PRDPRVDAQPhysical Review DPhys. Rev. D2470-00102470-0029American Physical Society10.1103/PhysRevD.99.015016ARTICLESBeyond the standard modelMiniBooNE, MINOS+ and IceCube data imply a baroque neutrino sectorMiniBooNE, MINOS+ AND IceCube DATA IMPLY A …JIAJUN LIAO, DANNY MARFATIA, AND KERRY WHISNANTLiaoJiajun^{1,2}MarfatiaDanny^{1}WhisnantKerry^{3}Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822, USASchool of Physics, Sun Yat-Sen University, Guangzhou 510275, ChinaDepartment of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA8January20191January20199910150163October2018Published by the American Physical Society2019authorsPublished by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP^{3}.

The 4.8σ anomaly in MiniBooNE data cannot be reconciled with MINOS+ and IceCube data within the vanilla framework of neutrino oscillations involving an eV-mass sterile neutrino. 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+1 neutrino scheme. It appears that either the neutrino sector is more elaborate than usually envisioned, or one or more data sets needs revision.

U.S. Department of Energy10.13039/100000015DE-SC0010504INTRODUCTION

The existence of an eV-scale neutrino has been a major open question in neutrino physics for more than two decades. Recently, the MiniBooNE Collaboration updated their analysis after 15 years of running and reported a 4.8σ C.L. excess in the electron and antielectron neutrino spectra close to the experimental threshold [1]. An explanation of the results via νμ→νe oscillation with a mass-squared difference δm2∼1eV2 is consistent with the LSND anomaly found at a similar L/E∼1m/MeV[2]. The two excesses combined have reached a significance of 6.1σ C.L. and urgently call for an explanation that makes them compatible with other experiments.

It is well known that the appearance data are in serious tension with disappearance data in global fits of the 3+1 oscillation framework [3–5]. To explain the LSND and MiniBooNE excess via sterile neutrino oscillations, a relatively large mixing amplitude sin22θμe≡4|Ue4Uμ4|2=sin22θ14sin2θ24 is required. Constraints on |Ue4|=sinθ14 are provided mainly by reactor neutrino experiments, with Daya Bay contributing a strong constraint on |Ue4| for δm412<0.5eV2[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 δm412≈1.3eV2 and |Ue4|2≈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 bottom/top ratios of the positron energy spectra in Ref. [8] gives the best-fit parameters δm412=1.4eV2, sin2θ14=0.016 with a χ2 value smaller by 10.8 than for the standard no oscillation case. The regions favored by DANSS are shown in Fig. 1. We see that DANSS data prefer an eV-scale neutrino oscillation with the mixing angle sin2θ14 in the 1σ range, 0.0087–0.023. Our results are consistent with those of Refs. [5,9] after taking into account the large systematic uncertainties due to the energy resolution and the sizes of the source and detector.

110.1103/PhysRevD.99.015016.f1

The 1σ, 2σ, and 3σ regions allowed by DANSS. The blue plus sign marks the best-fit point, δm412=1.4eV2 and sin2θ14=0.016.

Constraints on |Uμ4|=cosθ14sinθ24, which are mostly driven by the νμ disappearance experiments at IceCube [10] and MINOS+[11], rule out the 3+1 scenario for the MiniBooNE/LSND data. Hence, if we take the results of all three experiments, MiniBooNE, MINOS+ and IceCube, at face value, a baroque new physics scenario must be introduced to explain all the data. In this Letter, we first show that the MINOS+ constraints can be relaxed if there exist charged-current (CC) nonstandard interactions (NSI) in the detector. (An earlier analysis invoked CC NSI in the 3+1 scenario to explain a discrepancy between neutrino and antineutrino oscillations observed in early MiniBooNE data [12].) It is known that large neutral-current (NC) NSI, can suppress the resonant enhancement of high-energy atmospheric neutrino oscillations and weaken the IceCube constraints on sinθ24[13]. Since large NC NSI also modify the lower-energy atmospheric neutrino spectrum at DeepCore, here we study NSI effects on the combination of IceCube and DeepCore data.

