Probing light sterile neutrino signatures at reactor and Spallation Neutron Source neutrino experiments

TL;DR

This paper explores the potential to detect light sterile neutrinos using reactor and Spallation Neutron Source experiments, focusing on coherent elastic neutrino-nucleus scattering measurements with advanced Germanium detectors.

Contribution

It presents a detailed sensitivity analysis for TEXONO and COHERENT experiments to identify sterile neutrino effects, incorporating realistic nuclear structure models.

Findings

Potential to observe sterile neutrino signatures in existing experiments

Enhanced detection sensitivity with sub-keV Germanium detectors

Quantitative assessment of sterile neutrino impact on scattering rates

Abstract

We investigate the impact of a fourth sterile neutrino at reactor and Spallation Neutron Source neutrino detectors. Specifically, we explore the discovery potential of the TEXONO and COHERENT experiments to subleading sterile neutrino effects through the measurement of the coherent elastic neutrino-nucleus scattering event rate. Our dedicated $\chi^2$-sensitivity analysis employs realistic nuclear structure calculations adequate for high purity sub-keV threshold Germanium detectors.

Equations

$$⟨f|{\hat{H}}_{eff}|i⟩=\frac{G_F}{\sqrt{2}}\int d^3\mathbf{x}⟨{\ell }_f|{\hat{j}}_{\mu }^{lept}|{\ell }_i⟩⟨J_f|{\hat{\mathcal{J}}}^{\mu }(\mathbf{x})|J_i⟩,$$

$$⟨{\ell }_f|{\hat{j}}_{\mu }^{lept}|{\ell }_i⟩={\bar{\nu }}_{\alpha }{\gamma }_{\mu }(1-{\gamma }_5){\nu }_{\alpha }{e}^{-i\mathbf{q}\cdot \mathbf{x}},$$

$${\left(\frac{d\sigma }{d\cos \theta }\right)}_{\mathrm{SM}}=\frac{G_F^2}{2\pi }{E}_{\nu }^2\left(1+\cos \theta \right){\left|⟨gs||{\hat{\mathcal{M}}}_{00}(Q)||gs⟩\right|}^2.$$

$$\left|⟨gs||{\hat{\mathcal{M}}}_{00}(Q)||gs⟩\right|=\int d^{3}r{j}_0(|\mathbf{q}|r)$$

$$\times$$

$$\displaystyle+\left[(g_{\alpha\alpha}^{u,L}+g_{\alpha\alpha}^{u,R})+2(g_{\alpha\alpha}^{d,L}+g_{\alpha\alpha}^{d,R})\right]\rho_{n}(r)\Big{\}}\,,$$

$$-q_{\mu }{q}^{\mu }=Q^2=2E_{\nu }^2(1-\cos \theta ),$$

$$g_{\alpha \alpha }^{u,L}=$$

$$g_{\alpha \alpha }^{d,L}=$$

$$g_{\alpha \alpha }^{u,R}=$$

$$g_{\alpha \alpha }^{d,R}=$$

$$F_{N_n}(Q^2)=\frac{1}{N_n}\sum _j\sqrt{2j+1}⟨j|j_0(|\mathbf{q}|r)|j⟩{\left({\upsilon }_{N_n}^j\right)}^2,$$

$${\eta }_{{\nu }_e}^{\mathrm{SNS}}(E_{\nu })=$$

$${\eta }_{{\bar{\nu }}_{\mu }}^{\mathrm{SNS}}(E_{\nu })=$$

$$P_{ee}=1-4\sum _{i=1}^3\sum _{j>i}^4{\left|U_{ei}\right|}^2{\left|U_{ej}\right|}^2{\sin }^2\left({\Delta }_{ji}\right),$$

$$U_{e1}$$

$$U_{e2}$$

$$U_{e3}$$

$$U_{e4}$$

$$P_{ee}\simeq 1-$$

$$-$$

$$P_{ee}=1-{\sin }^{2}2{\theta }_{14}{\sin }^2\left(\frac{\Delta m_{41}^{2}L}{4E_{\nu }}\right).$$

$$\frac{d{N}_{\mathrm{sterile}}^{events}}{d{T}_N}=$$

$$\times {\int }_{-1}^{1}d\cos \theta \frac{d{\sigma }_{{\nu }_{\alpha }}}{d\cos \theta }\delta \left(T_N-\frac{Q^2}{2M}\right),$$

$$\lambda =\mathrm{react},\mathrm{SNS},$$

$$N_{\mathrm{sterile}}^{events}={\int }_{T_{\mathrm{thres}}}^{T_{\max }}\frac{d{N}_{\mathrm{sterile}}^{events}}{d{T}_N}d{T}_N,$$

