PHYSICAL REVIEW D 99, 015016 (2019)

MiniBooNE, MINOS + and IceCube data imply a baroque sector

Jiajun Liao,1,2 Danny Marfatia,1 and Kerry Whisnant3 1Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822, USA 2School of Physics, Sun Yat-Sen University, Guangzhou 510275, China 3Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

(Received 3 October 2018; published 8 January 2019)

The 4.8σ anomaly in MiniBooNE data cannot be reconciled with MINOSþ and IceCube data within the vanilla framework of neutrino oscillations involving an eV-mass . We show that an apparently consistent picture can be drawn if charged-current and neutral-current nonstandard neutrino interactions are at work in the 3 þ 1 neutrino scheme. It appears that either the neutrino sector is more elaborate than usually envisioned, or one or more data sets needs revision.

DOI: 10.1103/PhysRevD.99.015016

I. INTRODUCTION bottom/top ratios of the positron energy spectra in Ref. [8] δm2 ¼ 1 4 2 2 θ ¼ The existence of an eV-scale neutrino has been a major gives the best-fit parameters 41 . eV , sin 14 0 016 χ2 open question in neutrino physics for more than two . with a value smaller by 10.8 than for the standard decades. Recently, the MiniBooNE Collaboration updated no oscillation case. The regions favored by DANSS are their analysis after 15 years of running and reported a 4.8σ shown in Fig. 1. We see that DANSS data prefer an 2 θ C.L. excess in the electron and antielectron neutrino spectra eV-scale with the mixing angle sin 14 1σ – close to the experimental threshold [1]. An explanation of in the range, 0.0087 0.023. Our results are consistent the results via νμ → νe oscillation with a mass-squared with those of Refs. [5,9] after taking into account the large difference δm2 ∼ 1 eV2 is consistent with the LSND systematic uncertainties due to the energy resolution and anomaly found at a similar L=E ∼ 1 m=MeV [2]. The the sizes of the source and detector. Constraints on jUμ4j¼cos θ14 sin θ24, which are mostly two excesses combined have reached a significance of 6.1σ driven by the νμ disappearance experiments at IceCube [10] C.L. and urgently call for an explanation that makes them þ 3 þ 1 compatible with other experiments. and MINOS [11], rule out the scenario for the It is well known that the appearance data are in serious tension with disappearance data in global fits of the 3 þ 1 oscillation framework [3–5]. To explain the LSND and MiniBooNE excess via sterile neutrino oscillations, a 2 2 relatively large mixing amplitude sin 2θμe ≡ 4jUe4Uμ4j ¼ 2 2 sin 2θ14sin θ24 is required. Constraints on jUe4j¼sin θ14 are provided mainly by reactor neutrino experiments, with Daya Bay contributing a strong constraint on jUe4j for 2 2 δm41 < 0.5 eV [6]. Interestingly, recent fits to data from the reactor experiments, NEOS [7] and DANSS [8], suggest a sterile neutrino interpretation at the 3σ level with 2 2 2 δm41 ≈ 1.3 eV and jUe4j ≈ 0.01 [5,9]. In particular, since the DANSS experiment measured the ratios of energy spectra at different distances, the results are independent of the uncertain reactor ν¯e flux. Our analysis of the measured

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. FIG. 1. The 1σ, 2σ, and 3σ regions allowed by DANSS. The Further distribution of this work must maintain attribution to 2 2 the author(s) and the published article’s title, journal citation, blue plus sign marks the best-fit point, δm41 ¼ 1.4 eV and 3 2 and DOI. Funded by SCOAP . sin θ14 ¼ 0.016.

2470-0010=2019=99(1)=015016(6) 015016-1 Published by the American Physical Society LIAO, MARFATIA, and WHISNANT PHYS. REV. D 99, 015016 (2019)

