PHYSICAL REVIEW D 101, 075051 (2020)

Constraining sterile interpretations of the LSND and MiniBooNE anomalies with coherent neutrino scattering experiments

Carlos Blanco ,1,2 Dan Hooper,2,3,4 and Pedro Machado5 1Department of , , Chicago, Illinois 60637, USA 2Kavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois 60637, USA 3Theoretical Group, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 4Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA 5Theoretical Physics Department, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

(Received 14 February 2019; accepted 7 April 2020; published 29 April 2020)

We propose to test the light sterile neutrino solution to the Liquid Scintillator Neutrino Detector (LSND) and MiniBooNE anomalies by measuring the coherent elastic scattering rate of from a pulsed spallation source. Coherent scattering is universal across all active neutrino flavors, and thus can provide a measurement of the total Standard Model neutrino flux. By performing measurements over different baselines and making use of timing information, it is possible to significantly reduce the systematic uncertainties and to independently measure the fluxes of neutrinos that originate as νμ or as either νe or ν¯μ. We find that a 100 kg CsI detector would be sensitive to a large fraction of the sterile neutrino parameter space that could potentially account for the LSND and MiniBooNE anomalies.

DOI: 10.1103/PhysRevD.101.075051

I. INTRODUCTION Together, these anomalies appear to point to the exist- A large number of neutrino oscillation experiments ence of a sterile neutrino with a mass near the electronvolt carried out over the past two decades have lead to the scale. Complicating this interpretation, however, are the ν → ν establishment of a standard framework, in which the results of several experiments which measure μ μ neutrino sector is comprised of three massive neutrinos transitions. In particular, the IceCube [14] and MINOS/ with relatively large mixing angles and subelectronvolt MINOS+ [15] experiments should be sensitive to the mass splittings. Some of the data that has been collected, presence of such a sterile neutrino, but have observed no however, cannot be explained within the context of this deviation from the standard (three-neutrino) framework. standard framework. Particularly puzzling have been the Detailed statistical analyses of the combined short baseline neutrino data have revealed a large degree of tension, at the results of the Liquid Scintillator Neutrino Detector (LSND) 4 7σ ν → ν [1] and MiniBooNE [2] experiments. In the former, an . level, between the appearance ( μ e) and disap- pearance (νμ → νμ and νe → νe) datasets, at least within the excess of ν¯e events was observed from a source of pions decaying at rest, while in the latter an excess of electronlike context of oscillations with one or more sterile neutri- events was observed in both νμ and ν¯μ beams. Although nos [3,16,17]. these experiments bear very distinct neutrino energy Motivated by this tension, a number of alternative explanations for the short baseline anomalies have recently profiles, their results are each consistent with νμ → νe oscillations occurring over a short baseline, requiring a been put forward. For example, models in which neutrinos upscatter to heavier fermions can provide a good fit to relatively large mass splitting [3–6]. Moreover, reexami- MiniBooNE’s energy spectrum and angular distribution nations [5,7–9] of the Gallium calibration experiments [18–21], but cannot account for the LSND excess. Other [10,11] and reactor antineutrino fluxes [12,13] have explanations involving “dark” particles produced in the identified a deficit of νe events relative to theoretical beam have also been considered, but are strongly con- expectations. strained by the MiniBooNE beam dump run data [22,23]. Moreover, scenarios that connect the neutrino mass gen- eration to extra dimensions, leading to an infinite Kaluza- Klein tower of sterile neutrinos, also seem to be disfavored Published by the American Physical Society under the terms of by data [24–32]. Importantly, an alternative analysis of the the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to LSND data finds that the potential signal may be at the edge the author(s) and the published article’s title, journal citation, of the detector’s sensitivity [33]. At this time, the correct and DOI. Funded by SCOAP3. interpretation of this data remains unclear, and further

