Light vector mediator search in the low-energy data of the CONNIE reactor neutrino experiment

The CONNIE experiment is located at a distance of 30 m from the core of a commercial nuclear reactor, and has collected a 3.7 kg-day exposure using a CCD detector array sensitive to an $\sim$1 keV threshold for the study of coherent neutrino-nucleus elastic scattering. Here, we use the results previously published by the CONNIE collaboration to constrain the allowed region in the parameter space of a Standard Model extension with a light vector mediator. We obtain new world-leading constraints for a light vector mediator with mass $M_{Z^{\prime}}<$ 10 MeV. These results constitute the first use of the CONNIE data as a probe for physics beyond the Standard Model.


Introduction
Coherent Elastic Neutrino-Nucleus Scattering (CEνNS) is a Standard Model (SM) process predicted more than 40 years ago [1] where a neutrino interacts coherently with all nucleons present in an atomic nucleus, resulting in an enhancement of the scattering cross section. The enhancement is approximately proportional to the square of the number of neutrons in the nucleus. However, despite its large cross section, this process took a long time to be observed due to the difficulty of measuring the low-energy nuclear recoils produced by the neutrino-nucleus scattering events. Recently, CEνNS was detected by the COHERENT collaboration [2] thanks to the development of novel detectors and the unique neutrino beam facility of the Spallation Neutron Source (SNS) at the Oak Ridge National Laboratory.
The potential for CEνNS as a tool to search for new physics has been extensively discussed in the literature [3,4]. More recently, data from COHERENT have opened a window into the low-energy neutrino sector. The COHERENT data imposed new constraints on non-standard neutrino interactions (NSI) [5,6], and established new limits on sterile neutrino models [7,8]. Other searches for new physics with COHERENT data are discussed in [9] and [10].
The COHERENT experiment explores the high-energy tail of CEνNS, using neutrinos with energies above 20 MeV in order to produce observable nuclear recoils in detectors with thresholds of the order of 20 keV. On the other hand, several efforts are ongoing to observe the CEνNS using neutrinos from nuclear reactors [11][12][13][14], with typical neutrino energy of around 1 MeV. However, the SM signal has not yet been detected due to the very low-energy nuclear recoil signals produced.
The Coherent Neutrino-Nucleus Interaction Experiment (CONNIE) [15] uses low-noise fully depleted charge-coupled devices (CCDs) [16] with the goal of measuring low-energy recoils from CEνNS produced by reactor antineutrinos with silicon nuclei [17]. The CONNIE engineering run, carried out in 2014-2015, is discussed in [18]. The detector installed in 2016 has an active mass of 73.2 g (12 CCDs) and is located 30 m from the core of the Angra 2 nuclear reactor, which has a thermal power of 3.95 GW. The CONNIE detector explores recoil energies down to 1 keV. A search for neutrino events is performed by comparing data with the reactor on (2.1 kg-day) and the reactor off (1.6 kg-day), the results show no excess in the reactor-on data [19]. A model independent 95% Confidence Level (C.L.) limit for new physics was established at an event rate of ∼40 times the one expected from the SM at the lowest energies.
In this work we use the CONNIE results presented in [19] to constrain the parameter space for extensions of the SM containing a light, neutral vector boson Z , with mass M Z that is comparable to the momentum transfer. Such extensions of the SM are of interest because there are no constraints from the Large Hadron Collider (LHC) when the mediator mass is below the GeV scale [9]. From the theoretical side, these models have attracted considerable attention because, among other things, they connect to new ideas associated with sub-GeV dark matter in the range of MeV to GeV [9,20]. To keep things as simple as possible, we will assume that there is no Z-Z mixing and that the Z has a purely vector interaction with the fermions of the SM, with a universal flavor-conserving coupling to the first generation of quarks and leptons.
The paper is organized as follows. In Section 2, the event rate for CEνNS in CONNIE is calculated in both the SM and its extension with an additional light vector mediator. In Section 3, the results of the CONNIE experiment are used to establish a limit on the parameter space for the light vector mediator extension. Two appendices have been included with details of the neutrino flux and detector performance information needed to calculate the event rate. These details are published elsewhere and given here for completeness.

