abstract
The MiniBooNE experiment at Fermilab reports a total excess of 638.0±132.8 electron-like events (4.8σ) from a data sample corresponding to 18.75×10 20 protons-on-target in neutrino mode, which is a 46% increase in the data sample with respect to previously published results, and 11.27 × 10 20 protons-on-target in antineutrino mode. The additional statistics allow several studies to address questions on the source of the excess. First, we provide two-dimensional plots in visible energy and cosine of the angle of the outgoing lepton, which can provide valuable input to models for the event excess. Second, we test whether the excess may arise from photons that enter the detector from external events or photons exiting the detector from π 0 decays in two model independent ways. Beam timing information shows that almost all of the excess is in time with neutrinos that interact in the detector. The radius distribution shows that the excess is distributed throughout the volume, while tighter cuts on the fiducal volume increase the significance of the excess. We conclude that models of the event excess based on entering and exiting photons are disfavored.

II. THE MINIBOONE EXPERIMENT
The MiniBooNE experiment makes use of the Booster Neutrino Beam (BNB) that is produced by 8 GeV protons from the Fermilab Booster interacting on a beryllium target inside a magnetic focusing horn, followed by meson decay in a 50 m decay pipe. In neutrino mode, the ν µ ,ν µ , ν e , andν e flux contributions at the detector are 93.5%, 5.9%, 0.5%, and 0.1%, respectively, while in antineutrino mode, the flux contributions are 15.7%, 83.7%, 0.2%, and 0.4%, respectively. The ν µ andν µ fluxes peak at approximately 600 MeV and 400 MeV, respectively. The MiniBooNE detector, described in detail in reference [21], consists of a 12.2 m diameter sphere filled with 818 tonnes of pure mineral oil (CH 2 ) and is located 541 m from the beryllium target. The detector is covered by 1520 8-inch photomultiplier tubes (PMTs), where 1280 PMTs are in the interior detector region and 240 PMTs are located in the optically isolated outer veto region. The PMTs detect the directed Cherenkov light and the isotropic scintillation light produced by charged particles from neutrino interactions in the mineral oil. Events are reconstructed [22] from the hit PMT charge and time information, and the reconstructed neutrino energy, E QE ν , is estimated from the measured energy and angle of the outgoing muon or electron, assuming the kinematics of CCQE scattering [23].
The MiniBooNE experiment has collected data from 2002-2019, based on a total of 11.27 × 10 20 protons-on-target (POT) in antineutrino mode and 18.75×10 20 POT in neutrino mode.
Also, a special beam off-target run collected an additional 1.86×10 20 POT in a search for sub- GeV dark matter [24]. During the 17 years of running, the BNB and MiniBooNE detector have been stable to within 3% in neutrino energy. Fig. 1 shows the energy distribution of Michel electrons from stopped muon decay for the first (6.46×10 20 POT from 2002 to 2007), second (6.38 × 10 20 POT from 2015 to 2017), and third running periods (5.91 × 10 20 POT from 2017 to 2019) in neutrino mode. By adjusting the energy calibration by 2% for the second running period and by 3% for the third running period, good agreement is obtained for the Michel electron energy distribution.

III. DATA ANALYSIS
The data analysis is optimized to measure ν e -induced CCQE events and reject ν µ induced events, and is identical to the previous analysis [2]. The average selection efficiency is ∼ 20% (∼ 0.1%) for ν e -induced CCQE events (ν µ -induced background events) generated over the fiducial volume. The fraction of CCQE events in antineutrino mode that are from wrong-sign neutrino events was determined from the angular distributions of muons created in CCQE interactions and by measuring CC single π + events [25]. Table I shows the predicted but unconstrained ν e andν e CCQE background events for the neutrino energy MeV. Table I  Systematic uncertainties are determined by considering the predicted effects on the ν µ , ν µ , ν e , andν e CCQE rates from variations of model parameters that include uncertainties < 1250 MeV neutrino energy range from all of the backgrounds in the ν e andν e appearance analysis before using the constraint from the CC ν µ events. The "Other" backgrounds correspond mostly to neutrinonucleon and neutrino-electron elastic scattering. Also shown are the constrained background, as well as the expected number of events corresponding to the LSND best fit oscillation probability of 0.26%, assuming oscillations at large ∆m 2 . The table shows the diagonal-element systematic plus statistical uncertainties, which become substantially reduced in the oscillation fits when correlations between energy bins and between the ν e and ν µ events are included.

Process
Neutrino in the neutrino and antineutrino flux estimates, uncertainties in neutrino cross sections, uncertainties from nuclear effects, and uncertainties in detector modeling and reconstruction.
A covariance matrix in bins of E QE ν is constructed by considering the variation from each source of systematic uncertainty on the ν e andν e CCQE signal and background, and the ν µ andν µ CCQE prediction as a function of E QE ν . This matrix includes correlations between any of the ν e andν e CCQE signal and background and ν µ andν µ CCQE samples, and is used in the χ 2 calculation of the oscillation fits. 18.75 × 10 20 POT data, for ν e CCQE data (points with statistical errors) and background (colored histogram). The dashed histogram shows the best fit to the neutrino-mode data assuming twoneutrino oscillations. POT data, for ν e CCQE data (points with statistical errors) and background (colored histogram).
The dashed histogram shows the best fit to the neutrino-mode data assuming two-neutrino oscillations.
expectation or a 4.8σ excess.
In order to test physics models, the numbers of data events, unconstrained background events, excess events, and best-fit events in neutrino mode with visible energy between 150 and 1250 MeV are shown in Fig. 9      limits from the KARMEN [26] and OPERA [27] experiments. mode and antineutrino mode to the L/E distribution from LSND [1]. The error bars show statistical uncertainties only. As shown in the figure, there is agreement among all three data sets. Assuming two-neutrino oscillations, the curves show fits to the MiniBooNE data described above. The significance of the combined LSND (3.8σ) [1] and MiniBooNE (4.8σ) excesses is 6.1σ, which is obtained by adding the significances in quadrature, as the two experiments have completely different neutrino energies, neutrino fluxes, reconstructions, backgrounds, and systematic uncertainties.  Table I by direct measurements of these backgrounds in the MiniBooNE detector. The ν µ CC background has been well measured [28] by using the Michel electrons from muon decay to identify the event topology. Likewise, the NC π 0 background has also been well measured [29] by reconstructing the two-gamma invariant mass.