$$\mathcal{Q}u(T_N)=r_1{\left[\frac{T_N}{1\mathrm{keV}}\right]}^{r_2},r_1\simeq 0.256,r_2\simeq 0.153.$$

$$\mathcal{R}=\frac{N_{\mathrm{sterile}}^{events}}{N_{\mathrm{SM}}^{events}},$$

$${\chi }^2({\sin }^{2}2\theta ,\Delta m_{41}^2)=\underset{\xi }{\min }\left[{\chi }^2({\sin }^{2}2\theta ,\Delta m_{41}^2,\xi )\right]$$

$$=\underset{\xi }{\min }\left[{\left(\frac{N_{\mathrm{SM}}^{events}-N_{\mathrm{sterile}}^{events}(1+\xi )}{{\sigma }_{\mathrm{stat}}}\right)}^2+{\left(\frac{\xi }{{\sigma }_{\mathrm{sys}}}\right)}^2\right],$$

$${\chi }_{\min }^2({\sin }^{2}2\theta ,\Delta m_{41}^2)=\frac{{\left(N_{\mathrm{SM}}^{events}-N_{\mathrm{sterile}}^{events}\right)}^2}{{\sigma }_{\mathrm{stat}}^2+{\left({\sigma }_{\mathrm{sys}}{N}_{\mathrm{sterile}}^{events}\right)}^2}.$$

$${\sin }^{2}2{\theta }_{\alpha \alpha }$$

$${\sin }^{2}2{\theta }_{\alpha \beta }$$

$$P_{\alpha \alpha }$$

$$P_{\alpha \beta }$$

$${\sin }^{2}2{\theta }_{ee}\simeq 4|U_{e4}{|}^2.$$

$${\sin }^{2}2{\theta }_{\mu \mu }\simeq 4|U_{\mu 4}{|}^2.$$

$${\sin }^{2}2{\theta }_{e\mu }=\frac{1}{4}{\sin }^{2}2{\theta }_{ee}{\sin }^{2}2{\theta }_{\mu \mu },$$

Full text

I Introduction

Recently, several neutrino experiments have been designed to operate with exceptional high sensitivities in order to detect neutral-current coherent elastic neutrino-nucleus scattering (CE$\nu$NS) events Scholberg (2006); Wong (2010) for the first time Brice et al. (2014); Collar et al. (2015). Potential deviations from the standard model (SM) expectations would provide a glimpse on new physics Papoulias and Kosmas (2014, 2015a); Kosmas et al. (2015a). Indeed, the existence of a fourth sterile neutrino could be probed in ultralow threshold neutrino-nucleus coherent scattering, since it would generate tiny modifications in the final neutrino spectrum Anderson et al. (2012); Dutta et al. (2016a). The purely neutral character of CE$\nu$NS provides an important advantage Freedman (1974); Tubbs and Schramm (1975); Drukier and Stodolsky (1984), compared to neutrino-electron scattering since there is no need for disentangling the sterile neutrino mixing from that of the active neutrinos Formaggio et al. (2012).

On the other hand the solid evidence for neutrino oscillations implied by current solar and atmospheric data, and confirmed by reactor and accelerator neutrino experiments Kajita (2016); McDonald (2016); Forero et al. (2014); Valle and Romao (2015) still leaves some loopholes. These come in the form of controversial anomalies which do not fit in the three-neutrino oscillation paradigm. The Gallium Hampel et al. (1998); Abdurashitov et al. (2009), LSND Athanassopoulos et al. (1995); Aguilar et al. (2001), and MiniBooNE Aguilar-Arevalo et al. (2007, 2012, 2013) anomalies, as well as the new predictions for reactor neutrino fluxes Mention et al. (2011); Mueller et al. (2011); Huber (2011) have raised speculations on whether the actual number of neutrinos could exceed three. Taken at face value, these have suggested the possible existence of at least one sterile neutrino with new mixings to the three active neutrinos. The indicated squared mass splittings are of the order of $1\,$eV2 Gonzalez-Garcia and Maltoni (2008); Gariazzo et al. (2016). Following earlier theoretical Peltoniemi and Valle (1993); Peltoniemi et al. (1993) and phenomenological considerations Maltoni et al. (2004), the possible existence of a fourth neutrino has drawn a lot of attention and many recent studies have been carried out de Gouvea and Wytock (2009); Giunti and Laveder (2011); Kopp et al. (2013); An et al. (2014a); Giunti and Zavanin (2016). In fact, an arbitrary number of $\mathrm{SU(2)_{L}}$ singlet fermions are present in the generalized type I seesaw mechanism Schechter and Valle (1980) such as realized in low-scale seesaw schemes  Mohapatra and Valle (1986); Akhmedov et al. (1996a, b); Malinsky et al. (2005). If it exists, the sterile neutrino is expected to take part in neutrino oscillations. Notice however that, despite the limits on the number of sterile neutrino states coming from cosmology Lesgourgues et al. (2013), depending on the active-sterile mixing strength and their corresponding mass scale, such cosmological constraints may be adequately fulfilled Giunti (2016). Furthermore, sterile neutrino states may induce a number of processes with important phenomenological consequences to solar de Holanda and Smirnov (2011), reactor An et al. (2014b); Ahn et al. (2012); Abe et al. (2012) and accelerator Bandyopadhyay et al. (2009) neutrino oscillations at the sub-eV scale, possible neutrino electromagnetic interactions at the eV scale Balantekin and Vassh (2014), dark matter at the keV scale Ando and Kusenko (2010); Liao et al. (2014), etc. Moreover, the impact of a light sterile neutrino on the neutrinoless double beta-decay and single beta-decay processes has also received some attention Bilenky et al. (2003); Vergados et al. (2012); Giunti and Laveder (2010).