Event rate in CONNIE
The CEνNS interaction happens when the three-momentum transfer q = |q| is small enough so that q 2 R 2 < 1, with R being the nuclear radius. In the laboratory frame, this corresponds to an energy of the incident antineutrino below 50 MeV. For reactor antineutrinos, the energies involved are below ∼5 MeV and the above condition is well satisfied. In the SM, the differential cross section for the coherent elastic scattering of antineutrinos off a nucleus at rest, with Z protons, N neutrons and mass M is given by where G F is the Fermi coupling constant, Eν e is the antineutrino energy, E R is the nuclear recoil energy and is the weak charge. Here, θ W is the weak mixing angle and F (q) is the nuclear form factor, which can be expressed as in [21] as where A is the atomic mass of the nucleus, a = 0.7 × 10 −13 cm is the range of the Yukawa potential considered, R = r 0 A 1/3 is the nuclear radius and ρ 0 = 3/4πr 3 0 is the nuclear density, with r 0 = 1.3 × 10 −13 cm being the average radius of a proton in a nucleus. At low energies, sin 2 θ W = 0.23857 [22].
Let us now take into consideration the non-standard interactions associated to a light vector mediator Z with mass M Z and coupling g . At tree level, the net effect on the CEνNS is merely a modification of the global factor Q 2 W in Eq. (2.4) [5]. Thus, the differential cross section now becomes: where In particular, for silicon nuclei (N = Z = 14), the expressions in Eqs. (2.2) and (2.5) reduce The CEνNS event rate as a function of the nuclear recoil energy where dσ/dE R is the differential cross section (Eq. (2.1) or Eq. (2.4)), dΦ/dEν e is the reactor antineutrino flux (discussed in Appendix A), N T is the number of nuclei in the detector and is the minimal antineutrino energy that can produce a nuclear recoil with energy E R .
The CONNIE sensors detect the ionization produced by the recoiling silicon nuclei. As discussed in Appendix B, the quenching factor Q relates the ionizing energy E I to the recoil energy: Taking this relation into account we get the differential event rate as a function of E I , The total rate R in the CONNIE experiment is given by where E M is the measured energy, (E M ) denotes the reconstruction efficiency (see Appendix B) and E th = 0.064 keV is the detector threshold given by the efficiency curve. Assuming a Gaussian detector response, the differential event rate as a function of E M is where with σ 2 I = (0.034 keV) 2 +F E eh E I characterizing the energy resolution of a typical CONNIE CCD [23]. Here, F is the Fano factor (0.133) and E eh is the mean ionization energy required for photons to produce an electron-hole pair in silicon (0.003745 keV) [24].

Search for light vector mediator using CONNIE data
The results in the recent CONNIE run discussed in Ref. [19] establish new limits for the rate of low-energy antineutrino events coming from non-standard interactions R N SI based on a comparison of reactor-on (RON) and reactor-off (ROFF) data. These limits are shown in Fig. 1, together with the expected event rate for the Standard Model, R SM . From the lowest energy bin of this figure, we see that the 95% C.L. upper limit established by CONNIE is 41 times above the SM prediction using the measurements of quenching factor in Ref. [25]. This allows us to set the limit R N SI < R SM × 41 for 0.075 keV < E M < 0.275 keV (or recoil energies 0.784 keV < E R < 1.834 keV). Here, we apply this limit on R N SI in order to constrain a possible extension of the SM with a light vector mediator as described by Eq. (2.4). The 95% C.L. exclusion limits for the model parameters g and M Z are shown in Fig. 2. The most significant systematic uncertainty in this limit comes from the quenching factor measurement, as discussed in Ref. [19]. To quantify the effect of this uncertainty, we also include in Fig. 2 the exclusion region calculated using the quenching factor from Ref. [26]. g' Figure 2. Exclusion region in the (M Z , g ) plane from the CONNIE results assuming quenching given by the fit to the measurements in Ref. [25] (orange) and the expressions in Ref. [26] (red). The COHERENT limit curve [5] (blue) and the 2σ allowed region to explain the anomalous magnetic moment of the muon (∆a µ = 268 ± 63 × 10 −11 ) [27,28] (green) are shown for reference.
mediator, M Z √ 2M E R , the NSI contribution depends only on g and the limit becomes independent of mass. For a heavy mediator, M Z √ 2M E R , the NSI rate contribution is proportional to the ratio g /M Z c 2 . These two regimes are visible in Fig. 2. Moreover, the CONNIE limit curve confirms the statement in Ref. [5], disfavoring a light vector mediator to explain the discrepancy in the anomalous magnetic moment of the muon.