FRAMEWORK

We consider the simplest 3+1 mass scheme, with an eV-mass sterile neutrino in addition to the three active neutrinos. CC and NC NSI are motivated by new physics beyond the standard model, and their effects on neutrino oscillations have been extensively studied; for reviews see Refs. [14–16]. Similar to the standard electroweak interactions, the NSI we require can be described by the dimension-six operators: LNC-NSI=-22GFεαβfC[να¯γρPLνβ][f¯γρPCf],LCC-NSI=-22GFεαβff′C[νβ¯γρPLℓα][f¯′γρPCf],where α,β∈e,μ,τ,s, C=L, R, f≠f′∈u,d, f,f′≠e, and εαβfC and εαβff′C are dimensionless and parametrize the strength of the new interactions in units of the Fermi constant GF. The NC NSI mainly affect neutrino propagation in matter, and the CC NSI affect neutrino production and detection. Hence, when both NC and CC NSI are operative, the apparent oscillation probability measured in an experiment can be written as [17]P˜(ναS→νβD)=|[(1+εD)Te-iHL(1+εS)T]βα|2,where εαβS and εαβD are defined through the CC NSI parameters εαβff′C, and the Hamiltonian H is given by H=12E[V(00000δm2120000δm3120000δm412)V†]+Vm,with δmij2=mi2-mj2, and V=R34O24O14R23O13R12. Here Rij is a real rotation by an angle θij in the ij plane, and Oij is a complex rotation by θij and a phase δij. The matter potential in Eq. (4) is Vm=VCC(1+εeemεeμmεeτmεesmεeμm*εμμmεμτmεμsmεeτm*εμτm*εττmετsmεesm*εμsm*ετsm*κ+εssm),where VCC=2GFNe is the electron charged-current potential, κ=Nn2Ne≃0.5 is the standard NC/CC ratio, εαβm≡∑f,CεαβfCNfNe is the effective strength of NSI in matter, and Nf is the number density of fermion f.

To relax the MINOS+ and IceCube bounds, we employ Occam’s razor and assume that only εμμD, εμμm, εττm and εssm are nonzero. Note that CC NSI at the source may be different from those at the detector. Since neutrinos produced by the NuMI beam line mainly arise from pion decay and pions only couple to the axial-vector current, a vectorlike interaction, i.e., εμμudL=εμμudR, only yields CC NSI at the detector [12]. Then, εμμD=2εμμudL. We set θ34 and all phases to be equal to zero for simplicity. Since the νe flux is small compared to the νμ flux at these experiments, and the νe mixing is suppressed by s132 and s142, we ignore the νe component and consider a three-flavor system with only νμ, ντ, and νs. After a rotation by R24, the Hamiltonian that describes the three-neutrino propagation in matter can be written as R24†HR24≈δm3122E(s232+A^(c242εμμm+s242ε˜ssm)c23s23A^c24s24(εμμm-ε˜ssm)c23s23c232+A^εττm0A^c24s24(εμμm-ε˜ssm)0R+A^(c242ε˜ssm+s242εμμm)),where R≡δm412/δm312, A^=22GFNeEν/δm312, ε˜ssm≡κ+εssm, and we have dropped δm212-dependent terms since they are very small. For R≫A^c24s24(εμμm-ε˜ssm), the measured νμ→νμ oscillation probability after averaging over the fast oscillation is ⟨P˜μμ⟩≈(1+2εμμD-2s242)(1-sin22θ˜23sin2Δ˜31),where sin22θ˜23=sin22θ23C, Δ˜31=δm312L4EνC, and C=sin22θ23+[cos2θ23-A^(c242εμμm-εττm+s242ε˜ssm)]2. If εμμD≃s242and εμμm-εττm≃s242(εμμm-εssm-κ),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: δm412=1.4eV2,sin2θ14=sin2θ24=εμμD=0.02,εμμm=-0.7,εττm=-0.5,εssm=6.In the left panel in Fig. 2, we plot the difference of the measured oscillation probabilities between the sterile and 3ν cases at the MINOS+ far detector (FD) after averaging out the fast oscillations. We see that in the presence of CC NSI, the measured oscillation probability at the MINOS+ FD is almost the same as the standard case, so using the MINOS+ FD data alone cannot distinguish the 3+1 case from the standard three-neutrino oscillation case.

210.1103/PhysRevD.99.015016.f2

The difference of the measured oscillation probabilities between the 3+1 and standard three-neutrino oscillation cases at the MINOS+ far detector (left) and near detector (right). The solid (dashed) curve corresponds to the case with (without) NSI. Here δm412=1.4eV2, sin2θ14=sin2θ14=εμμD=0.02, εμμm=-0.7, εττm=-0.5, and εssm=6, and the other mixing angles and mass-squared differences are the best-fit values in Ref. [18]. The fast oscillations have been averaged out. The shaded band represents the 1σ systematic uncertainties at the near detector.

