Significant Excess of ElectronLike Events in the MiniBooNE Short-Baseline Neutrino Experiment

The MiniBooNE experiment at Fermilab reports results from an analysis of $\nu_e$ appearance data from $12.84 \times 10^{20}$ protons on target in neutrino mode, an increase of approximately a factor of two over previously reported results. A $\nu_e$ charged-current quasielastic event excess of $381.2 \pm 85.2$ events ($4.5 \sigma$) is observed in the energy range $200<E_\nu^{QE}<1250$~MeV. Combining these data with the $\bar \nu_e$ appearance data from $11.27 \times 10^{20}$ protons on target in antineutrino mode, a total $\nu_e$ plus $\bar \nu_e$ charged-current quasielastic event excess of $460.5 \pm 99.0$ events ($4.7 \sigma$) is observed. If interpreted in a two-neutrino oscillation model, ${\nu}_{\mu} \rightarrow {\nu}_e$, the best oscillation fit to the excess has a probability of $21.1\%$, while the background-only fit has a $\chi^2$ probability of $6 \times 10^{-7}$ relative to the best fit. The MiniBooNE data are consistent in energy and magnitude with the excess of events reported by the Liquid Scintillator Neutrino Detector (LSND), and the significance of the combined LSND and MiniBooNE excesses is $6.0 \sigma$. A two-neutrino oscillation interpretation of the data would require at least four neutrino types and indicate physics beyond the three neutrino paradigm.Although the data are fit with a two-neutrino oscillation model, other models may provide better fits to the data.

