Search for exotic neutrino-electron interactions using solar neutrinos in XMASS-I

We have searched for exotic neutrino-electron interactions that could be produced by a neutrino millicharge, by a neutrino magnetic moment, or by dark photons using solar neutrinos in the XMASS-I liquid xenon detector. We observed no significant signals in 711 days of data. We obtain an upper limit for neutrino millicharge of 5.4$\times$10$^{-12} e$ at 90\% confidence level assuming all three species of neutrino have common millicharge. We also set flavor dependent limits assuming the respective neutrino flavor is the only one carrying a millicharge, $7.3 \times 10^{-12} e$ for $\nu_e$, $1.1 \times 10^{-11} e$ for $\nu_{\mu}$, and $1.1 \times 10^{-11} e$ for $\nu_{\tau}$. These limits are the most stringent yet obtained from direct measurements. We also obtain an upper limit for the neutrino magnetic moment of 1.8$\times$10$^{-10}$ Bohr magnetons. In addition, we obtain upper limits for the coupling constant of dark photons in the $U(1)_{B-L}$ model of 1.3$\times$10$^{-6}$ if the dark photon mass is 1$\times 10^{-3}$ MeV$/c^{2}$, and 8.8$\times$10$^{-5}$ if it is 10 MeV$/c^{2}$.


Introduction
Liquid xenon (LXe) detectors continue to set stringent limits on weakly interacting massive particle (WIMP) dark-matter models [1,2,3,4]. Yet these detectors are also able to explore other physics topics due to their low backgrounds (BGs) and low energy threshold. A study using solar neutrinos was suggested in [5]. Solar neutrinos are generated by nuclear fusion in the Sun. The majority of solar neutrinos come from the proton-proton (pp) reaction, p + p → d + e + + ν e , which produces approximately 99% of the total solar energy. The energy spectrum of the pp solar neutrinos is continuous with its endpoint at 422 keV. Another significant source of solar neutrinos is electron capture on 7 Be, which mainly produces a monochromatic line at a neutrino energy of 862 keV. Here we search for interactions between these abundant low energy solar neutrinos and the electrons in the detector's LXe target that could be signatures of a neutrino millicharge due to electromagnetic interactions, a neutrino magnetic moment, or interactions mediated by dark photons.

Neutrino millicharge
The electric charge of neutrinos is assumed to be zero in the Standard Model (SM). In general, the existence of a neutrino millicharge would give hints on models beyond the SM. In a simple extension of the SM with the introduction of the right-handed neutrino ν R , the neutrino is a Dirac particle and the three neutrino mass eigenstates share a common millicharge due to gauge invariance [6]. Any differences of millicharge among neutrinos and antineutrinos would be an indication of CPT violation [7]. Moreover, an experimental study on millicharge of individual neutrino flavors is still of interest.
Past experiments have searched for neutrino millicharge, but no evidence has been found so far. The most stringent upper limit is 1.5 × 10 −12 e [8]. This limit and the second most stringent one, 2.1 × 10 −12 e [9], were both obtained using reactor neutrinos, meaning electron antineutrinos, but also containing negligible amounts of other neutrino species such asν µ andν τ . Thus these are antineutrino limits. The most stringent limit for neutrinos, on the other hand, is < 3 × 10 −8 e for neutrino masses of less than 10 meV, and was obtained by a vacuum birefringence experiment [10]. This birefringence limit applies to all neutrino flavors. Solar neutrinos are produced as electron neutrinos, but due to neutrino oscillation at Earth they also contain ν µ and ν τ . In this paper we search for millicharge in all three neutrino flavors.

Neutrino magnetic moment
The massless neutrinos of the SM do not have any magnetic moment. However, a minimally-extended SM with Dirac neutrino masses predicts a finite neutrino magnetic moment of Here m e is the electron mass, G F is the Fermi coupling constant, and µ B is the Bohr magneton. Considering the observed small squared mass differences of neutrinos, it is not currently feasible to detect that small a neutrino magnetic moment experimentally. However, other extensions of SM theory yield neutrino magnetic moments at currently observable levels. For example, if the neutrino is a Majorana particle, the transition magnetic moment is estimated to be O(10 −10 ∼ 10 −12 )µ B in an extension that goes beyond a minimally-extended SM [12]. The Borexino experiment searched for a neutrino magnetic moment using 7 Be solar neutrinos. Borexino found no significant excess and set an upper limit of 2.8 × 10 −11 µ B [13]. Similarly, the GEMMA experiment, using reactor antineutrinos, obtained an upper limit of 2.9 × 10 −11 µ B [14].