Here we examine the possibility of probing light sterile neutrinos at short-baseline CE$\nu$NS experiments operating with nuclear detectors of low-threshold capabilities Soma et al. (2016); Dutta et al. (2016b); Chen et al. (2016). A number of experiments are now planned in order to probe possible oscillation features due to the presence of sterile neutrinos. Specifically we examine the observation potential of the COHERENT experiment at Oak Ridge Akimov et al. (2015) and the TEXONO experiment in Taiwan Kerman et al. (2016); Sevda et al. (2017). Other relevant projects looking for this signature are the $\nu$GeN Belov et al. (2015) and the GEMMA Beda et al. (2013) experiments in Russia, as well as the CONNIE project in Brazil Fernandez Moroni et al. (2015); Aguilar-Arevalo et al. (2016) and the MINER experiment at Texas A&M University Agnolet et al. (2017). Notable efforts aiming at observing CE$\nu$NS by using cryogenic detector techniques include the Ricochet Billard et al. (2017) and the $\nu$-cleus Strauss et al. (2017) experiments. Our calculations are performed using advanced nuclear physics techniques, such as the quasiparticle random phase approximation (QRPA), in which the required nuclear form factors are obtained with high accuracy Papoulias and Kosmas (2015b). We also address the quenching effects which are crucial in order to provide realistic results Kosmas et al. (2015b). For the specific case of the aforementioned reactor and spallation neutron source (SNS) experiments, we perform a $\chi^{2}$ sensitivity analysis to explore the possibility that the detection of CE$\nu$NS Lindner et al. (2017); Dent et al. (2016); Coloma et al. (2017) constitutes an efficient probe for sterile neutrino searches at low energies.

The paper has been organized as follows. We first go through a brief description of the relevant formalism of CE$\nu$NS including sterile neutrinos in Sec. II. In Sec. III we summarise the main features of the relevant experiments, such as TEXONO and COHERENT, necessary for our work. In Sec. IV we discuss the impact of a light sterile neutrino in neutrino-nucleus scattering. The results of our calculations are discussed in Sec. V, where we extract the expected sensitivities on the model parameters. Finally, in Sec. VI we close with a summary of our main conclusions.

II Coherent elastic neutrino-nucleus scattering

At low and intermediate energies, considered in the present study, the neutral-current neutrino-nucleus processes are described by the matrix elements of an effective interaction Hamiltonian, written in terms of the leptonic $\hat{j}_{\mu}^{lept}$ and hadronic (nuclear) $\hat{\mathcal{J}}^{\mu}$ currents as

[TABLE]

where $G_{F}$ is the Fermi constant. The matrix element of the leptonic current, between an initial $|\ell_{i}\rangle$ and a final lepton state $|\ell_{f}\rangle$ takes the usual V-A form

[TABLE]

with $\alpha=\{e,\mu,\tau\}$ being the neutrino flavor and $\mathbf{q}$ denoting the three momentum transfer. The hadronic matrix element is obtained through a multipole decomposition as described in Refs. Giannaka and Kosmas (2015); Chasioti and Kosmas (2009). Then, the differential cross section with respect to the scattering angle $\theta$, for the CE$\nu$NS ($gs\rightarrow gs$ transitions) off a spherical spin-zero nucleus, reads Papoulias and Kosmas (2014, 2015b)

[TABLE]

The coherent nuclear matrix element is written in terms of the left- and right-handed couplings of the $u$- and $d$-quarks to the $Z$-boson as Papoulias and Kosmas (2014)