To analyze the MINOS and MINOS+ data, we follow the procedure described in Ref. [11], with the χ2 defined as χ2=∑i=171∑j=171(xi-μi)[V-1]ij(xj-μj),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/MINOS+ mainly comes from the FD since the oscillation effects at the MINOS/MINOS+ near detector (ND) are negligible, and (ii) the systematic uncertainties at the ND are very large (see Fig. 2) and a precise determination of the spectrum at the ND has been called into question [20].

Since the MINOS/MINOS+ data are not sensitive to θ14, we fix sin2θ14=0.02. Hence, the χ2 function for the 3+1 scenario with CC NSI depends only on sin2θ23, δm232, sin2θ24, δm412, and the NSI parameters. For a fixed set of NSI parameters, we marginalize over sin2θ23 and δm232 for each point in the (sin2θ24,δm412) plane and calculate Δχ2(sin2θ24,δm412)=χmin2(sin2θ24,δm412)-χmin,3ν2 to obtain the exclusion limits on the 3+1 model. The resulting χmin,3ν2=74.8 represents a good fit to the 71 data points used in our analysis.

The 90% C.L. exclusion limits in the (sin2θ24, δm412) plane for εμμD=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+1 case from our analysis of the FD data only; clearly, the limits are in good agreement for δm412<3eV2. The red curve corresponds to the NSI cases with εμμD=0.02. (Note that the current bounds on vectorlike εμμud are rather weak [21].) The limits can be understood from Eq. (8). In general, the bounds become weaker as εμμD is increased. For sin2θ14=0.01, the LSND/MiniBooNE allowed region is consistent with the MINOS/MINOS+ data for εμμD>0.03. Since larger values of θ14 require correspondingly smaller values of θ24 to explain the LSND/MiniBooNE data, for sin2θ14=0.02, large parts of the regions allowed by the appearance data are not constrained by the MINOS/MINOS+ data. From the dashed and dotted red curves we see that NC NSI have a tiny effect on the bounds for eV-scale sterile neutrinos. Note that CC NSI also increase the number of events at the MINOS/MINOS+ ND. However, these changes are within the systematic uncertainties at the ND [22]; see the shaded band in the right panel in Fig. 2.

310.1103/PhysRevD.99.015016.f3

The 90% C.L. exclusion limits for the 3+1 scenario from MINOS and MINOS+ data. The dashed black curve is extracted from Ref. [11], and the black solid curve corresponds to the 3+1 case from our analysis of the FD data only. The red curves correspond to the 3+1+NSI case with εμμD=0.02. The solid red curve corresponds to no NC NSI, while the dashed red curve corresponds to εμμm=-4.3 and εττm=-4, and the dotted red curve corresponds to εμμm=-0.7, εττm=-0.5 and εssm=6. The shaded (hatched) region corresponds to the 3σ allowed region for the combined LSND and MiniBooNE appearance analysis [5] with sin2θ14=0.01 (0.02). The gray curve corresponds to the CERN Dortmund Heidelberg Saclay neutrino experiment 90% C.L. exclusion limit, as shown in Ref. [11]. The blue plus sign marks the point in Eq. (10).

ICECUBE/DEEPCORE ANALYSIS

We now study the atmospheric neutrino constraints in the presence of large NC NSI by combining the IceCube data at high energy and the DeepCore data at low energy. For the IceCube analysis, we follow the procedure of Ref. [13], which analyzed 13 bins in the reconstructed muon energy range, 501GeV≤Eμrec≤10TeV, and 10 bins in the zenith angle range, -1≤cosθz≤0[23]. For the DeepCore analysis, we use the publicly available data from Ref. [24], which has eight bins in the reconstructed energy range, 6GeV≤Eμrec≤56GeV, and eight bins in the zenith angle range, -1≤cosθz≤0. The expected number of observed events at DeepCore is given by Nijexp=∫dcosθz∫dEνΦνμ(Eν,cosθz)Pνμνμ(Eν,cosθz)×Aeff(Eμ,irec,cosθz,j,Eν,cosθz)+(ν→ν¯),where cosθz is the cosine of the zenith angle, Φνμ(Eν,cosθz) is the atmospheric νμ flux at the surface of Earth [25], Pνμνμ(Eν,cosθz) is the νμ→νμ oscillation probability at the detector, and Aeff is the neutrino effective area given in Ref. [24].