(Dated: May 31, 2018) The MiniBooNE experiment at Fermilab reports results from an analysis of νe appearance data from 12.84 × 10 20 protons on target in neutrino mode, an increase of approximately a factor of two over previously reported results.A νe charged-current quasi-elastic event excess of 381.2 ± 85.2 events (4.5σ) is observed in the energy range 200 < E QE ν < 1250 MeV.Combining these data with the νe appearance data from 11.27 × 10 20 protons on target in antineutrino mode, a total νe plus νe charged-current quasi-elastic event excess of 460.5 ± 95.8 events (4.8σ) is observed.If interpreted in a standard two-neutrino oscillation model, νµ → νe, the best oscillation fit to the excess has a probability of 20.1% while the background-only fit has a χ 2 -probability of 5 × 10 −7 relative to the best fit.The MiniBooNE data are consistent in energy and magnitude with the excess of events reported by the Liquid Scintillator Neutrino Detector (LSND), and the significance of the combined LSND and MiniBooNE excesses is 6.1σ.All of the major backgrounds are constrained by in-situ event measurements, so non-oscillation explanations would need to invoke new anomalous background processes.Although the data are fit with a standard oscillation model, other models may provide better fits to the data.
Evidence for short-baseline neutrino anomalies at an L/E ν ∼ 1 m/MeV, where E ν is the neutrino energy and L is the distance that the neutrino travelled before detection, comes from both neutrino appearance and disappearance experiments.The appearance anomalies include the excess of ν e and νe charge-current quasielastic (CCQE) events observed by the LSND [1] and MiniBooNE [2,3] experiments, while the disappearance anomalies include the deficit of ν e and νe events observed by reactor [4] and radioactive-source experiments [5].As the masses and mixings within the 3-generation neutrino matrix have been attached to solar and long-baseline neutrino experiments, more exotic models are typically used to explain these anomalies, including, for example, 3+N neutrino oscillation models involving three active neutrinos and N additional sterile neutrinos [6][7][8][9][10][11][12][13][14], resonant neutrino oscillations [15], Lorentz violation [16], sterile neutrino decay [17], sterile neutrino non-standard interactions [18], and sterile neutrino extra dimensions [19].This paper presents improved MiniBooNE ν e and arXiv:1805.12028v1[hep-ex] 30 May 2018 νe appearance results, assuming standard oscillation with probability P = sin 2 (2θ) sin 2 (1.27∆m 2 L/E), where θ is the mixing angle, ∆m 2 is the difference in neutrino mass eigenstates squared, L is the distance traveled by the neutrino, and E is the neutrino energy.
The Booster Neutrino Beam (BNB) at Fermilab delivers to the MiniBooNE experiment a flux of neutrinos and antineutrinos that is simulated using information from external measurements [20].The BNB is produced by 8 GeV protons from the Fermilab Booster interacting on a beryllium target inside a magnetic focusing horn.Depending on the polarity of the horn, either π + are focused and π − are defocused to produce a fairly pure beam of ν µ , or π − are focused and π + are defocused to produce a somewhat pure beam of νµ .In neutrino mode, the ν µ , νµ , ν e , and νe 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 and νµ fluxes peak at approximately 600 MeV and 400 MeV, respectively.
The MiniBooNE detector is described in detail in reference [21].The detector consists of a 40-foot diameter sphere filled with 818 tons 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.Charged particles produced by neutrino interactions in the mineral oil emit both directed Cherenkov light and isotropic scintillation light that is detected by the PMTs.Event reconstruction [22] and particle identification make use of 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].
Since 2002, the MiniBooNE experiment has collected a total of 11.27 × 10 20 POT in antineutrino mode, 12.84 × 10 20 POT in neutrino mode, and a further 1.86 × 10 20 POT in a special beam-off target mode to search for sub-GeV dark matter [24].The published neutrino-mode data corresponds to 6.46 × 10 20 POT, while 6.38 × 10 20 POT were obtained in 2016 and 2017.The neutrino sample has approximately doubled in size since the previous publication [3].During the 15 years of runnning, the BNB and MiniBooNE detector have been stable to within 2% in neutrino energy.
The analysis is optimized to measure ν e and νe induced CCQE events, and the event reconstruction [22] and selection are identical to the previous analysis [3].The average reconstruction efficiency is ∼ 20% (∼ 0.1%) for ν einduced CCQE events (ν µ -induced background events) generated over the fiducial volume.The fraction of CCQE events in antineutrino mode that are from wrongsign neutrino events was determined from the angular distributions of muons created in CCQE interactions and by measuring CC single π + events [25].
The predicted but unconstrained ν e and νe CCQE background events for the neutrino oscillation energy range 200 < E QE ν < 1250 MeV are shown in Table I for both neutrino mode and antineutrino mode.The estimated size of the intrinsic ν e and gamma backgrounds are based on MiniBooNE event measurements and uncertainties from these constraints are included in the analysis.The intrinsic ν e /ν e background from muon decay is directly related to the large sample of observed ν µ /ν µ events, as these events constrain the muons that decay in the 50 m decay region.This constraint uses a joint fit of the observed ν µ /ν µ and ν e /ν e events, assuming that there are no substantial ν µ /ν µ disappearance oscillations.The other intrinsic ν e background component from kaon decay is constrained by fits to kaon production data and SciBooNE measurements [26].Other backgrounds from mis-identified ν µ or νµ [27,28] events are also constrained by the observed CCQE sample.Note that the ν µ CCQE events are poorly measured below 200 MeV, which accounts for the lower muon-energy cut.
The gamma background from neutral-current (NC) π 0 production and ∆ → N γ radiative decay [29] are constrained by the associated large two-gamma sample (mainly from ∆ production) observed in the MiniBooNE data, where the new π 0 data agrees well with the published data [30].Other neutrino-induced single gamma production processes provide a negligible contribution here [31].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 [32].The background from external neutrino interactions is now better determined to be approximately 7% larger than in the previous publication [3].A new technique to measure or constrain the gamma and dirt backgrounds based on event timing relative to the beam is in development.
Systematic uncertainties are determined by considering the predicted effects on the ν µ , νµ , ν e , and νe CCQE rates from variations of uncertainty parameters.The parameters include uncertainties in the neutrino and antineutrino flux estimates, uncertainties in neutrino cross sections, most of which are determined by in-situ crosssection measurements at MiniBooNE [27,30], 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 and νe CCQE signal and background, and the ν µ and νµ CCQE prediction as a function of E QE ν .This matrix includes correlations between any of the ν e and νe CCQE signal and background and ν µ and νµ CCQE samples, and is used in the χ 2 calculation of the oscillation fits.
Fig. 1 shows the E QE ν distribution for ν e CCQE data and background in neutrino mode over the full available < 1250 MeV neutrino energy range from all of the backgrounds in the νe and νe appearance analysis.Also shown are the constrained background and the expected number of events corresponding to the LSND best fit oscillation probability of 0.26%.The table shows the diagonal-element systematic uncertainties, which become substantially reduced in the oscillation fits when correlations between energy bins and between the electron and muon neutrino events are included.The antineutrino numbers are from a previous analysis [3].