[TABLE]

where the notation $r=|\mathbf{x}|$ has been introduced. In the latter expression, $\rho_{p}(r)$ and $\rho_{n}(r)$ are the corresponding proton and neutron charge density distributions computed through realistic nuclear structure calculations in the context of the QRPA method. In such calculations, the finite nucleon and nuclear size are taken into consideration by weighting the differential cross section with corrections provided by the associated proton (neutron) nuclear form factors $F_{Z(N)}(Q^{2})$ that depend on the square of the four momentum transfer

[TABLE]

or $Q=2E_{\nu}\sin(\theta/2)$. In Eq.(4), the $u$- and $d$-quark couplings to the $Z$-boson include the relevant radiative corrections, through the expressions

[TABLE]

with $\hat{s}^{2}_{Z}=\sin^{2}\theta_{W}=0.23120$, $\rho_{\nu N}^{NC}=1.0086$, $\hat{\kappa}_{\nu N}=0.9978$, $\lambda^{u,L}=-0.0031$, $\lambda^{d,L}=-0.0025$ and $\lambda^{d,R}=2\lambda^{u,R}=7.5\times 10^{-5}$ Beringer et al. (2012).

II.1 Nuclear physics calculations

It can be noticed that the CE$\nu$NS cross section is rather sensitive to the neutron form factor, calculable in the context of a nuclear structure model. In this work, the reliability of the evaluated cross sections is maximized by performing QRPA calculations, incorporating realistic strong nuclear forces within the framework of a comprehensive phenomenological meson-exchange theory for the reliable description of the nucleon-nucleon interaction. Our QRPA code, for the two-nucleon residual interaction utilizes the C-D version of the well-known Bonn potential Machleidt et al. (1987); Stoks et al. (1994). This way, the invariance under any rotation in isospin space, is reproduced accurately. The off shell behaviour of Bonn C-D is based upon the relativistic Feynman amplitudes for meson-exchange ($\eta,\pi,\rho,\omega,\sigma$ and $\,\phi$ mesons in our case), a fact that has attractive consequences in nuclear structure applications Machleidt (2001).

Motivated by its successful application on similar calculations for various semileptonic nuclear processes Kosmas and Vergados (1992); Kosmas et al. (2001); Kosmas and Vergados (1989); Tsakstara and Kosmas (2011), the QRPA method is employed in this work to construct explicitly the nuclear ground state, $|gs\rangle\equiv|0^{+}\rangle$, of the studied even-even isotope (76Ge in our case) through the numerical solution of the BCS equations. The vector proton (neutron) nuclear form factors are evaluated as

[TABLE]

where $N_{n}=Z\,\,(\mathrm{or}\,\,N)$ and $\upsilon^{j}_{N_{n}}$ denotes the occupation probability amplitude of the $j$th single-nucleon orbit (see e.g. Ref. Papoulias and Kosmas (2015b)).

III Experimental Setups

III.1 Reactor neutrino experiments

Recently, it became feasible to detect neutrino-nucleus scattering events by using high purity germanium-based detectors (HPGe detector) Soma et al. (2016); Kosmas et al. (2015b). In this work, we are interested in the possibility of probing the existence of a fourth light sterile neutrino through potential deviations on the low-energy CE$\nu$NS measurements at reactor neutrino experimental facilities, such as TEXONO Kerman et al. (2016); Sevda et al. (2017), $\nu$GeN Belov et al. (2015), GEMMA Beda et al. (2013), CONNIE Fernandez Moroni et al. (2015); Aguilar-Arevalo et al. (2016) and MINER Agnolet et al. (2017). We have considered as reference experimental setup 1 kg of 76Ge detector and a detection threshold of 100 $\mathrm{eV_{ee}}$ 111$\mathrm{eV_{ee}}$ refers to the electron equivalent energy, and should be distinguished from the nuclear recoil energy, $\mathrm{eV_{nr}}$ (see Sec. V).. We note, however, that the absence of precise information regarding the fuel composition restricts us to take into account only the dominant component of the antineutrino spectrum provided by 235U. In this respect, for the present study we assume a typical flux of $\Phi_{\bar{\nu}_{e}}\sim 10^{13}$ $\nu\,\mathrm{s^{-1}\,cm^{-2}}$ for a detector located at 28 m from the 2.9 GW reactor core. In order to estimate the emitted $\bar{\nu}_{e}$ energy-distribution, $\eta_{\bar{\nu}_{e}}^{\mathrm{react}}(E_{\nu})$, for energies above 2 MeV, existing experimental data from Ref. Mueller et al. (2011) are employed, while for energies $E_{\bar{\nu}_{e}}<2$ MeV existing theoretical estimations Kopeikin et al. (1997) are assumed.