2470-0010=2020=101(7)=075051(6) 075051-1 Published by the American Physical Society CARLOS BLANCO, DAN HOOPER, and PEDRO MACHADO PHYS. REV. D 101, 075051 (2020) information will be required in order to clarify this dσ G2 M ¼ F ½N − Zð1 − 4 2θ Þ2 confusing situation. dE 4π sin W T In this paper, we propose to measure or constrain the E ME E2 occurrence of short-baseline active-to-sterile neutrino oscil- 1 − T − T þ T F2ðE Þ; ð Þ × E 2E2 2E2 T 2 lations using neutrinos from a source of pions decaying at ν ν ν rest, which are then measured via neutral current coherent E E θ elastic neutrino-nucleus scattering. This interaction, which where T is the recoil energy, ν is the neutrino energy, W is M N Z has recently been observed for the first time by the the weak mixing angle, is the target nuclear mass, ( )is F COHERENT Collaboration [34], using a CsI target [35], the number of neutrons (protons) in the nucleus, and is the is universal across all three active neutrino flavors, and thus Helm nuclear form factor given by the following [46]: can provide a measurement of the total (all flavor) active 3j1ðR0QÞ Qs neutrino flux [36,37] (see also Refs. [38–40]). Furthermore, FðQÞ¼ exp − ; by taking data on two different baselines, we can sub- R0Q 2 x x stantially reduce the systematic uncertainties associated j ðxÞ¼sin − cos ; ð Þ with the detector efficiency, as well as with the overall flux 1 x2 x 3 and cross section [38,41–43]. The use of timing informa- tion provides information pertaining to neutrino flavor, where j1 is the first-order spherical-Bessel function, Q2 ¼ −p pμ ¼ 2ME allowing us to disentangle the effects of sterile neutrino pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiμ T is the momentum transfer, and mixing with νμ and νe, and thus providing a powerful probe 2 2 2 R0 ¼ R − 5s is determined by the surface thickness, of the LSND and MiniBooNE anomalies. s ¼ 0.5ðfmÞ, and the effective nuclear radius, R ¼ 1 1.2A3 ðfmÞ [47]. In this study, we will focus on the case II. COHERENT NEUTRINO SCATTERING of CsI as our target for coherent scattering. We have For our experimental setup, we have in mind a source of neglected spin-dependent contributions to the cross section neutrinos that is functionally similar to the Spallation which come from axial couplings since, relative to the vector Neutron Source at the Oak Ridge National Laboratory contributions, axial contributions should be suppressed by a 1= [44,45]. In particular, we consider a pulsed beam of 1 GeV factor of A [48]. 23 −1 The total coherent scattering cross section is given by protons with a luminosity of L0 ¼ 4 × 10 yr , of which approximately 8% (6%) produce a πþ (π−) upon striking integrating Eq. (2) up to a maximum recoil energy of E ¼ð2E2=ðM þ 2E ÞÞ the spallation target. T max ν ν . We also include a signal The high-Z nature of the liquid mercury target depletes acceptance function, which we take to interpolate linearly E ¼ 2 5 E ¼ 5 virtually all of the negatively charged pions through nuclear between zero at T . keV and 100% at T keV. capture (only ∼2.3 × 10−5 decay prior to nuclear capture), This represents an improvement of a factor of 2 in the E while the positively charged pions are rapidly slowed but midpoint T over that described in Ref. [34]. not captured [44]. These particles then decay at rest, via By utilizing timing information, it is possible to dis- þ þ þ tinguish the νμ flux from the combined flux of νe and ν¯μ.In π → μ νμ → e νeν¯μνμ, yielding the following isotropic þ particular, the muon lifetime (τμ ¼ 2.197 μs) delays the νe spectrum per π : and ν¯μ arrival times to a degree that is long compared to both the pion lifetime (0.026 μs) and the Gaussian pulse dN 2 2 width (0.16 μs), but short compared to the time between νμ mπ − mμ ¼ δ Eν − ; pulses at the Spallation Neutron Source (0.017 s). This is dE μ 2m νμ π illustrated in Fig. 1, where we show the time profile of the dN 6E2 m 2 neutrino luminosity from such a pulsed spallation source. ν¯μ ¼ ν¯μ μ − E ;E≤ m =2; 4 ν¯μ ν¯μ μ These profiles are calculated by convolving the decay dEν¯ ðmμ=2Þ 2 3 μ profile of each progenitor particle with the time profile dN 12E2 m νe νe μ of the beam pulse. ¼ − Eν ;Eν ≤ mμ=2; ð1Þ dE ðm =2Þ4 2 e e νe μ III. PROJECTED SENSITIVITY TO STERILE NEUTRINOS where mμ and mπ are the masses of the muon and pion, α respectively. The probability of a neutrino of flavor oscillating to β After traveling to the location of the detector, these flavor is given by the following: neutrinos can be observed through coherent elastic neutrino- X Δm2 L jk nucleus scattering. The cross section for this process is given Pα→β ¼ Uα;jUβ;jUα;kUβ;k exp −i ; ð4Þ 2Eν as follows: j;k