Dark photons
There are many unsolved problems that cannot be explained by the SM, such as neutrino mass and the particle nature of dark matter, and new physics scenarios beyond the SM are required. The hidden sector scenario is one of such scenario. It contains a dark photon, which is thought to influence the interaction of neutrinos. The idea that the light vector boson of this hidden sector appears as a dark photon has been around for a long time [15,16], and the possibility that it appears at low energy has received wide interest. In the context of one such scenario, we search for a dark photon derived from a gauged U(1) B−L symmetry, in which the enhancement is expected to noticeably affect electrons recoiling from solar neutrino interactions [17,18]. The mass M A ′ of the dark photon A ′ and coupling constant g B−L are already constrained by various experimental and astrophysical analyses [18]. The dark photon model with U(1) B−L is also one of the candidates for explaining the muon g − 2 anomaly if the dark photon mass is O(1 ∼ 1000) keV/c 2 with g B−L ∼ O(10 −3 ∼ 10 −4 ) [19].
These considerations motivate us in our search for exotic neutrino interactions. Since solar neutrinos provide the largest available flux, we used it to search for exotic neutrino interactions with the using solar neutrinos XMASS-I detector.

The XMASS-I detector
The XMASS-I detector [20] is located at the Kamioka Observatory in Japan, underground at a depth of 2,700 meters water-equivalent. It consists of a water-Cherenkov outer detector (OD) and a single-phase LXe inner detector (ID). The OD, which is a cylindrical water tank 11 m high and 10 m in diameter, is equipped with 72 20-inch photomultiplier tubes (PMTs) used to veto cosmic-ray muons. Data acquisition for the OD is triggered when eight or more of its PMTs register a signal within 200 ns. The ID is located at the center of the OD. An active target containing 832 kg of LXe is held in the copper structure of the ID. The ID's inner surface is ∼40 cm away from the center and covered with 642 low-radioactivity PMTs (Hamamatsu R10789). Data-acquisition is triggered for the ID when four or more hits occur within 200 ns. Energy calibrations in the energy range between 1.2 keV and 2.6 MeV were conducted via the insertion of 55 Fe, 109 Cd, 241 Am, 57 Co, and 137 Cs sources along the vertical axis into the detector's sensitive volume, and by setting 60 Co and 232 Th sources outside the ID's vacuum vessel [20,21]. The time variation of the energy scale was traced via irradiation with 60 Co every week and by the insertion of 57 Co every other week.

Simulation
In the process of an interaction between a neutrino and an electron mediated by a neutrino magnetic moment [22] or by a dark photon from the U(1) B−L model [18], the total number of events N tot is given by integrating the differential rate in free electron approximation: where "SM" indicates the term for the standard weak interaction in the SM, "ex" indicates the exotic interaction term. For the dark photon analysis, interference effects with the weak interaction as in [18] are included in the exotic interaction term. T is the neutrino-energy deposition, t is the total livetime used in this analysis, N is the number of xenon atoms, σ νe − is the respective cross section between neutrino and electron, E ν is the neutrino energy, and Φ ν is the solar neutrino flux. At Earth the relevant fluxes are estimated to be Φ ν = 5.98 × 10 10 cm −2 s −1 for pp neutrinos and 5.00 × 10 9 cm −2 s −1 for 7 Be neutrinos, respectively [23]. To account for atomic effects in xenon, which affect the signal expectation, we follow previous publications in using the free electron approximation (FEA) in our dark photon and magnetic moment analyses. Effectively this approximation uses a series of step functions, one for every electron in the atom, each with the step at the respective electron's binding energy [24]. In our millicharge analysis on the other hand we follow [25] and use their results from their ab-initio multi-configuration relativistic random phase approximation (RRPA) [26]. At 5 keV deposited energy the FEA cross section is about a factor of five less than the RRPA one. Despite this the result for the magnetic moment analysis would change by less than 5% had we used RRPA instead of FEA. Figure 1 shows the deposited energy spectra of neutrino-electron interactions in xenon. The event rates due to dark photons is proportional to the fourth power of g B−L and the spectral shape depends upon M A ′ while the event rates due to a neutrino magnetic moment and to neutrino millicharge are proportional to the second power of these quantities. The expected signal spectrum results from the respective electron recoil spectrum in Figure 1 being folded with the detection efficiency of the detector, which is a function of energy : where E recon is the reconstructed energy and S(T, E recon ) is the signal efficiency after the data reduction process. We performed the detector simulation using the GEANT4 simulation package [27] for both signal and BG. The Monte Carlo (MC) simulation takes into account the non-linearity of the scintillation response in LXe as well as corrections derived from the detector calibrations. The electron equivalent energy is calculated from photoelectron counts (PE), with the conversion factor from PE to electron equivalent energy determined by comparing calibration data to MC simulation. The energy transferred in the interactions relevant to this paper ultimately becomes detectable as scintillation light emitted by electrons emerging from that interaction. As the transferred energies becomes low, such as X-ray and Auger electrons from xenon atom determine how much of that energy becomes transferred to electrons that can produce the scintillation signal. We conservatively assume that the scintillation efficiency below 1 keV is zero since we have a large uncertainty [21].