III.2 Spallation Neutron Source experiments

The Spallation Neutron Source at Oak Ridge Scholberg (2006) has been recently considered as a promising facility to measure CE$\nu$NS events within the SM Collar et al. (2015); Papoulias and Kosmas (2015b) as well as to explore exotic neutrino properties Papoulias and Kosmas (2014); Kosmas et al. (2015a); Papoulias and Kosmas (2015a). The COHERENT experiment Akimov et al. (2015) aims to use intense neutrino beams (of the order of $\Phi_{\nu_{\alpha}}\sim 10^{7}\,\nu\,\mathrm{s^{-1}cm^{-2}}$ per flavor) resulting from pion decay. Specifically, the stopped-pion neutrino beam consists of: (i) monochromatic muon-neutrino $\nu_{\mu}$ flux with energy 29.9 MeV produced via pion decay at rest $\pi^{+}\rightarrow\mu^{+}\nu_{\mu}$ within $\tau=26\,\mathrm{ns}$ (prompt flux) and (ii) electron neutrinos, $\nu_{e}$, and muon antineutrinos, $\bar{\nu}_{\mu}$, that are emitted from the muon-decay $\mu^{+}\rightarrow\nu_{e}e^{+}\bar{\nu}_{\mu}$ within $\tau=2.2\,\mathrm{\mu s}$ (delayed flux) Efremenko and Hix (2009). The delayed flux is described by the well-known normalized distributions Aguilar-Arevalo et al. (2009); Louis (2009)

[TABLE]

with $E_{\nu}^{\text{max}}=M_{\mu}/2$ and $M_{\mu}=105.6\,\mathrm{MeV}$ denoting the muon rest mass.

In this work, the calculation is performed for two cases corresponding to (i) the “current” configuration: a (20Ne, 40Ar, 76Ge, 132Xe) target with mass (391, 456, 100, 100) kg located at (46, 46, 20, 40) m from the source with energy threshold of (30, 20, 10, 8) $\mathrm{keV_{nr}}$ and a running time of $2.4\times 10^{7}$s, and (ii) the “future” configuration: 1 ton of detector mass located at 20 m from the source with energy threshold $1~{}\mathrm{keV_{nr}}$ and 1 year of data taking time (see e.g Ref. Kosmas et al. (2015a)).

IV Neutrino oscillations with a light sterile neutrino

In the present study, we employ a minimal extension of the standard model by considering a fourth light sterile neutrino state added to the three active neutrinos. In this case, neutrino flavor eigenstates $\nu_{\alpha}$, with $\alpha=\{e,\mu,\tau,s,\cdots\}$ are related to neutrino mass eigenstates $\nu_{i}$, with $i=\{1,2,3,4,\cdots\}$ through a unitary transformation as $\nu_{\alpha}=\sum_{i}U_{\alpha i}\nu_{i}$. Sterile neutrino mass schemes have been considered in the literature with various motivations. Attractive possibilities are the early 2+2 models Peltoniemi and Valle (1993); Peltoniemi et al. (1993). While they still constitute probably one of the most interesting sterile extensions of the standard model, their original motivation is gone. On the other hand, they are strongly restricted by solar and atmospheric data and do not allow for the eV-scale neutrino mass we are interested in here Maltoni et al. (2003, 2004); Kopp et al. (2011). For this reason, we focus on the (3+1) scheme, which does allow for eV-neutrino masses as long as the doublet-singlet mixing angles are adequately small, so that the sterile state decouples from both solar and atmospheric conversions, a possibility absent in the 2+2 schemes.

The generated reactor antineutrinos $\bar{\nu}_{e}$ of energy $E_{\nu}$ are expected to travel the propagation distance $L$ with the survival probability

[TABLE]

where $\Delta_{ji}=\Delta m^{2}_{ji}L/4E_{\nu}$, with the mass splittings denoted as $\Delta m^{2}_{ji}=m^{2}_{j}-m^{2}_{i}$. In this work we will consider values of $\Delta m^{2}_{ji}$ of the order of $1~{}\mathrm{eV}^{2}$, as required in order to account for the current neutrino anomalies. The matrix elements entering Eq.(9) take the form

[TABLE]

In this framework, the hypothesis of a fourth neutrino generation yields the approximate electron neutrino survival probability for a given value of ($L/E_{\nu}$)

[TABLE]

Note that, for vanishing $\theta_{14}$ or neutrino paths larger than 100 m, the latter expression reduces to the well-known oscillation probability for short-baselines probed at the new generation of reactor experiments such as Daya Bay An et al. (2014b), RENO Ahn et al. (2012) and Double Chooz Abe et al. (2012). On the contrary, at shorter distances, atmospheric neutrino driven oscillations can be neglected and the neutrino survival probability can be effectively parametrized as

[TABLE]