S D MiniBooNE/LSND data. Hence, if we take the results of all where ϵαβ and ϵαβ are defined through the CC NSI three experiments, MiniBooNE, MINOSþ and IceCube, at ff0C parameters ϵ , and the Hamiltonian H is given by face value, a baroque new physics scenario must be αβ introduced to explain all the data. In this Letter, we first 2 0 1 3 00 0 0 show that the MINOSþ constraints can be relaxed if there 6 B 2 C 7 exist charged-current (CC) nonstandard interactions (NSI) 1 6 B 0 δm21 00C 7 H ¼ 6VB CV†7 þ V ; ð4Þ in the detector. (An earlier analysis invoked CC NSI in the 2E 4 @ 00δm2 0 A 5 m 3 þ 1 scenario to explain a discrepancy between neutrino 31 00 0δm2 and antineutrino oscillations observed in early MiniBooNE 41 data [12].) It is known that large neutral-current (NC) NSI, 2 2 2 can suppress the resonant enhancement of high-energy with δmij ¼ mi − mj , and V ¼ R34O24O14R23O13R12. atmospheric neutrino oscillations and weaken the IceCube Here Rij is a real rotation by an angle θij in the ij plane, θ constraints on sin 24 [13]. Since large NC NSI also modify and Oij is a complex rotation by θij and a phase δij. The the lower-energy atmospheric neutrino spectrum at matter potential in Eq. (4) is DeepCore, here we study NSI effects on the combination of IceCube and DeepCore data. 0 m m m m 1 1 þ ϵee ϵeμ ϵeτ ϵes B m m m m C II. FRAMEWORK B ϵeμ ϵμμ ϵμτ ϵμs C Vm ¼ VCCB C; ð5Þ @ ϵm ϵm ϵm ϵm A We consider the simplest 3 þ 1 mass scheme, with an eτ μτ ττ τs m m m m eV-mass sterile neutrino in addition to the three active ϵes ϵμs ϵτs κ þ ϵss . CC and NC NSI are motivated by new physics pffiffiffi beyond the , and their effects on neutrino where VCC ¼ 2GFNe is the electron charged-current oscillations have been extensively studied; for reviews see Nn m potential, κ ¼ ≃ 0.5 is the standard NC/CC ratio, ϵαβ ≡ Refs. [14–16]. Similar to the standard electroweak inter- 2Ne P fC N actions, the NSI we require can be described by the ϵ f is the effective strength of NSI in matter, and f;C αβ Ne dimension-six operators: Nf is the number density of fermion f. pffiffiffi þ fC To relax the MINOS and IceCube bounds, we employ L ¼ −2 2G ϵ ½ν γρP ν ½f¯γ P f; ð Þ D m m m NC-NSI F αβ α L β ρ C 1 Occam’s razor and assume that only ϵμμ, ϵμμ, ϵττ and ϵss are pffiffiffi nonzero. Note that CC NSI at the source may be different L ¼ −2 2G ϵff0C½ν γρP l ½f¯ 0γ P f; ð Þ CC-NSI F αβ β L α ρ C 2 from those at the detector. Since neutrinos produced by the NuMI beam line mainly arise from pion decay and pions 0 0 where α; β ∈ e; μ; τ;s, C ¼ L, R, f ≠ f ∈ u; d, f; f ≠ e, only couple to the axial-vector current, a vectorlike fC ff0C udL udR and ϵαβ and ϵαβ are dimensionless and parametrize the interaction, i.e., ϵμμ ¼ ϵμμ , only yields CC NSI at the D udL strength of the new interactions in units of the Fermi detector [12]. Then, ϵμμ ¼ 2ϵμμ . We set θ34 and all phases constant GF. The NC NSI mainly affect neutrino propa- to be equal to zero for simplicity. Since the νe flux is small gation in matter, and the CC NSI affect neutrino production compared to the νμ flux at these experiments, and the νe 2 2 and detection. Hence, when both NC and CC NSI are mixing is suppressed by s13 and s14, we ignore the νe operative, the apparent oscillation probability measured in component and consider a three-flavor system with only νμ, an experiment can be written as [17] ντ, and νs. After a rotation by R24, the Hamiltonian that describes the three-neutrino propagation in matter can be P˜ ðνS → νDÞ ¼ j½ð1 þ ϵDÞTe−iHLð1 þ ϵSÞT j2; ð Þ α β βα 3 written as