Dataset and event selection
We analyzed the data, accumulated in the same period as [4], between November 2013 and March 2016. The total livetime is 711 days, which is slightly increased due to the recovery of some data in this analysis. The event-selection criteria were as follows: We required that (1) the ID trigger is not accompanied by an OD trigger, (2) there was no after pulse or Cherenkov event 7 , (3) R(Timing) < 38 cm, and (4) R(PE) < 20 cm, where R(Timing) and R(PE) were the distances from the center of the detector to the reconstructed vertex obtained by timing-based reconstruction [28] and by PE-based reconstruction [20], respectively. The fiducial mass of natural xenon in that 20 cm volume is 97 kg. The analyzed energy range was then set to be 2-15 keV for the neutrino millicharge search and 2-200 keV for the neutrino magnetic moment and dark photon searches. The analyzed energy range 2-200 keV covers the expected signal after applying all reduction steps; it contains about 98% of the signal MC events for neutrino-magnetic-moment interactions, > 99% for dark photons of mass 1×10 −3 MeV/c 2 , and about 92% for dark photons of mass 10 MeV/c 2 .
The systematic uncertainties in the signal were of two types. One came from the theoretical calculation of the signal. The uncertainty in the solar neutrino fluxes from the pp and 7 Be reactions are ±0.6% and ±7%, respectively [23]. Also of this type is the uncertainty in the atomic effects in neutrino-electron interactions in xenon, which is ±5%. The other type of systematic uncertainty is related to the detector response. The most considerable systematic uncertainty in the signal is ∼15% for the neutrino millicharge analysis, which came from the scintillation efficiency for electrons at low energy. For energies > 30 keV, the uncertainty from the R(PE) cut became dominant with ∼ 6%. It was estimated from the difference of reconstructed position between data and MC in the 241 Am and 57 Co source calibrations. The uncertainty in the scintillation-decay time for electron recoils and in the optical properties were accounted for in the same way as in [4].
The BG components in the fiducial volume were discussed in [4] for E recon < 30 keV and in [29] for E recon > 30 keV, respectively. The dominant BG component for E recon < 30 keV derives from the radioactive isotopes (RI) that existed at the inner surface of the detector. The RI we took into account are 238 U, 235 U, 232 Th, 40 K, 60 Co and 210 Pb in the detector-surface materials. RI induced surface events were often misidentified as events in the fiducial volume in the event reconstruction. All detector materials except for the LXe had been assayed using high-purity germanium (HPGe) detectors or a surface-alpha counter [30]. The RI activities in the detector were estimated by an analysis of alpha events and the energy spectrum without a fiducial volume cut. The dominant BG component for E recon >30 keV was from RI dissolved in the LXe. Such events were distributed uniformly in the LXe and could not be removed by a fiducial-volume cut. Two categories of RI were found to be dissolved in the LXe: One was impurities such as 222 Rn, 85 Kr, 39 Ar and 14 C. The 222 Rn and 85 Kr activities were estimated using event coincidence in the full volume of the ID. In [29], we identified 39 Ar and 14 C in the detector from gas analysis of xenon samples and by performing spectral fitting. The other category were mostly xenon isotopes: 136 Xe, which undergoes 2νββ decay, and 125 I, 131m Xe and 133 Xe produced by neutron activation of common xenon isotopes. We estimated the concentration of 136 Xe from its natural abundance and that of 125 I from that of its precursor 124 Xe and the thermal-neutron flux at the Kamioka Observatory, respectively. The concentrations of 131m Xe and 133 Xe were estimated with a spectral fit performed in [29].
We applied a data-driven correction to the simulated BG spectrum for E recon < 40 keV in order to take into account the systematic difference in the mis-reconstruction rate caused by dead PMTs as we did in [31]. The dead PMTs (9 out of 642 PMTs which had been found to be noisy or delivered strange responses) had been turned off. We evaluated the systematic difference of the probability with which events occurring close to the dead PMTs were reconstructed inside the fiducial volume. The difference between data and BG MC was found to be non-negligible below 40 keV. We applied a correction factor for the BG MC spectrum for such differences in each of the energy regions 5-15, 15-20, 20-30 and 30-40 keV. These correction factors were estimated by comparing of the distance between the projection of the reconstructed vertex onto the detector surface and the dead-PMT position between data and BG MC in the fiducial volume. There are two systematic uncertainties associated with this correction factor. The first contribution was estimated by the difference in the correction factor estimated from the systematic difference of event rates in the fiducial volume by deliberately masking normal PMTs. The second contribution stems from the statistical uncertainty of the correction-factor estimate. The resultant correction and the systematic uncertainty of our BG model are shown in the inset of the bottom panel of Figure 2.
The systematic uncertainties in the BG MC were basically the same as those used in our previous WIMP-search analysis [4] for E recon < 30 keV except for the dead PMT contribution. The dominant uncertainties came from uncertainty about the condition of the detector surface. For 30-200 keV, we re-evaluate the systematic errors for uncertainties in the performance of the reconstruction, the scintillation-decay time, and the optical parameters of the LXe. Again most significant systematic uncertainly in this energy range comes from the position reconstruction, and is ∼6 % as discussed before. Its estimation method was the same as for the signal MC. Figure 2 shows the energy distribution of the BG simulation after the event selection from 2 to 200 keV.