V Numerical results

Reactor neutrino experiments are sensitive to the mixing matrix element $U_{e4}$, while SNS experiments are sensitive to both $U_{e4}$ and $U_{\mu 4}$, through the measurement of $\sin^{2}2\theta_{14}$. In the presence of sterile neutrinos, the differential event rate in terms of the nuclear recoil energy $T_{N}$, reads

[TABLE]

where $M$ is the nuclear mass and $K=N_{targ}\Phi_{\nu_{\alpha}}t_{tot}$, with $N_{targ}$ denoting the total number of atoms in the detector and $t_{tot}$ the time window of exposure. The incident neutrino flux is given by $\Phi_{\nu_{\alpha}}$, while $\eta^{\mathrm{react}}_{\nu_{\alpha}}$ and $\eta^{\mathrm{SNS}}_{\nu_{\alpha}}$ denote the neutrino energy-distributions at reactor experiments and SNS, respectively. Note that, in contrast to our previous studies Kosmas et al. (2015a, b), the above expression includes the effect of flavor oscillations in the neutrino propagation. Then, the number of events for a given detector threshold, $T_{\mathrm{thres}}$, is evaluated through the integral

[TABLE]

where $T_{\mathrm{max}}$ is the maximum recoil energy obtained from the kinematics of the process Papoulias and Kosmas (2014).

Focusing on the relevant CE$\nu$NS experiments, the detectable energy is lower than the energy imparted to the nuclear target ($\mathrm{eV_{nr}}$), since the employed detectors are sensitive to an ionization energy equivalent to an electron energy ($\mathrm{eV_{ee}}$) Giomataris and Vergados (2006). To account for the energy loss due to the conversion to phonons in such measurements, the present calculations take into consideration the quenching effect on the nuclear recoil events by multiplying the energy scale by a quenching factor, $\mathcal{Q}_{f}$ Vergados et al. (2009). In general, $\mathcal{Q}_{f}$ varies with the nuclear recoil energy and, usually, for its estimation the following empirical form is considered Simon et al. (2003):

[TABLE]

The dependence of $\mathcal{Q}_{f}$ on the nuclear recoil energy, $T_{N}$, is shown in Fig. 1 where the equivalent electron energy as a function of $T_{N}$ is also presented. The top panel of Fig. 2, illustrates the variation of the expected CE$\nu$NS event rates at different thresholds and quenching factors at the TEXONO reactor experiment. On the other hand, in the bottom panel of Fig. 2, based on the $\chi^{2}(\mathcal{Q}_{f})=\min_{\xi}\left[\chi^{2}(\mathcal{Q},\xi)\right]$ function we examine how well the quenching factor is required to be known in order to record a clear signal, assuming SM interactions only. For this calculation, a 1 kg 76Ge detector has been assumed with a threshold of 100 $\mathrm{eV_{ee}}$, one year of exposure and various systematic errors. Following Ref. Soma et al. (2016), the considered background is set at 1 cpd e.g. 1 event  $\mathrm{day^{-1}~{}kg^{-1}~{}keV^{-1}}$ ensuring a signal-to-noise ratio $>22$ (for its spectral shape the reader is referred to Ref Lindner et al. (2017)).

In order to get an idea of how the presence of sterile neutrinos affects the expected number of events at a given detector, we define the ratio

[TABLE]

i.e., the portion of events originated from sterile neutrinos in the total number of SM events. We mention that $\mathcal{R}$ is independent of the detector mass and may also limit inevitable flux uncertainties. Apparently, the equality $\mathcal{R}=\left\langle\sigma\right\rangle_{\mathrm{sterile}}/\left\langle\sigma\right\rangle_{\mathrm{SM}}$ holds true, where $\left\langle\sigma\right\rangle_{\mathrm{SM}}$ stands for the SM cross section averaged over the reactor neutrino flux distribution, while $\left\langle\sigma\right\rangle_{\mathrm{sterile}}$ denotes the corresponding flux-averaged cross section that includes also the oscillation probability. Figure 3 shows the variation of $\mathcal{R}$ with the distance $L$ for various choices of the sterile neutrino parameters, assuming a 76Ge detector with mass 1 kg and an energy threshold of $T_{\mathrm{thres}}=100~{}\mathrm{eV_{ee}}$ at the TEXONO experiment. The quenching effect is taken into account, while for comparison, the corresponding results obtained by neglecting the quenching effect are also illustrated.