0 2 ˆ 2 m 2 m ˆ m m 1 s23 þ Aðc24ϵμμ þ s24ϵ˜ssÞ c23s23 Ac24s24ðϵμμ − ϵ˜ssÞ δm2 B C R† HR ≈ 31 @ c s c2 þ Aˆ ϵm 0 A; ð Þ 24 24 2E 23 23 23 ττ 6 ˆ m m ˆ 2 m 2 m Ac24s24ðϵμμ − ϵ˜ssÞ 0 R þ Aðc24ϵ˜ss þ s24ϵμμÞ

pffiffiffi R ≡ δm2 =δm2 Aˆ ¼ 2 2G N E =δm2 ϵ˜m ≡ ˜ D 2 2 ˜ 2 ˜ where 41 31, F e ν 31, ss hPμμi ≈ ð1 þ 2ϵμμ − 2s24Þð1 − sin 2θ23sin Δ31Þ; ð7Þ m 2 κ þ ϵss, and we have dropped δm21-dependent terms R ≫ Acˆ s ðϵm − ϵ˜m Þ since they are very small. For 24 24 μμ ss , the 2 δm2 Lpffiffiffiffi 2 ˜ sin 2θ23 ˜ 31 2 where sin 2θ23 ¼ , Δ31 ¼ C, and C¼sin 2θ23þ measured νμ → νμ oscillation probability after averaging C 4Eν ˆ 2 m m 2 m 2 over the fast oscillation is ½cos2θ23 −Aðc24ϵμμ −ϵττ þs24ϵ˜ssÞ .If

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D 2 ϵμμ ≃ s24 ð8Þ and

m m 2 m m ϵμμ − ϵττ ≃ s24ðϵμμ − ϵss − κÞ; ð9Þ the measured νμ → νμ oscillation probability reduces to the standard three-neutrino result. In the rest of the paper, we choose the following parameter set to demonstrate consistency with various data:

2 2 2 2 D δm41 ¼ 1.4 eV ; sin θ14 ¼ sin θ24 ¼ ϵμμ ¼ 0.02; ϵm ¼ −0 7; ϵm ¼ −0 5; ϵm ¼ 6: ð Þ μμ . ττ . ss 10 FIG. 2. The difference of the measured oscillation probabilities between the 3 þ 1 and standard three-neutrino oscillation cases at In the left panel in Fig. 2, we plot the difference of the the MINOSþ far detector (left) and near detector (right). The measured oscillation probabilities between the sterile and solid (dashed) curve corresponds to the case with (without) NSI. 3ν þ 2 2 2 2 D m cases at the MINOS far detector (FD) after averaging Here δm41 ¼1.4eV ,sinθ14 ¼ sin θ14 ¼ ϵμμ ¼ 0.02, ϵμμ ¼ −0.7, m m out the fast oscillations. We see that in the presence of CC ϵττ ¼ −0.5, and ϵss ¼ 6, and the other mixing angles and mass- NSI, the measured oscillation probability at the MINOSþ squared differences are the best-fit values in Ref. [18]. The fast FD is almost the same as the standard case, so using the oscillations have been averaged out. The shaded band represents MINOSþ FD data alone cannot distinguish the 3 þ 1 case the 1σ systematic uncertainties at the near detector. from the standard three-neutrino oscillation case.

III. MINOS=MINOS + ANALYSIS To analyze the MINOS and MINOSþ data, we follow the procedure described in Ref. [11], with the χ2 defined as