Process
Neutrino energy range for the total 12.84 × 10 20 POT data.Each bin of reconstructed E QE ν corresponds to a distribution of "true" generated neutrino energies, which can overlap adjacent bins.In neutrino mode, a total of 1959 data events pass the ν e CCQE event selection requirements with 200 < E QE ν < 1250 MeV, compared to a background expectation of 1577.8 ± 39.7(stat.)± 75.4(syst.)events.The excess is then 381.2 ± 85.2 events or a 4.5σ effect.Note that the 162.0 event excess in the first 6.46 × 10 20 POT data is approximately 1σ lower than the average excess, while the 219.2 event excess in the second 6.38 × 10 20 POT data is approximately 1σ higher than the average excess.Combining the Mini-BooNE neutrino and antineutrino data, there are a total of 2437 events in the 200 < E QE ν < 1250 MeV energy region, compared to a background expectation of 1976.5±44.5(stat.)±84.8(syst.)events.This corresponds to a total ν e plus νe CCQE excess of 460.5 ± 95.8 events with respect to expectation or a 4.8σ excess.The significance of the combined LSND (3.8σ) [1] and MiniBooNE (4.8σ) excesses is 6.1σ.Fig. 2 shows the total event excesses as a function of E QE ν in both neutrino mode and antineutrino mode.The dashed curves show the best fits to standard two-neutrino oscillations.
Fig. 3 compares the L/E QE ν distributions for the Mini-BooNE data excesses in neutrino 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.Fitting these data to standard two-neutrino oscillations including statistical errors only, the best fit oc-  curs at ∆m 2 = 0.040 eV 2 and sin 2 2θ = 0.894 with a χ 2 /ndf = 35.2/28,corresponding to a probability of 16.4%.This best fit agrees with the MiniBooNE only best fit described below.The MiniBooNE excess of events in both oscillation probability and L/E spectrum is, therefore, consistent with the LSND excess of events, even though the two experiments have completely different neutrino energies, neutrino fluxes, reconstruction, backgrounds, and systematic uncertainties.A standard two-neutrino model is assumed for the MiniBooNE oscillation fits.Note, however, that there are tensions with fits presented here between appearance and disappearance experiments [10,12], and other models [15][16][17][18][19] may provide better fits to the data.The oscillation parameters are extracted from a combined fit of the observed E QE ν event distributions for muon-like and electron-like events using the full covariance matrix described previously.The fit assumes the same oscillation probability for both the right-sign ν e and wrong-sign νe , and no significant ν µ , νµ , ν e , or νe disappearance.Using a likelihood-ratio technique [3], the confidence level values for the fitting statistic, ∆χ 2 = χ 2 (point) − χ 2 (best), as a function of oscillation parameters, ∆m 2 and sin 2 2θ, is determined from frequentist, fake data studies.With this technique, the best neutrino oscillation fit in neutrino mode for 200 < E QE ν < 1250 MeV occurs at (∆m 2 , sin 2 2θ) = (0.037 eV 2 , 0.958), as shown in Fig. 4. The χ 2 /ndf is 10.0/6.6 with a probability of 15.4%.The background-only fit has a χ 2 -probability of 0.02% relative to the best oscillation fit and a χ 2 /ndf = 26.7/8.8 with a probability of 0.14%.Fig. 4 shows the MiniBooNE closed confidence level (CL) contours for ν e appearance oscillations in neutrino mode in the 200 < E QE ν < 1250 MeV energy range.
Nuclear effects associated with neutrino interactions on carbon can affect the reconstruction of the neutrino energy, E QE ν , and the determination of the neutrino oscillation parameters [33].These effects were studied previously [3] and were found to not affect substantially the oscillation fit.In addition, they do not affect the gamma  [34] and OPERA [35] experiments.
background, which is determined from direct measurements of NC π 0 and dirt backgrounds.
Fig. 5 shows the MiniBooNE allowed regions in both neutrino mode and antineutrino mode [3] for events with 200 < E QE ν < 1250 MeV within a two-neutrino oscillation model.For this oscillation fit the entire data set is used and includes the 12.84 × 10 20 POT in neutrino mode and the 11.27×10 20 POT in antineutrino mode.As shown in the figure, the MiniBooNE favored allowed region overlaps with the LSND allowed region.Also shown are 90% C.L. limits from the KARMEN [34] and OPERA [35] experiments.The best combined neutrino oscillation fit occurs at (∆m 2 , sin 2 2θ) = (0.041 eV 2 , 0.958).The χ 2 /ndf for the best-fit point is 19.5/15.4 with a probability of 20.1%, and the background-only fit has a χ 2probability of 5 × 10 −7 relative to the best oscillation fit and a χ 2 /ndf = 49.3/17.5 with a probability of 0.007%.Fitting both LSND and MiniBooNE data, the best fit remains at (∆m 2 , sin 2 2θ) = (0.041 eV 2 , 0.958) with a χ 2 /ndf = 22.4/23.4,corresponding to a probability of 52.0%.
In summary, the MiniBooNE experiment observes a total ν e CCQE event excess in both neutrino and an-  [34] and OPERA [35] experiments.
tineutrino running modes of 460.5 ± 95.8 events (4.8σ) in the energy range 200 < E QE ν < 1250 MeV.The Mini-BooNE L/E distribution, shown in Fig. 3, and the allowed region from a standard two-neutrino oscillation fit to the data, shown in Fig. 5, are consistent with the L/E distribution and allowed region reported by the LSND experiment [1].The significance of the combined LSND and MiniBooNE excesses is 6.1σ.All of the major backgrounds are constrained by in-situ event measurements, so non-oscillation explanations would need to invoke new anomalous background processes.Although the data are fit with a standard oscillation model, other models may provide better fits to the data.The MiniBooNE event excess will be further studied by the Fermilab short-baseline neutrino (SBN) program [36].
We acknowledge the support of Fermilab, the Department of Energy, and the National Science Foundation, and we acknowledge Los Alamos National Laboratory for LDRD funding.Appendix: Evis and Uz Plots Fig. 6 shows the visible energy (Evis) and cos θ e (Uz) distributions for the electron-neutrino candidate events in neutrino mode (top) and antineutrino mode (bottom).Also shown in the figures are the expectations from all known backgrounds and from the oscillation best fit.