To calculate the statistical significance of an oscillation scenario, we define χDC2=2∑i,j=18[Nijth(α,β)-Nijobs+NijobslnNijobsNijth(α,β)]+(1-α)2σα2,where Nijobs is the observed event counts per bin and Nijth(α,β)=αNijexp+βNijbkg with Nijbkg being the atmospheric muon background per bin. We take the uncertainty in the atmospheric neutrino flux normalization to be σα=20% at the energies relevant to DeepCore, and we allow the normalization of the atmospheric muon background to float freely [24]. We find χDC,min,3ν2=60.7 with α=0.869 and β=0.184 and confirmed that the confidence regions for the standard 3ν oscillation from our analysis agree with those in Ref. [24].

To obtain the exclusion regions for the combined IceCube and DeepCore data in the 3+1 scenarios, we calculate ΔχIC+DC2(sin2θ24,δm412)=χIC+DC,min2(sin2θ24,δm412)-χIC+DC,min,3ν2, where χIC+DC2=χIC2+χDC2 for each set of parameters; χIC+DC,min,3ν2=172.7. The exclusion region for the 3+1 scenario without NSI is shown as the black line in Fig. 4. We see that the LSND/MiniBooNE allowed region is excluded by the IceCube/DeepCore data.

410.1103/PhysRevD.99.015016.f4

The 90% C.L. exclusion limits for the 3+1 scenario from IceCube and DeepCore data. The solid black curve corresponds to the 3+1 oscillations without NSI, and the solid red [blue] curve corresponds to the 3+1+NSI (a) [(b)] case. The red (blue) dashed contour corresponds to the 90% C.L. allowed region in case (a) [(b)]. The shaded (hatched) region corresponds to the 3σ allowed region for the combined LSND and MiniBooNE appearance analysis [5] with sin2θ14=0.01 (0.02). εμμD=0.02 for the NSI scenarios. The blue plus sign marks the point in Eq. (10).

We consider two NSI cases: (a) only εμμm and εττm are nonzero, and (b) εμμm, εττm, and εssm are all nonzero. For case (a), we scan the parameter space, |εττm|<6 and |εμμm-εττm|<0.5. For case (b), we scan the parameter space, |εssm|<6, |εττm|<0.5 and |εμμm-εττm|<0.5. We note that large εμμm and εeem=0 yield large εμμm-εeem, which may be constrained by solar data [26]. Therefore, in order to accommodate a small value for εμμm-εeem, we allow large εssm in case (b). (The global analysis of Ref. [26] uses solar data to place constraints on εμμm-εeem, which however do not apply to our scenario because it includes a sterile neutrino.) We also fixed εμμD=0.02 for both cases. Our results are not sensitive to the value of εμμD, since εμμD only affects the overall normalization of the expected events and the uncertainty of the atmospheric neutrino flux normalization is large. The minimum values of χIC+DC2 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+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.

OTHER DATA

The Super-Kamiokande (SK) experiment has collected 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 [27]; see Fig. 5. For the sub-GeV events at SK, systematic uncertainties are very large due to the poor angular correlation between the neutrino and outgoing lepton [28].

510.1103/PhysRevD.99.015016.f5

Zenith angle distributions of the averaged atmospheric muon neutrino and antineutrino survival probabilities for two Super-Kamiokande energy bins. The solid (dashed) [dotted] curve corresponds to the 3+1+NSI (3+1) [3ν] case. For the 3+1 case without NSI, the spectra are normalized by a factor of 1.04 to compare with the 3ν case. The oscillation parameters are the same as in Fig. 2.

Solar neutrino propagation is sensitive to modifications of the matter potential. To analyze solar neutrino data, we follow the procedure of Ref. [29] in conjunction with the Standard Solar Model fluxes [30]. The survival probabilities obtained from the Borexino measurements of the pp[31], Be7[32], and pep neutrinos [33], and the SNO CC measurement of the high-energy (B8 and hep) neutrinos [34], are the four data points in Fig. 6. The survival probabilities for the 3ν and NSI cases are also shown. We find χ2=1.79 and 2.13 for the 3ν and NSI case, respectively, demonstrating compatibility of the 3+1+NSI scenario with current solar data. Note that since NSI shift the upturn in the survival probability to lower energies, the tension between KamLAND and B8 neutrino data is eased.

610.1103/PhysRevD.99.015016.f6

The survival probabilities of solar neutrinos for the 3ν, 3+1, and 3+1+NSI cases. The oscillation parameters are the same as in Fig. 2.

We mention in passing that data from the appearance channels at current long-baseline experiments cannot distinguish between the 3ν and NSI cases.