X71 X71 2 −1 χ ¼ ðxi − μiÞ½V ijðxj − μjÞ; ð11Þ i¼1 j¼1 where xi (μi) are the number of observed (predicted) events at the FD and the covariance matrix V is taken from the ancillary files of Ref. [11]. We modified the oscillation probabilities in the code provided in the ancillary files of Ref. [11] by using the GLoBES software [19], which includes the new physics tools developed in Ref. [17]. In our analysis, we only use the FD data for two reasons: (i) for the mass-squared difference relevant to LSND/ MiniBooNE, the sensitivity to constrain sterile neutrinos at MINOS=MINOSþ mainly comes from the FD since the = þ oscillation effects at the MINOS MINOS near detector FIG. 3. The 90% C.L. exclusion limits for the 3 þ 1 scenario (ND) are negligible, and (ii) the systematic uncertainties at from MINOS and MINOSþ data. The dashed black curve is the ND are very large (see Fig. 2) and a precise determi- extracted from Ref. [11], and the black solid curve corresponds to nation of the spectrum at the ND has been called into the 3 þ 1 case from our analysis of the FD data only. The red D question [20]. curves correspond to the 3 þ 1 þ NSI case with ϵμμ ¼ 0.02. The Since the MINOS=MINOSþ data are not sensitive to θ14, solid red curve corresponds to no NC NSI, while the dashed red 2 2 ϵm ¼ −4 3 ϵm ¼ −4 we fix sin θ14 ¼ 0.02.Hence,theχ function for the 3 þ 1 curve corresponds to μμ . and ττ , and the dotted red m m m 2 2 curve corresponds to ϵμμ ¼ −0.7, ϵττ ¼ −0.5 and ϵss ¼ 6. The scenario with CC NSI depends only on sin θ23, δm23, 2 2 shaded (hatched) region corresponds to the 3σ allowed region for sin θ24, δm41, and the NSI parameters. For a fixed set of 2 θ δm2 the combined LSND and MiniBooNE appearance analysis [5] NSI parameters, we marginalize over sin 23 and 23 for 2 θ ¼ 0 01 ð 2 θ ; δm2 Þ with sin 14 . (0.02). The gray curve corresponds to the each point in the sin 24 41 plane and calculate CERN Dortmund Heidelberg Saclay neutrino experiment Δχ2ð 2θ ;δm2 Þ¼χ2 ð 2θ ;δm2 Þ − χ2 sin 24 41 min sin 24 41 min;3ν to obtain 90% C.L. exclusion limit, as shown in Ref. [11]. The blue plus the exclusion limits on the 3 þ 1 model. The resulting sign marks the point in Eq. (10).

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χ2 ¼ 74 8 min;3ν . represents a good fit to the 71 data points used in our analysis. 2 2 The 90% C.L. exclusion limits in the (sin θ24, δm41) D plane for ϵμμ ¼ 0.02 are shown in Fig. 3. The dashed black curve is extracted from Ref. [11] and was obtained from an analysis of both the ND and FD data, and the solid black curve corresponds to the 3 þ 1 case from our analysis of the FD data only; clearly, the limits are in good agreement for 2 2 δm41 < 3 eV . The red curve corresponds to the NSI cases D with ϵμμ ¼ 0.02. (Note that the current bounds on vector- ud like ϵμμ are rather weak [21].) The limits can be understood D from Eq. (8). In general, the bounds become weaker as ϵμμ 2 is increased. For sin θ14 ¼ 0.01, the LSND/MiniBooNE allowed region is consistent with the MINOS=MINOSþ D data for ϵμμ > 0.03. Since larger values of θ14 require correspondingly smaller values of θ24 to explain the LSND/ 2 MiniBooNE data, for sin θ14 ¼ 0.02, large parts of the regions allowed by the