The reactor antineutrino anomaly and low energy threshold neutrino experiments

Short distance reactor antineutrino experiments measure an antineutrino spectrum a few percent lower than expected from theoretical predictions. In this work we study the potential of low energy threshold reactor experiments in the context of a light sterile neutrino signal. We discuss the perspectives of the recently detected coherent elastic neutrino-nucleus scattering in future reactor antineutrino experiments. We find that the expectations to improve the current constraints on the mixing with sterile neutrinos are promising. We also analyse the measurements of antineutrino scattering off electrons from short distance reactor experiments. In this case, despite the statistics is not competitive with inverse beta decay experiments, the restrictions play an important role when we compare it with the Gallium anomaly.

At the same time, we also discuss in more detail the case of a different prescription for the reactor antineutrino flux as a solution to the so called reactor anomaly. After the recent evaluation of the antineutrino spectrum by Daya Bay [36], the need for a better understanding of the spectrum has been pointed out. Moreover, the possibility that the reactor anomaly can be solved by a revaluation of the antineutrino flux has also been considered [37]. Since the data in the reactor signal for sterile neutrinos come from IBD experiments, it will be interesting to consider alternative detection technologies as a complementary test to this anomaly. For this reason we study here the current data from neutrino electron scattering, as well as the prospects of CENNS.

II. ANTINEUTRINO ELECTRON SCATTERING MEASUREMENT
In this section we concentrate our study in experiments that use the electron antineutrino scattering off electrons as the detection process. For this purpose, we have reanalyzed the experimental results, using the current prescription for the reactor antineutrino flux [34], to obtain a restriction on the mixing parameters of a sterile neutrino. Following this approach, the effective survival probability for short baseline antineutrino experiments in the 3+1 mixing scheme 1 can be written as [43] P SBL νe→νe = sin 2 2θ ee sin 2 ∆m 2 where The expected number of events, in the presence of a fourth, sterile, neutrino state, will be given in this case as where λ(E ν ) stands for the antineutrino spectrum; for energies above 2 MeV, this spectrum has been taken according to Ref [34]; on the other hand, if we need to include energies bellow 2 MeV, we have included the spectrum computed in Ref. [44]. R(T, T ) is the resolution function for the given experiment, P SBL να→να is the effective survival probability as given in Eq. (1), and dσ dT is the differential cross section for the antineutrino scattering off electrons, given as [45] dσ where m e stands for the electron mass and G F is the Fermi constant. In this expression, g L = 1/2 + sin 2 θ W and g R = sin 2 θ W are the usual Standard Model couplings. Several experiments using neutrino electron scattering as detection reaction have been performed along the years. Some of them have searched for a non-zero neutrino magnetic moment [46]. The experiments for our analysis will be TEXONO, MUNU, Rovno and Krasnoyarsk. The most recent experimental result has been given by the TEXONO Collaboration [9], that has reported the measurement of ten bins with an electron recoil energy between 3 and 8 MeV. The energy resolution for this experiment was σ(T ) = 0.0325 √ T [47]. A previous experiment, with a lower threshold, was performed by the MUNU Collaboration [48]. In this case, the error in the electron recoil energy was considered to be σ(T ) = 0.08T 0.7 [49]. We also considered the Rovno [7] and Krasnoyarsk [6] results. For these experiments, the fuel proportions, as well as the electron recoil energy window, are shown in Table I.
We have performed a goodness of fit analysis for the experiments quoted above. After performing the combined fit using the four reactor experiments, we have have obtained the restriction for the sterile oscillation parameters, sin 2 2θ ee and ∆m 2 41 , as shown in Fig. (1). We also show in this figure the allowed regions for the Gallium anomaly, recomputed from Ref. [50], taking into account the recent measurements of the Gamow-Teller transitions represented by Gallium-FF, Galliun-HF, and Gallium-HK cases. It is possible to notice that, although the restriction is not competitive with the signal reported by IBD experiments, the current resolution is enough to constrain a small region of the Gallium anomaly.