Fitting the energy spectrum
Based on the BG estimate, we searched for the signatures of exotic neutrino-electron interactions by fitting the energy spectrum of the data with those of the BG MC and the respective signal MC. We define the fit by the following χ 2 : where D i , B i , and S i are the numbers of events in the data, the BG estimate, and the signal MC of the exotic neutrino interactions, respectively. The index i denotes the i-th energy bin. The value of α scales the signal-MC contribution. The quantity B i contains various kinds of BG sources. The terms B i and S i can be written as where j is the index of the BG components, and k, and l are indices for systematic uncertainties in the BG and signal, respectively. We write the uncertainty in the amount of RI activity, systematic uncertainty in the BG and signal as σ(B RI ) j , σ(B sys ) ijk and σ(W sys ) il , respectively. We scaled the RIs activities and the fraction of systematic errors by p j , q k and r l , respectively, while constraining them with a pull term (χ 2 pull ). The fitting range is 2-15 keV in the neutrino millicharge search, and is 2-200 keV in the dark photon and neutrino magnetic moment searches. We note that the constraints due to the RI activity from 14 C, 39 Ar, 131m Xe and 133 Xe are not applied in the dark photon or neutrino magnetic moment searches because the expected signals are distributed at energies above 30 keV where spectrum fitting was performed to determine the RI activities in [29].

Search for neutrino millicharge
We found no significant signal excess, which would have been expected around 5 keV, and accordingly we set an upper limit for neutrino millicharge of 5.4 × 10 −12 e at the 90% confidence level (CL), assuming all three species of neutrino have common millicharge. The best fit χ 2 is obtained at zero millicharge. Figure 3 shows the data and the best-fit signal + BG MC with the signal MC at the 90% CL upper limit. This limit is for neutrinos, not antineutrinos, and for neutrinos it is more stringent than the previous limit by more than three orders of magnitude [10]. Though the originally emitted solar neutrinos are ν e , the neutrinos arriving at Earth consist of all three flavors, which are produced by neutrino oscillations: At Earth 54±2% are ν e , 23±1% are ν µ , and 23±1% are ν τ [19,32]. Using this, we set upper limits for each flavor to be 7.3 × 10 −12 e for ν e , 1.1 × 10 −11 e for ν µ , and 1.1 × 10 −11 e for ν τ . These limits assume that only the neutrino flavor for which the limit is quoted carries a millicharge and thus contributes to the expected signal.