The relevant experiments searching for CE$\nu$NS are subject to a number of uncertainties that should be effectively taken into account in order to come out with realistic estimates of the sensitivity to possible new physics phenomena. In such type of experiments the dominant contributions to systematic uncertainties are linked to the lack of precise knowledge on the neutrino flux, the quenching factor, the detector threshold, mass and performance, distance from the source, etc Lindner et al. (2017). Background uncertainties depend on the various experimental setups and include mostly beam-related backgrounds (e.g. neutrino-induced neutrons), internal beta- and gamma-radioactivity and other secondary backgrounds from shielding materials Dent et al. (2016). Based on the pull method, in our attempt to quantify the sensitivity of a given CE$\nu$NS experiment to sterile neutrinos, we define the $\chi^{2}$ function

[TABLE]

with $\sigma_{\mathrm{stat}}=\sqrt{N_{\mathrm{SM}}^{events}+N_{\mathrm{bkg}}^{events}}$, minimized over the nuisance parameter $\xi$. Following a conservative approach, in this work we adopt typical values to account for the systematic error, i.e. $\sigma_{\mathrm{sys}}=10\%$. For the case of TEXONO we consider a background level of 1 cpd, while for the case of COHERENT we assume that the number of background events is of the order of $20\%$ of the $N_{\mathrm{SM}}^{events}$ Akimov et al. (2015). For convenience it is also useful to obtain the minimum $\chi^{2}$ with respect to $\xi$ analytically, as

[TABLE]

Note that, by neglecting the systematic uncertainty, the latter reduces to the simple $\chi^{2}$ form employed in our previous works Kosmas et al. (2015b, a).

We mention that, due to the smallness of $\theta_{13}$, recently measured at Daya Bay An et al. (2014b), for simplicity in our calculations we set $\sin^{2}2\theta_{13}=0$. Moreover, we use the fact that, within the framework of the (3+1) scheme, it holds

[TABLE]

where $\alpha,\beta=e,\mu,\tau,s$. Focusing on the relevant short-baseline (SBL) neutrino experiments, the above expressions enter into the respective effective survival and transition probabilities, valid for neutrinos and antineutrinos

[TABLE]

In Fig. 4 we illustrate the 90% C.L. sensitivity contours in the $(|U_{e4}|^{2},\,\Delta m^{2}_{41})$ plane for the TEXONO experiment, obtained from a two-parameter $\chi^{2}$ analysis as described above and by taking into account the quenching effect. The present calculations consider a 76Ge detector with: 1 kg mass, $100~{}\mathrm{eV_{ee}}$ energy threshold and one year of data collection time. For comparison, also shown is the corresponding sensitivity region in the $(|U_{\mu 4}|^{2},\,\Delta m^{2}_{41})$ plane for the case of the COHERENT experiment assuming its “current” setup (see Sec. III).

Our present results indicate clearly that a dedicated experiment searching for CE$\nu$NS has also satisfactory capabilities to probe sterile neutrinos. For the case of the TEXONO experiment, the lack of $\bar{\nu}_{e}$ disappearance results in the sensitivity regions are depicted in the top panel of Fig. 5 after one year of data taking time by considering two extreme possibilities for the detector mass (e.g. 1 kg and 100 kg). In each case the assumed experimental setup consists of a 76Ge detector with a $100~{}\mathrm{eV_{ee}}$ threshold and a background level of 1 cpd. For comparison purposes, apart from the typical $\sigma_{\mathrm{sys}}=10\%$, two additional more optimistic possibilities of the systematic error are also taken into account: $\sigma_{\mathrm{sys}}=5\%$ and $\sigma_{\mathrm{sys}}=1\%$. Moreover, we also explore a more conservative scenario by assuming a 10 cpd background level which shows differences only for the case of 1% systematic error. On the other hand, in the bottom panel of Fig. 5 by neglecting systematic errors and background events, the results are also illustrated for two different values of the 76Ge target mass (1 kg and 100 kg) and four possible energy thresholds ($1~{}\mathrm{eV_{ee}}$, $10~{}\mathrm{eV_{ee}}$, $100~{}\mathrm{eV_{ee}}$, $400~{}\mathrm{eV_{ee}}$). For these thresholds, by using Eq.(18) the corresponding quenching factors become $\mathcal{Q}u=(0.12,0.16,0.23,0.27)$ leading to nuclear recoil thresholds ($8~{}\mathrm{eV_{nr}}$, $60~{}\mathrm{eV_{nr}}$, $442~{}\mathrm{eV_{nr}}$, $1472~{}\mathrm{eV_{nr}}$), respectively. Note, that this is also consistent with the choice $\mathcal{Q}_{f}=0.20-0.25$ employed in our previous work where we only considered a $100~{}\mathrm{eV_{ee}}$ threshold Kosmas et al. (2015b). We furthermore note that, by assuming a threshold as high as $T_{\mathrm{thres}}=400~{}\mathrm{eV_{ee}}$, the results indicate that TEXONO has no sensitivity to sterile parameters for the case of 1 kg 76Ge detector mass. One also sees that large values of $\sin^{2}2\theta_{ee}$ would be ruled out by the exclusion curves, in agreement with the results of Refs. Mention et al. (2011); Giunti and Laveder (2011). In addition, as stated in Ref. Giunti and Zavanin (2016), the requirement of large $|U_{e1}|^{2}+|U_{e2}|^{2}$ for solar neutrino oscillations, implies that values of $|U_{e4}|^{2}$ close to unity are excluded. Therefore, for small $\sin^{2}2\theta_{ee}$ one has

[TABLE]

which satisfies the general expectation that the fourth generation massive neutrino is mostly sterile.