appearance data are not constrained FIG. 4. The 90% C.L. exclusion limits for the 3 þ 1 scenario by the MINOS=MINOSþ data. From the dashed and from IceCube and DeepCore data. The solid black curve dotted red curves we see that NC NSI have a tiny effect corresponds to the 3 þ 1 oscillations without NSI, and the solid on the bounds for eV-scale sterile neutrinos. Note that red [blue] curve corresponds to the 3 þ 1 þ NSI (a) [(b)] case. CC NSI also increase the number of events at the The red (blue) dashed contour corresponds to the 90% C.L. MINOS=MINOSþ ND. However, these changes are within allowed region in case (a) [(b)]. The shaded (hatched) region corresponds to the 3σ allowed region for the combined LSND and the systematic uncertainties at the ND [22]; see the shaded 2 MiniBooNE appearance analysis [5] with sin θ14 ¼ 0.01 (0.02). band in the right panel in Fig. 2. D ϵμμ ¼ 0.02 for the NSI scenarios. The blue plus sign marks the point in Eq. (10). IV. ICECUBE/DEEPCORE ANALYSIS   X8 obs We now study the atmospheric neutrino constraints in the Nij χ2 ¼ 2 Nthðα; βÞ − Nobs þ Nobs ln presence of large NC NSI by combining the IceCube data at DC ij ij ij Nthðα; βÞ high energy and the DeepCore data at low energy. For the i;j¼1 ij IceCube analysis, we follow the procedure of Ref. [13], ð1 − αÞ2 þ ; ð Þ which analyzed 13 bins in the reconstructed muon energy σ2 13 rec α range, 501 GeV ≤ Eμ ≤ 10 TeV, and 10 bins in the zenith angle range, −1 ≤ cos θz ≤ 0 [23]. For the obs DeepCore analysis, we use the publicly available data where Nij is the observed event counts per bin and from Ref. [24], which has eight bins in the reconstructed Nthðα; βÞ¼αNexp þ βNbkg Nbkg rec ij ij ij with ij being the atmos- energy range, 6 GeV ≤ Eμ ≤ 56 GeV, and eight bins in pheric muon background per bin. We take the uncertainty the zenith angle range, −1 ≤ cos θz ≤ 0. The expected in the atmospheric neutrino flux normalization to be σα ¼ number of observed events at DeepCore is given by 20% at the energies relevant to DeepCore, and we allow the Z Z normalization of the atmospheric muon background to float χ2 ¼ 60 7 α ¼ 0 869 exp freely [24]. We find DC;min;3ν . with . and N ¼ d cos θz dEνΦν ðEν; cos θzÞPν ν ðEν; cos θzÞ ij μ μ μ β ¼ 0.184 and confirmed that the confidence regions for rec the standard 3ν oscillation from our analysis agree with × A ðE ; cos θz;j;Eν; cos θzÞþðν → ν¯Þ; ð12Þ eff μ;i those in Ref. [24]. To obtain the exclusion regions for the combined IceCube 3 þ 1 where cos θz is the cosine of the zenith angle, and DeepCore data in the scenarios, we cal- 2 2 2 2 2 2 Φ ðE ; θ Þ ν culate Δχ ðsin θ24;δm Þ¼χ ðsin θ24;δm Þ− νμ ν cos z is the atmospheric μ flux at the surface ICþDC 41 ICþDC;min 41 P ðE ; θ Þ ν → ν χ2 , where χ2 ¼ χ2 þ χ2 for each set of of Earth [25], νμνμ ν cos z is the μ μ oscillation ICþDC;min;3ν ICþDC IC DC A χ2 ¼ 172 7 probability at the detector, and eff is the neutrino effective parameters; ICþDC;min;3ν . . The exclusion region area given in Ref. [24]. for the 3 þ 1 scenario without NSI is shown as the black To calculate the statistical significance of an oscillation line in Fig. 4. We see that the LSND/MiniBooNE allowed scenario, we define region is excluded by the IceCube/DeepCore data.