Conclusion
We use the recent results of the CONNIE experiment [19] to examine the constraints on neutrino neutral-current interactions associated to a light vector-boson extension of the SM. As a result of this analysis, a new world-leading limit is established for the low-mass regime M Z < 10 MeV, extending beyond the region excluded by the COHERENT results [18].
This analysis demonstrates the power of combining a high flux of low-energy antineutrinos from a nuclear reactor with a low-threshold detector as a tool for exploring new physics. The results constitute the first search for NSI with reactor neutrinos and CCDs, and are expected to be the first in a series of searches using the CONNIE data.
Two features of the present study are expected to be improved in the future. The current analysis is based on a counting experiment, comparing the number of events above threshold in CONNIE with the expectations from a model with a light vector mediator. A more powerful limit is expected when spectral information of the CONNIE data is included in the analysis. Additionally, the CONNIE collaboration has recently modified the operation of the detector, performing hardware binning on the CCDs (adding charge of several pixels before readout) and reducing the effect of readout noise for the low-energy events. This operating mode improves the efficiency of the detector at low energies. An updated result using data taken with this mode is expected soon.

A Reactor flux
The CONNIE detector is located 30 m from the core of the Angra 2 reactor of the Almirante Alvaro Alberto Nuclear Power Plant, in Rio de Janeiro, Brazil. The thermal power of this reactor is 3.95 GW = 2.46 × 10 22 MeV/s. Considering that the average energy released per fission is 205.24 MeV, the number of fissions per second for this reactor is n f = 1.2 × 10 20 .
The β decays of the fission products, following the fission of four principal fissile isotopes ( 235 U, 238 U, 239 Pu and 241 Pu), produce a large number ofν e , contributing approximately 84% to the total reactor's antineutrino flux. Each fissile isotope has its ownν e spectrum, which has been taken from [29]. For energies below 2 MeV, the antineutrino spectra are given as tabulated values in Table 1 where the fitted parameters are listed in Table 2.
Another process that contributes approximately 16% to the reactor antineutrino flux is the neutron capture of 238 U nuclei. These nuclei capture 0.6 neutrons per fission via the reaction 238 U + n → 239 U → 239 Np → 239 Pu. The β decay of 239 U produces twoν e . The antineutrino spectrum of this process was extracted from [30].
Each process previously considered has its ownν e yield and fission rate. The respective values were taken from [30] and are shown in Table 3.  Table 3. Typical relative fission contribution andν e yield for each process considered [30].
In order to obtain the total antineutrino reactor spectrum per fission per MeV, dNν e /dEν e , the individual spectra were summed after being normalized and multiplied by their correspondingν e yield per fission.
The total antineutrino flux, i.e. the number of antineutrinos per MeV per cm 2 per second, crossing the CONNIE detector is given by where d = 30 × 10 2 cm is the distance between the reactor and the detector. The flux expected at the CONNIE detector is shown in Fig. 3.

B Fitting functions for quenching factor and efficiency
When a nuclear recoil is produced inside the detector, a part of its energy generates charge carriers (E I ) and the rest contributes to the increase of the thermal energy of the system. The nuclear recoil quenching factor Q is defined as the fraction of the total recoil energy E R that is used to produce ionization For E R 4 keV, the nuclear recoil quenching factor is well modelled by Lindhard [26]. Two measurements of the quenching factor for E R below 4 keV were performed using similar detectors in different experiments [25,31]. An analytical fit to the measurements in [25] is used here, parametrized as with p 0 = 56 keV 3 , p 1 = 1096 keV 2 , p 2 = 382 keV, p 3 = 168 keV 2 and p 4 = 155 keV, as shown in Fig. 4.  In order to extract and reconstruct the events registered during a CCD exposure, a set of processing tools is used. The reconstruction efficiency for these tools has been evaluated in Ref. [19] using simulated events. The computed efficiency is fitted well for E M > 64 eV by