Search for neutrino magnetic moment
We also searched for a signal excess due to a neutrino magnetic moment, but again found no significant excess. The top part of Figure 5   shows the energy distribution of the data and the best-fit signal + BG. The contribution a neutrino magnetic moment at our 90% CL signal limit would have made is also shown again. The best fit neutrino magnetic moment was µ ν =1.3×10 −10 µ B , with a χ 2 /d.o.f = 85.9/98, while µ ν = 0 yielded χ 2 /d.o.f = 88.2/98. The 90% CL upper limit for the neutrino magnetic moment is estimated from the χ 2 probability density function to be µ ν =1.8×10 −10 µ B .

Search for neutrino interactions due to dark photons
We also searched for a signal excess due to a dark photon with M A ′ in the range from 1×10 −3 MeV/c 2 to 1×10 3 MeV/c 2 . Again we found no significant excess. The middle and bottom parts of Figure 5 show the energy distributions of the data and the best-fit signal + BG. The contribution dark photons would have made at our 90% CL limit is also shown in the figure. The value of g B−L from the best fit is 1.1×10 −6 with a χ 2 /d.o.f = 85.3/98 for M A ′ =1×10 −3 MeV/c 2 and is null with χ 2 /d.o.f = 88.2/98 for 10 MeV/c 2 . The upper limits for g B−L for M A ′ =1×10 −3 MeV/c 2 and 10 MeV/c 2 are 1.3 × 10 −6 and 8.8 × 10 −5 at 90% CL, respectively. The 90% CL upper limit on the coupling constant as a function of the dark photon mass is shown in Figure 6, together with the limits and allowed region from other experimental and astrophysical analyses [18]. Like the other neutrino and anti-neutrino scattering experiments we exclude a wide area in this parameter space, and for neutrinos our limit on g B−L is more stringent than Borexino's for M A ′ < 0.1 MeV/c 2 . While the exclusion areas derived in [18] from other experi-  ments' publications already exclude an area larger than the one excluded by our analysis, our analysis is a dedicated one, incorporating our full knowledge of the detector response and our validated background models. Also most of the parameter space for the (g − 2) dark photon prediction [18] was excluded by our analysis.

Conclusions
We conducted searches for exotic neutrino-electron interactions from solar neutrinos using 711 days of data in a 97 kg fiducial volume of the XMASS-I detector. We observed no significant signal. In the neutrino millicharge search, we set a neutrino millicharge upper limit of 5.4 × 10 −12 e at 90% CL assuming all three species of neutrino have common millicharge. This is comparable to limits from previous experiments using antineutrinos. It is however three orders of magnitude better than the best previous limit for neutrinos [10]. We set upper limits for individual flavors at 7.3 × 10 −12 e for ν e , 1.1 × 10 −11 e for ν µ , and 1.1 × 10 −11 e for ν τ . Our upper limit for a neutrino magnetic moment is 1.8×10 −10 µ B . Our result on dark photons in the U(1) B−L model imposes severe new restrictions on the coupling constant with neutrino from M A ′ =1×10 −3 to 1×10 3 MeV/c 2 . In particular we almost exclude the area in which the U(1) B−L model can solve the g − 2 anomaly. Figure 5: The energy distribution of the data, the best fit signal + BG and the 90% CL signal limit from 2 to 200 keV for the neutrino magnetic moment analysis (top) and the dark photon analysis (middle: dark photon mass M A ′ = 1×10 −3 MeV/c 2 , bottom M A ′ = 10 MeV/c 2 ). The black points show the data. The blue histogram shows the signal + BG MC for the best fit, and the red-dotted histogram shows the 90% CL upper limit for the signal. Figure 6: 90% CL exclusion limits and allowed region on the coupling constant g B−L as a function of the dark photon mass M A ′ . The black-solid line shows the exclusion limit of our analysis (XMASS). The 2σ-allowed-region band from the muon (g−2) experiment is shown as "(g − 2) DP" as the red-meshed region. The blue and magenta regions are excluded by laboratory experiments ((g − 2) µ , (g − 2) e , atomic phys., fixed target, B-factory [18] and NA48/2 [33]), respectively. The cyan and orange regions are excluded by cosmological and astrophysical constraints (Globular clusters, BBN [18]), respectively. BBN: the constraints of Big Bang nucleosynthesis on the mass of a light vector boson and its coupling constant to neutrinos in the B−L scenario. In this case, Dirac neutrinos ν R are assumed [34]. The range of region follows as [18]. The dotted lines are the estimated limit curves from neutrino-scattering experiments (GEMMA (ν e ), Borexino (solar ν), TEXONO-CsI (ν e ) and CHARM II (ν µ )) from [18].