Constraints have been placed on the various backgrounds in
In addition, a fit to the vertex radial distribution, shown in Fig. 14, allows a constraint to be placed on the NC π 0 background, due to this background having more events near the edge of the 5 m radius fiducial volume. (NC π 0 events near the edge of the fiducial volume have a greater chance of one photon leaving the detector with the remaining photon then mis-reconstructing as an electron candidate.) Fig. 15 shows the excess event radial distribution, where different processes are normalized to explain the event excess, while Table II shows the result of log-likelihood shape-only fits to the radial distribution. The two-neutrino hypothesis fits the radial distribution best with a χ 2 = 6.6/9ndf , while the NC π 0 hypothesis has a much worse fit with a χ 2 = 20.8/9ndf . Therefore, NC π 0 background is strongly disfavored as an explanation for the MiniBooNE event excess.
Single-gamma backgrounds from external neutrino interactions ("dirt" backgrounds) are estimated using topological and spatial cuts to isolate the events whose vertices are near the edge of the detector and point towards the detector center [30]. The external event back-  The two-neutrino hypothesis fits the radial distribution best with a χ 2 = 6.6/9ndf , while the NC π 0 hypothesis has a much worse fit with a χ 2 = 20.8/9ndf .  Fig. 16 shows that the event excess peaks in the 8 ns window associated with beam bunch time, as expected from neutrino events in the detector, and is inconsistent with external neutrino events or beam-off events, which would be approximately flat in time. Also, the observed background level outside of the beam agrees well with the predicted background estimate. The timing reconstruction performed here is similar to the reconstruction in reference [24], but with a different time offset applied.

Hypothesis
The ∆ → N + γ background is determined from the NC π 0 event sample [29], which has contributions from ∆ production in 12 C (52.2%), ∆ production in H 2 (15.1%), coherent scattering on 12 C (12.5%), coherent scattering on H 2 (3.1%), higher-mass resonances (12.9%), and non-resonant background (4.2%). The fraction of ∆ decays to π 0 is 2/3 from the Clebsch-Gordon coefficients, and the probability of pion escape from the 12 C nucleus is estimated to be 62.5%. The ∆ radiative branching fraction is 0.60% for 12 C and 0.68% for H 2 after integraton over all the invariant mass range, where the single gamma production branching ratio increases below the pion production threshold. With these values, the ratio of single gamma events to NC π 0 events, R, can be estimated to be R = 0.151 × 0.0068 × 1.5 + 0.522 × 0.0060 × 1.5/0.625 = 0.0091.
Note that single gamma events are assumed to come entirely from ∆ radiative decay. The total uncertainty on this ratio is 14.0% (15.6%) in neutrino (antineutrino) mode. This estimate of R = 0.0091 ± 0.0013 agrees fairly well with theoretical calculations of the single gamma event rate [31].
The intrinsic ν e background comes almost entirely from muon and kaon decay-in-flight in the beam decay pipe. MiniBooNE ν µ CCQE event measurements [28] constrain the size and energy dependence of the intrinsic ν e background from muon decay, while the intrinsic ν e background from kaon decay is constrained by fits to kaon production data and SciBooNE measurements [32]. Furthermore, due to the higher energy of the intrinsic ν e background, this background is disfavored from the fit to the radial distribution, as shown in Table II.
Finally, backgrounds from exotic π 0 decay in the neutrino production target are ruled out from the MiniBooNE beam-dump run, where the incident proton beam was steered above the Be target and interacted in the steel beam dump at the downstream end of the decay pipe. No excess of events was observed [24], which set limits on light dark matter and other exotic π 0 decays. Explanations for the event excess have included unsimulated photons entering the detector from external interactions and the undersimulation of photons lost from π 0 production within the detector. To test these explanations in a model-independent way, we can use our higher event statistics to study the change in the excess as a function of tighter fiducial volume cuts. The NC π 0 and external event backgrounds preferentially populate higher radius compared to electron neutrino interactions. Therefore, reducing the fiducial radius is expected to reduce the significance of the excess if it is due to these backgrounds and increase the significance of the excess if its distribution is ν e -like. If we change the stan-  POT data in neutrino mode, for ν e CCQE data (points with statistical errors) and background (histogram) with radius less than 4 m. The dashed histogram shows the best fit to the neutrinomode data assuming two-neutrino oscillations.

VIII. CONCLUSION
In summary, the MiniBooNE experiment observes a total excess of 638.0±132.8 electronlike events (4.8σ) in the energy range 200 < E QE ν < 1250 MeV in both neutrino and antineutrino running modes. All of the major backgrounds are constrained by in situ event measurements. Beam timing information shows that almost all of the excess is in time with neutrinos that interact in the detector. The radius distribution shows that the excess is distributed throughout the volume, while tighter cuts on the fiducal volume increase the significance of the excess. We conclude that models of the event excess based on entering and exiting photons are disfavored. The MiniBooNE event excess will be further studied by the Fermilab short-baseline neutrino (SBN) program [33] and by the JSNS 2 experiment at J-PARC [34].