075051-2 CONSTRAINING STERILE NEUTRINO INTERPRETATIONS OF … PHYS. REV. D 101, 075051 (2020)

which the three Standard Model neutrinos are each much lighter than the sterile state (m1;2;3 ≪ m4), we can simplify 2 2 2 the problem by setting Δm41 ≈Δm42 ≈Δm43. Furthermore, Eq. (4) simplifies considerably on short baselines, for which oscillations between Standard Model (nonsterile) neutrinos are negligible. In this regime, the probability of a neutrino of flavor α arriving at the detector as an active neutrino is given as follows: X Δm2L P ¼ 1 − 4jU j2 1 − jU j2 2 ; α→e;μ;τ α4 β4 sin 4E β¼e;μ;τ ð5Þ

2 2 2 2 FIG. 1. The neutrino luminosity from a pulsed source of charged where Δm ≡ Δm41 ≈ Δm42 ≈ Δm43. After appropriate pions decaying at rest. The muon lifetime (τμ ¼ 2.197 μs) delays unit conversions, the argument of the sine function can ν ν¯ 2 2 the e and μ emission to a degree that is long compared to the pion be rewritten as 1.27 × ðΔm =eV ÞðL=mÞðMeV=EÞ. lifetime (0.026 μs) and pulse width (0.16 μs), but is very short To estimate the sensitivity of a coherent scattering compared to the time between pulses at the Spallation Neutron experiment to a sterile neutrino, we calculate the number Source (0.017 s). This makes it possible to use timing information ν ν ν¯ of events predicted to be observed in four time bins, to separate the μ flux from the combined flux of e and μ. Note – – – 2–10 μ t ¼ 0 5 μ corresponding to 0 0.5, 0.5 1, 1 2, and s, defined that we have defined the time axis such that . s is at the t ¼ 0 5 μ center of the pulse. such that . s is at the center of the pion pulse. By taking into account this timing information, we are able to measure independently the flux of neutrinos that originate L U where is the distance traveled, is the neutrino mixing as νμ, as well and those that originate as either νe or ν¯μ.We Δm2 ¼ m2 − m2 matrix, jk j k is the mass squared difference consider measurements made over two baselines (20 and between two neutrino mass eigenstates, and Eν is the 40 meters), using a target consisting of 100 kg of CsI, over neutrino energy. Given that we are interested in the case in a total observation time of either 3 or 10 years (half of the

FIG. 2. The projected constraints on the sterile neutrino parameter space for a 100 kg CsI detector and source that generates 4 × 1023 protons on target per year with an energy of 1 GeV, after collecting data for a total of 3 years (left) or 10 years (right). In each case, we have assumed that the detector was located at a distance of 20 meters from the source during the first half of the exposure, and at a distance of 40 meters during the second half. These constraints are compared to the regions that could potentially account for the LSND [1] and MiniBooNE [2] anomalies (at the 99% confidence level).