Appendix: Data vs Monte Carlo Comparisons
Various comparisons between the neutrino data, corresponding to 12.84 × 10 20 POT, and the Monte Carlo simulation have been performed to check and confirm the accuracy of the simulation.Fig. 7 shows an absolute comparison of the π 0 reconstructed mass distribution between the data and the simulation for NC π 0 events.Excellent agreement is obtained, and the ratio of the number of data events (42,483) to the number of Monte Carlo events (42,530) is equal to 0.999.Fig. 8 shows an absolute comparison of the reconstructed neutrino energy distribution for CCQE events between the data and the simulation.Excellent agreement is also obtained, and the ratio of the number of data events (232,096) to the number of Monte Carlo events (236,145) is equal to 0.983.
In order to check the particle identification (PID) cuts, Figs. 9, 10, and 11 show comparisons between the data and simulation for the electron-muon likelihood distribution, the electron-pion likelihood distribution, and the gamma-gamma mass distribution.In each figure, distributions are shown after successive cuts are applied: no PID cut, electron-muon likelihood cut, electron-muon plus electron-pion likelihood cuts, and electron-muon plus electron-pion likelihood cuts and a gamma-gamma mass cut.The last plot in each figure shows distributions with the final event selection.The vertical lines in the figures show the range of energy-dependent cut values.Good agreement between the data and the simulation is obtained outside the cut values, while an excess of events is observed inside the cut values.

Appendix: Stability Checks
Many checks have been performed on the data, including beam and detector stability checks that show that the neutrino event rate of 1 event per 10 15 POT has been stable to < 2% over the 15 year MiniBooNE running period, as shown in Fig. 12.This is within the expected errors from time variations in BNB performance, such as target/horn change, beam rate monitoring, etc.A small change in the detector energy response between the first and second neutrino data set has been corrected by increasing the measured energy in the second data set by 2%.About half of the energy change is from PMT failures in the intervening years, and the remainder is within the detector response error from gain variations, oil properties, etc.With this energy correction, the first and second data sets are found to agree well.Fig. 13 compares the visible ν µ CCQE energy distributions for the second data set in 2016 and 2017 to the first data set, where good agreement is obtained.Likewise, Fig. 14 shows that the       full available energy range for the first 6.46 × 10 20 POT data set and the second 6.38 × 10 20 POT data set.Fig. 17 shows the ν e CCQE data and background in antineutrino mode.Each bin of reconstructed E QE ν corresponds to a distribution of "true" generated neutrino energies, which can overlap adjacent bins.Note that the 162.0 event excess in the 6.46 × 10 20 POT data is approximately 1σ lower than the average excess, while the 235.5 event excess in the 6.38 × 10 20 POT data is approximately 1σ higher than the average excess.In antineutrino mode, a total of 478 data events pass the ν e CCQE event selection requirements with 200 < E QE ν < 1250 MeV, compared to a background expectation of 398.7 ± 20.0(stat.) ± 20.5(syst.)events.The excess is then 79.3 ± 28.6 events or a 2.8σ effect.Figs.18 and 19 show the event excesses as a function of E QE ν in neutrino mode, while Fig. 20 shows the event excess in antineutrino mode.