III. PERSPECTIVES FOR COHERENT NEUTRINO NUCLEUS SCATTERING IN REACTOR EXPERIMENTS
The CENNS is another interesting process to explore physics beyond the Standard Model. This interaction was proposed more than four decades ago within the SM context [22,51]. Different Collaborations and experimental proposals have considered the possibility of detecting the coherent neutrino-nucleus scattering [52][53][54][55]. Recently the COHERENT Collaboration has achieved the first detection of CENNS, opening a promising new era of low energy neutrino experiments.
In this section we will study four different proposals that plan to use a reactor as their antineutrino source. They are the TEXONO, MINER, RED100, and CONNIE experiments, that we describe briefly in what follows.
• The TEXONO Collaboration has proposed the use of high purity Germanium-based detectors, with a threshold energy of T thres ∼ 100 eV [52,56]. The Collaboration expects to develop a modular detector and reach 1 kg mass for the target. The reactor flux would come from the Kuo-Sheng nuclear power plant and the detector would be located 28 m away from the reactor. For a quenching factor Q f = 0.25 the expected number of events would be 4000 kg −1 year −1 [52].
• The MINER Collaboration will use a detector made of 72 Ge and 28 Si with a 2 : 1 proportion and with a threshold energy, T thres ∼ 10 eV. A TRIGA-type pool reactor will deliver an antineutrino flux with a fuel average proportion of ( 235 U: 238 U: 239 Pu: 241 Pu) given by [54] (0.967:0.013:0.02:0.001). With this special type of reactor, the detector can be located at a distance of 1 − 3 m from the source. An event rate of 5 − 20 kg −1 day −1 is forecast for this configuration [57]. In our simulations we will consider a 20 kg 72 Ge detector with one year of data taking at an event rate of 5 events kg −1 day −1 .
• The Kalinin power plant has also a program to detect CENNS. At least two different options appear in the literature. One is a germanium detector, νGeN [58], while the other one considers the use of liquid Xenon, RED100 [59]. We focus in the Xenon case as this material has been of interest for different experimental groups [60] and it is a different target with an energy threshold of T thres ∼ 0.5 keV [61]. The expected distance to the Kalinin reactor is about 15 m and they expect to detect 433 events per day. The expected fiducial mass is 100 kg [59]. As in the previous proposals, we consider one year of data taking.
• The CONNIE Collaboration [53] is currently working at the Angra-2 reactor using Charged-Coupled Devices (CCD's) as a detector, at 30 m from the reactor. The CCDs have an energy threshold of 50 eV. Although the expected events should be few, due to the CCD's low mass, the high resolution of the detectors may help to the detection of the CENNS. In this work we will consider as a benchmark 100 events.
In order to calculate the number of events for any of the above proposals, we use the following expression for the cross section, here, M is the mass of the nucleus, E ν is the neutrino energy, T is the nucleus recoil energy, F (q 2 ) is the nuclear form factor, and the neutral current vector couplings (including radiative corrections) are given by [24] g where ρ N C νN = 1.0082,ŝ 2 Z = sin 2 θ W = 0.23126,κ νN = 0.9972, λ uL = −0.0031, λ dL = −0.0025, and λ dR = 2λ uR = 7.5 × 10 −5 [62]. We have checked that, for a first analysis of the expected sensitivity to a sterile neutrino signal, the corresponding form factors, F (q 2 ), will not play a significant role 2 and, therefore we have taken them as unity in what follows. For estimating the number of expected events (SM) in the detector, we use the expression, where M detector is the mass of the detector, φ 0 is the total neutrino flux, t is the data taking time period, λ(E ν ) is the neutrino spectrum, E ν is the neutrino energy, and T is the nucleus recoil energy. The maximum recoil energy is related with the neutrino energy and the nucleus mass through the relation T max (E ν ) = 2E 2 ν /(M + 2E ν ). In all the cases we will consider one year of data taking.
For the oscillation to a fourth sterile family, we will consider the two families case in vacuum, where the number of events is In the above equation, P SBL να→να represents the neutrino survival probability as expressed in Eq. (1). The differential cross section has just been discussed above, and the antineutrino flux will depend on the specific reactor under consideration. With this expression we can make a forecast for different experimental setups. We will consider the case of the MINER, RED100, and TEXONO proposal with the fluxes and thresholds mentioned above. We will assume that each experiment will measure exactly the standard prediction for the three active neutrino picture. With this hypothesis we will obtain an expected χ 2 analysis assuming only statistical errors.