075051-3 CARLOS BLANCO, DAN HOOPER, and PEDRO MACHADO PHYS. REV. D 101, 075051 (2020) total time is assumed to be in each of the 20 and 40 meter where the sum is taken over the time bin described above, configurations). In each configuration, we include in N0 is the expected number of events without sterile- 2 the event rate calculation a steady-state background of mediated oscillations, NtðUe4;Ue4; Δm Þ is the number 1.45 × 10−10 counts=kg=μs, which can be precisely deter- of events expected as a function of the sterile mixing matrix mined by measuring the off-pulse event rate [34]. Although elements and mass splitting, α is a systematic parameter this is a factor of 10 lower than the rate reported in corresponding to the uncertainty in the signal rate, and Bss Ref. [34], this degree of improvement is achievable through is the estimated steady-state background. We minimize the 2 2 the application of additional shielding and well-understood χ over α for values of Ue4;Ue4; Δm during our analysis in techniques to reduce the dominant internal radiocontami- order to obtain our sensitivity contours. nations of CsI [49] (see also Refs. [50–52]). We also Additionally, the systematic uncertainties associated include in our analysis an overall systematic uncertainty of with the flux normalization, coherent scattering cross 28% on the overall signal rate, corresponding to uncer- section, and detector efficiencies could be reduced signifi- tainties associated with the cross section, detector effi- cantly by taking ratios of the event rates at the two baselines ciency, and overall neutrino flux. This uncertainty budget is and calibrating the detectors in order to understand any adopted from the experimental analysis performed by the possible differences in their response functions [43]. COHERENT collaboration using a detector technology The main results of our analysis are shown in Figs. 2 equivalent to the one described herein. [34] We define a χ2 and 3. In the first of these figures, we show the projected as follows: constraints on the sterile neutrino parameter space from an experiment utilizing a 100 kg CsI detector and X ðN0 − N ðU ;U ; Δm2Þð1 þ αÞÞ2 α 2 4 1023 χ2 ¼ t t e4 e4 þ ; source producing a luminosity of × protons on 0 0 28 target per year with an energy of 1 GeV. We present t Nt þ 2Bss . this result in terms of the effective mixing parameter ð Þ 2 2 2 6 sin ð2θμeÞ ≡ 4jUe4j jUμ4j . For simplicity, we have limited

2 2 2 2 FIG. 3. As in Fig. 2, but in terms of the jUμ4j vs jUe4j parameter space, for the choice of either Δm ¼ 0.55 eV (upper frames) or Δm2 ¼ 1.3 eV2 (lower frames). Again, the left (right) frames are after collecting data for 3 (10) years. These constraints are compared to the regions that could potentially account for the LSND [1] and MiniBooNE [2] anomalies (at the 99% confidence level).

075051-4 CONSTRAINING STERILE NEUTRINO INTERPRETATIONS OF … PHYS. REV. D 101, 075051 (2020) our discussion to the case of jUτ4j¼0. In Fig. 3, we show sterile neutrino scenarios motivated by the LSND and 2 2 these constraints in the jUμ4j vs jUe4j plane, for two MiniBooNE anomalies. By making use of timing informa- choices of Δm2. When these constraints are compared to tion, one independently measures the fluxes of neutrinos the regions favored by LSND and MiniBooNE, we con- that originate as νμ or as either νe or ν¯μ. Furthermore, by clude that the search proposed here would be sensitive to comparing the coherent scattering rates observed by a given the vast majority of the sterile neutrino parameter space that detector while positioned at multiple distances from the could potentially account for these anomalies. Note that source, it is possible to significantly reduce systematic 2 timing information gives this analysis sensitivity to jUμ4j uncertainties associated with the flux normalization, 2 and jUe4j approximately independently. Since this can coherent scattering cross section, and detector efficiencies. disentangle the mixing of a sterile neutrino with electron Alternatively, two 50 kg CsI detectors could be used to and muon neutrinos, the sensitivity to oscillation will carve simultaneously take data and therefore reduce any out approximately vertical and horizontal regions in the time dependent flux uncertainty. We find that such an 2 2 experiment would be sensitive to much of the relevant jUμ4j vs jUe4j plane which is particularly effective in probing the otherwise diagonal best-fit region. parameter space and would help to clarify the nature of the In these projections, we have considered measurements mysterious results reported by the LSND and MiniBooNE taken over baselines of 20 and 40 meters. If the separation Collaborations. between these distances were increased (decreased), the exclusion contours would shift downward (upward) in ACKNOWLEDGMENTS Δm2, as a consequence of the dependence on L and We would like to thank Juan Collar for helpful dis- Δm2 in Eq. (5). cussions. C. B. is supported by the U.S. National Science Foundation Graduate Research Fellowship under Grants IV. SUMMARY AND CONCLUSIONS No. DGE-1144082 and No. DGE-1746045. This manu- In this paper, we have proposed using a 100 kg CsI script has been authored by Fermi Research Alliance, LLC, coherent neutrino detector located near a pulsed source of under Contract No. DE-AC02-07CH11359 with the U.S. neutrinos functionally similar to the Spallation Neutron Department of Energy, Office of Science, Office of High Source at the Oak Ridge National Laboratory to test Energy Physics.

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