FIG. 2 :
FIG. 2: The MiniBooNE total event excesses as a function of E QE ν in both neutrino mode and antineutrino mode, corresponding to 12.84 × 10 20 POT and 11.27 × 10 20 POT, respectively.(Error bars include both statistical and correlated systematic uncertainties.)The dashed curves show the best fits to the neutrino-mode and antineutrino-mode data assuming standard two-neutrino oscillations.
FIG.3:A comparison between the L/E QE ν distributions for the MiniBooNE data excesses in neutrino mode(12.84× 10 20 POT) and antineutrino mode(11.27× 10 20 POT) to the L/E distribution from LSND[1].The error bars show statistical uncertainties only.The solid curve shows the best fit to the LSND and MiniBooNE data assuming standard two-neutrino oscillations.The excess of MiniBooNE electron-neutrino candidate events is consistent with the LSND excess.

FIG. 6 :
FIG.6:The visible energy (Evis) and cos θe (Uz) distributions for the electron-neutrino candidate events in neutrino mode (top) and antineutrino mode (bottom).(The error bars show only statistical uncertainties.)Also shown in the figure are the expectations from all known backgrounds and from the oscillation best fit.

FIG. 7 :
FIG.7:An absolute comparison of the π 0 reconstructed mass distribution between the neutrino data (12.84 × 10 20 POT) and the simulation for NC π 0 events (top).Also shown is the ratio between the data and Monte Carlo simulation (bottom).

FIG. 8 :
FIG.8:An absolute comparison of the reconstructed neutrino energy distribution for CCQE events between the neutrino data (12.84×10 20POT) and the simulation (top).Also shown is the ratio between the data and Monte Carlo simulation (bottom).

FIG. 9 :
FIG.9: Comparisons between the data and simulation for the electron-muon likelihood distribution after successive cuts are applied: (a) no PID cut, (b) electron-muon likelihood cut, (c) electron-muon plus electron-pion likelihood cuts, and (d) electron-muon plus electron pion likelihood cuts plus a gamma-gamma mass cut.The vertical lines in the figures show the range of energy-dependent cut values.

FIG. 10 :
FIG. 10: Comparisons between the data and simulation for the electron-pion likelihood distribution after successive cuts are applied: (a) no PID cut, (b) electron-muon likelihood cut, (c) electron-muon plus electron-pion likelihood cuts, and (d) electron-muon plus electron pion likelihood cuts plus a gamma-gamma mass cut.The vertical lines in the figures show the range of energy-dependent cut values.

FIG. 11 :
FIG. 11:  Comparisons between the data and simulation for the gamma-gamma mass distribution after successive cuts are applied: (a) no PID cut, (b) electron-muon likelihood cut, (c) electron-muon plus electron-pion likelihood cuts, and (d) electron-muon plus electron pion likelihood cuts plus a gamma-gamma mass cut.The vertical lines in the figures show the range of energy-dependent cut values.

FIG. 13 :
FIG.13:The top plot shows a comparison between the visible νµ CCQE energy distributions for the second data set in 2016 and 2017(6.38 × 10 20 POT) to the first data set (6.46 × 10 20 POT).The bottom plot shows the ratio of the second data set to the first data set, where the red and blue lines show the expected ratios.

π 0 FIG. 14 :
Figs.15 and 16  show the E QE ν distribution for ν e CCQE data and background in neutrino mode over the

FIG. 15 :
FIG. 15: The neutrino mode E QE ν distributions, corresponding to the first 6.46 × 10 20 POT data set, for νe CCQE data (points with statistical errors) and background (histogram with systematic errors).

FIG. 16 :
FIG. 16: The neutrino mode E QE ν distributions, corresponding to the second 6.38×10 20 POT data set, for νe CCQE data (points with statistical errors) and background (histogram with systematic errors).

FIG. 18 :FIG. 19 :FIG. 20 :
FIG. 18: The neutrino mode νe CCQE event excesses, corresponding to the first 6.46 × 10 20 POT data set, as a function of E QE ν .(Error bars include both the statistical and systematic uncertainties.)Also shown are the expectations from the best two-neutrino oscillation fit.

TABLE I :
The expected (unconstrained) number of events for the 200 < E QE ν total 12.84 × 10 20 POT data, for νe CCQE data (points with statistical errors) and background (histogram with systematic errors).The dashed curve shows the best fit to the neutrino-mode data assuming standard twoneutrino oscillations.