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χ2 TABLE I. The minimum ICþDC for the best-fit scenarios. In m case (a), the scanned parameter ranges are jϵττj < 6 and m m jϵμμ − ϵττj < 0.5; in case (b), the scanned parameter ranges are m m m m jϵssj < 6, jϵττj < 0.5 and jϵμμ − ϵττj < 0.5. There are 130 Ice- Cube and 64 DeepCore data points in the analysis. ϵm ϵm ϵm 2 θ δm2 χ2 χ2 χ2 Case μμ ττ ss sin 24 41 IC DC ICþDC;min (a) −4.3 −4 0 0.063 0.32 103.4 54.9 158.3 (b) −0.7 −0.5 6 0.032 0.63 102.7 56.5 159.2

m m We consider two NSI cases: (a) only ϵμμ and ϵττ are m m m nonzero, and (b) ϵμμ, ϵττ, and ϵss are all nonzero. For case m (a), we scan the parameter space, jϵττj < 6 and FIG. 5. Zenith angle distributions of the averaged atmospheric m m jϵμμ − ϵττj < 0.5. For case (b), we scan the parameter and antineutrino survival probabilities for two m m m m space, jϵssj < 6, jϵττj < 0.5 and jϵμμ − ϵττj < 0.5. We note Super-Kamiokande energy bins. The solid (dashed) [dotted] m m m m 3 þ 1 þ 3 þ 1 3ν that large ϵμμ and ϵee ¼ 0 yield large ϵμμ − ϵee, which may curve corresponds to the NSI ( )[ ] case. For the 3 þ 1 case without NSI, the spectra are normalized by a factor be constrained by solar data [26]. Therefore, in order to 3ν ϵm − ϵm ϵm of 1.04 to compare with the case. The oscillation parameters accommodate a small value for μμ ee, we allow large ss are the same as in Fig. 2. in case (b). (The global analysis of Ref. [26] uses solar data m m to place constraints on ϵμμ − ϵee, which however do not apply to our scenario because it includes a sterile neutrino.) D We also fixed ϵμμ ¼ 0.02 for both cases. Our results are not D D sensitive to the value of ϵμμ, since ϵμμ only affects the overall normalization of the expected events and the uncertainty of the atmospheric neutrino flux normalization χ2 is large. The minimum values of ICþDC for both cases are given in Table I. We find an allowed region that is consistent with the LSND and MiniBooNE data for each case. The best-fit parameters in both cases are consistent with Eq. (9). The exclusion regions for the 3 þ 1 scenario in the presence of NSI are shown as the blue [red] lines in Fig. 4 for case (a) [(b)]. We see that the LSND and MiniBooNE allowed region is consistent with IceCube/ DeepCore data in the presence of large NC NSI in the active neutrino sector or large NC NSI in the sterile neutrino sector and small NC NSI in the active neutrino sector.

V. OTHER DATA FIG. 6. The survival probabilities of solar neutrinos for the 3ν, 3 þ 1, and 3 þ 1 þ NSI cases. The oscillation parameters are the The Super-Kamiokande (SK) experiment has collected same as in Fig. 2. atmospheric neutrino events with energies lower than at DeepCore. We checked that the differences of the survival probabilities between the NSI and 3ν cases are within the statistical uncertainties for two SK multi-GeV energy bins [34], are the four data points in Fig. 6. The survival [27]; see Fig. 5. For the sub-GeV events at SK, systematic probabilities for the 3ν and NSI cases are also shown. uncertainties are very large due to the poor angular We find χ2 ¼ 1.79 and 2.13 for the 3ν and NSI case, correlation between the neutrino and outgoing lepton [28]. respectively, demonstrating compatibility of the 3 þ 1 þ propagation is sensitive to modifications NSI scenario with current solar data. Note that since NSI of the matter potential. To analyze solar neutrino data, we shift the upturn in the survival probability to lower energies, follow the procedure of Ref. [29] in conjunction with the the tension between KamLAND and 8B neutrino data Standard Solar Model fluxes [30]. The survival probabil- is eased. ities obtained from the Borexino measurements of the pp We mention in passing that data from the appearance [31], 7Be [32], and pep neutrinos [33], and the SNO CC channels at current long-baseline experiments cannot dis- measurement of the high-energy (8B and hep) neutrinos tinguish between the 3ν and NSI cases.

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VI. SUMMARY fit of the 3 þ 1 þ NSI scenario is needed to conclusively confirm our findings. MINOSþ and IceCube data present a challenge to an udL The CC NSI parameter ϵμμ can be directly constrained explanation of the LSND/MiniBooNE anomaly with the at the Deep Underground Neutrino Experiment [35] and 3 þ 1 simple model. If the measurements of these experi- MuOn-decay MEdium baseline NeuTrino beam facility ments are accepted prima facie, the 3 þ 1 model must be [36] experiments. Also, large diagonal NC NSI will lead to extended by introducing baroque new physics to make the a modification of the matter potential, which will be tested data compatible with each other. We find that effects of the at future long-baseline experiments [37]. A study of early sterile neutrino at MINOSþ can be canceled by CC NSI at Universe cosmology in the 3 þ 1 scenario with CC and NC D udL the detector via ϵμμ ¼ 2ϵμμ , thereby significantly weak- NSI is underway by a subset of us. ening the MINOSþ constraint on the sterile neutrino parameter space. Also, the LSND/MiniBooNE allowed ACKNOWLEDGMENTS regions can be made consistent with IceCube and We thank A. Aurisano and J. Todd for helpful corre- DeepCore data by including large matter NSI parameters, spondence. K. W. thanks the University of Hawaii for its m m m m m ϵμμ and ϵττ, or large ϵss and small ϵμμ and ϵττ. The CC and hospitality while this work was in progress. This research NC NSI parameter values required do not impact the data was supported in part by the U.S. Department of Energy taken by the MiniBooNE and LSND experiments. A global under Grant No. DE-SC0010504.

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