The result of this computations for the MINER Collaboration is shown in the Fig. (2), where we have considered two different baselines of 1 m and 3 m. Since we are using only statistical errors, our analysis can be considered as very optimistic. In order to consider the more realistic counterpart, we have also shown in the same figure the case where the detector can only achieve a 50 % efficiency. We can notice that for a baseline of 1 m the MINER Collaboration could exclude the current best fit point to the sterile neutrino analysis [64]. A similar analysis was done for the case of the RED100 proposal where we have considered the Kalinin nuclear power plant as the antineutrino flux source. We show in Fig. (3) the case of two different baselines and two possible efficiencies. The expectative to improve the current constraints on the mixing with a sterile neutrino is also promising in this case, despite the relatively high detection energy threshold. We have also analyzed the case of the TEXONO proposal. The results are shown in Fig. (4). As in the previous cases, we have also considered different possibilities for this proposal. In particular, we take into account different quenching factors for the detector. This factor represents the ratio of the electron recoil to nucleus recoil energy [65], which gives us an important correction since the detector response to a nucleus recoil energy is different from the response coming from electron calibration sources. The quenching factor is given by where E ee represents the electron equivalent energy and E N r is the nuclear recoil energy. In the case of the TEXONO experiment, we calculated the expected number of events for the quenching factors Q f = 1 and Q f = 0.2. The regions of mixing angle and squared-mass splitting favored by different combinations of quenching factors and detector efficiencies are shown in the Fig.(4). The results are in agreement with the previous work of Ref. [31] and shows other cases with a different quenching factor. The expectations for this proposal are competitive with the MINER and RED100 proposals as can be seen from Figs. (2) and (3).
We conclude this section comparing the expected signal for these proposals in two very different situations. Recently, the theoretical estimates for the antineutrino flux have been under deep scrutiny (see for instance [37,66]) and the Reactor anomaly might be solved by a re-evaluation of the neutrino fluxes. In this case, it is also possible that the CENNS experiments give a confirmation of this result, especially if several CENNS experiments with different baselines are performed, as seems to be the case. This situation is illustrated in Fig. (5), where we show what will be the antineutrino rate measured by these proposals if a 5 % decrease in the 235 U is considered [37] (without any sterile effect). On the other hand, we also show the expected ratio for the same experiments, in the case that the sterile neutrino is the responsible for the deficit. For this case we consider ∆m 2 = 1.7 eV 2 and sin 2 2θ ee = 0.062, according to the most recent fit of antineutrino disappearance data [64]. As expected, the different baselines will give a different ratio for the sterile solution. The situation is different if the reactor anomaly is due to a correction in the antineutrino flux, where the expected number of events will be different than for the oscillation explanation, especially for the RED100 and the MINER (1 m) cases. In this case, as expected, the complementarity of different experiments using different baselines, thresholds, and fuel proportions could be very helpful in discriminating what is the real explanation of the reactor anomaly.  neutrino with a sin 2 θ ee = 0.062 and ∆m 2 = 1.7 eV. The blue dots give the ratio for the case of a decrease in the 235 U of 5 % as proposed in a recent article [37]. The black line represents the average probability for a mean energy of 4 MeV, and the dotted black curve corresponds to an energy of 6.5 MeV, both with an energy resolution of 15 %.
And finally the error bars account for the statistical errors.

IV. CONCLUSIONS
In this work we have studied the reactor anomaly in the context of future CENNS experiments and in antineutrino electron scattering data from short baseline reactor neutrino experiments. Concerning antineutrino-electron scattering we conclude that this interaction can give limited information due to the relatively poor statistics, although it is possible to constrain a small region of the Gallium anomaly. On other hand, the recent observation of CENNS by the COHERENT Collaboration strongly motivates the further exploration of physics beyond the Standard Model in this context. We show that CENNS experiments could play an important role in the determination, or exclusion, of the sterile signal. Particularly, the RED100, TEXONO, and MINER proposals could test the current best fit point of the sterile allowed parameter space. Regarding the need of a precise antineutrino flux determination, CENNS is particularly attractive, since the detection technique is different from that of IBD detectors. In this case, we obtained the ratios between predicted and expected data in two different cases: considering sterile neutrinos and taking a decrease in the antineutrino flux as it is suggested by some recent works. Both situations could be of interest in order to explain the reactor antineutrino anomaly.