At this point we turn our attention on the capability of the COHERENT experiment Akimov et al. (2015) at the SNS, Oak Ridge, to probe the sterile neutrino parameters (for a comprehensive analysis, see also Ref. Anderson et al. (2012)). Although SNS experiments in general involve both $U_{e4}$ and $U_{\mu 4}$, here we concentrate just on the latter since COHERENT is optimized to record muonic neutrino beams Kosmas et al. (2015b). Focusing on various promising nuclear targets at the SNS, in Fig. 6 we illustrate the expected sensitivity of the COHERENT to sterile neutrino parameters in the $(\sin^{2}2\theta_{\mu\mu},\,\Delta m_{41}^{2})$ plane, by assuming only the $\bar{\nu}_{\mu}$ component of the delayed neutrino flux. For the sake of comparison, the bottom panel of Fig. 6 shows the corresponding sensitivity by neglecting systematic uncertainties and background events for the case of 76Ge. The obtained results, in conjunction with the large values of $|U_{\mu 1}|^{2}+|U_{\mu 2}|^{2}+|U_{\mu 3}|^{2}$ that are indicated by atmospheric neutrino data Maltoni and Schwetz (2007), imply small values of $|U_{\mu 4}|^{2}$. Then, similarly to reactor neutrino experiments, one may write

[TABLE]

Furthermore, a combination of Eq.(23) with Eqs.(25) and (26) yields the appearance-disappearance constraint Bilenky et al. (1998)

[TABLE]

which implies that $\sin^{2}2\theta_{e\mu}$ is doubly suppressed for small values of $\sin^{2}2\theta_{ee}$ and $\sin^{2}2\theta_{\mu\mu}$. From the corresponding exclusion curve in Fig. 7 by assuming various nuclear targets and the previously described systematic uncertainties and backgrounds as well as in Fig. 8 for zero background events and statistical errors only, we find that a combined analysis leads to a high sensitivity for sterile neutrino searches. Confronting the present results with the respective allowed regions by LSND Aguilar et al. (2001) and MiniBooNE Aguilar-Arevalo et al. (2010, 2012, 2013) (see Figs. 7 and 8), we conclude that the expected sensitivity from CE$\nu$NS has the potential to probe them, especially after the future upgrade of COHERENT and TEXONO. These results are also competitive with recent sterile neutrino fits obtained from global analyses of SBL neutrino oscillation searches Kopp et al. (2011); Giunti and Laveder (2011).

VI Conclusions

We have examined the potential of short-baseline coherent elastic neutrino-nucleus scattering experiments to probe effects associated to light sterile neutrinos. For definiteness we have focused on the normal (3+1) neutrino mass scheme. We have found that the planned TEXONO and COHERENT experiments offer good prospects of providing key information concerning the existence of light sterile neutrinos. From our present results we conclude that dedicated low-energy neutrino experiments looking for CE$\nu$NS events could be complementary to charged-current appearance and disappearance searches. We have also verified that, by employing high-purity Germanium detectors with sub-keV thresholds, better sensitivities can be reached on the sterile neutrino mixing parameters. Such measurements would provide a deeper understanding of neutrino interactions over a very wide energy range and could possibly provide evidence for new physics in the lepton sector.

Acknowledgements

Work supported by MINECO grants FPA2014-58183-P, Multidark CSD2009-00064, SEV-2014-0398, and the PROMETEOII/2014/084 grant from Generalitat Valenciana. M. T. is also supported by the grant GV2016-142 (Generalitat Valenciana) and by a Ramón y Cajal contract (MINECO). One of us, DKP, wishes to thank Prof. O. Miranda for stimulating discussions and Dr. R. Fonseca for technical assistance. JWFV acknowledges Prof. W.C. Louis for providing relevant experimental data.

Note Added

Recently, the COHERENT collaboration announced the observation of CE$\nu$NS for the first time at a 6.7 sigma confidence level, using a low-background, 14.6 kg CsI[Na] scintillator Akimov et al. (2017). This enhances the significance of our results related to the COHERENT experiment.