SUMMARY

MINOS+ and IceCube data present a challenge to an explanation of the LSND/MiniBooNE anomaly with the simple 3+1 model. If the measurements of these experiments are accepted prima facie, the 3+1 model must be extended by introducing baroque new physics to make the data compatible with each other. We find that effects of the sterile neutrino at MINOS+ can be canceled by CC NSI at the detector via εμμD=2εμμudL, thereby significantly weakening the MINOS+ constraint on the sterile neutrino parameter space. Also, the LSND/MiniBooNE allowed regions can be made consistent with IceCube and DeepCore data by including large matter NSI parameters, εμμm and εττm, or large εssm and small εμμm and εττm. The CC and NC NSI parameter values required do not impact the data taken by the MiniBooNE and LSND experiments. A global fit of the 3+1+NSI scenario is needed to conclusively confirm our findings.

The CC NSI parameter εμμudL can be directly constrained at the Deep Underground Neutrino Experiment [35] and MuOn-decay MEdium baseline NeuTrino beam facility [36] experiments. Also, large diagonal NC NSI will lead to a modification of the matter potential, which will be tested at future long-baseline experiments [37]. A study of early Universe cosmology in the 3+1 scenario with CC and NC NSI is underway by a subset of us.

I10.1103/PhysRevD.99.015016.t1

The minimum χIC+DC2 for the best-fit scenarios. In case (a), the scanned parameter ranges are |εττm|<6 and |εμμm-εττm|<0.5; in case (b), the scanned parameter ranges are |εssm|<6, |εττm|<0.5 and |εμμm-εττm|<0.5. There are 130 IceCube and 64 DeepCore data points in the analysis.

We thank A. Aurisano and J. Todd for helpful correspondence. K. W. thanks the University of Hawaii for its hospitality while this work was in progress. This research was supported in part by the U.S. Department of Energy under Grant No. DE-SC0010504.

1A. A. Aguilar-Arevalo (MiniBooNE Collaboration), 2A. Aguilar-Arevalo (LSND Collaboration), 3G. H. Collin, C. A. Arguelles, J. M. Conrad, and M. H. Shaevitz, 4S. Gariazzo, C. Giunti, M. Laveder, and Y. F. Li, 5M. Dentler, A. Hernandez-Cabezudo, J. Kopp, P. Machado, M. Maltoni, I. Martinez-Soler, and T. Schwetz, 6F. P. An (Daya Bay Collaboration), 7Y. J. Ko (NEOS Collaboration), 8I. Alekseev (DANSS Collaboration), 9S. Gariazzo, C. Giunti, M. Laveder, and Y. F. Li, 10M. G. Aartsen (IceCube Collaboration), 11P. Adamson (MINOS Collaboration), arXiv:1710.06488.12E. Akhmedov and T. Schwetz, 13J. Liao and D. Marfatia, 14T. Ohlsson, 15O. G. Miranda and H. Nunokawa, 16Y. Farzan and M. Tortola, 17J. Kopp, M. Lindner, T. Ota, and J. Sato, 18I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, and T. Schwetz, 19aP. Huber, M. Lindner, and W. Winter, 19bP. Huber, J. Kopp, M. Lindner, M. Rolinec, and W. Winter, 20W. C. Louis, arXiv:1803.11488.21C. Biggio, M. Blennow, and E. Fernandez-Martinez, 22J. Conrad (private communication).23M. G. Aartsen (IceCube Collaboration), 24M. G. Aartsen (IceCube Collaboration), 25M. Honda, M. Sajjad Athar, T. Kajita, K. Kasahara, and S. Midorikawa, 26I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, and J. Salvado, 27K. Abe (Super-Kamiokande Collaboration), 28T. Kajita, E. Kearns, and M. Shiozawa (Super-Kamiokande Collaboration), 29aV. Barger, D. Marfatia, and K. Whisnant, 29bV. Barger, D. Marfatia, and K. Whisnant30N. Vinyoles, A. M. Serenelli, F. L. Villante, S. Basu, J. Bergström, M. C. Gonzalez-Garcia, M. Maltoni, C. Peña-Garay, and N. Song, 31G. Bellini (BOREXINO Collaboration), 32G. Bellini, 33G. Bellini (Borexino Collaboration), 34B. Aharmim (SNO Collaboration), 35P. Bakhti, A. N. Khan, and W. Wang, 36J. Tang and Y. Zhang, 37See e.g., J. Liao, D. Marfatia, and K. Whisnant,