Sterile neutrino searches with reactor antineutrinos using coherent neutrino-nucleus scattering experiments

: We present an analysis on the sensitivity to the active-sterile neutrino mixing with Germanium (Ge) and Silicon (Si) detectors in the context of proposed coherent elastic neutrino-nucleus experiment in India. The study has been carried out with 3 (active) + 1 (sterile) neutrino oscillation model. It is observed that the measurements that can be carried out with Ge detector give better sensitivity for the active-sterile neutrino mixing as compared to Si detector. Both the detectors are able to exclude most of the anomaly regions observed by the GALLIUM experiment. The Ge detector with mass 10 kg can observe the active sterile neutrino oscillation at 95 % conﬁdence level provided sin 2 2 θ 14 ≥ 0 . 09 at ∆ m 241 = 1.0 eV 2 for an exposure of 1-yr. At higher values of ∆ m 241 the better sensitivity is obtained at short baseline. It is also found that the threshold as well as resolution of detectors play a crucial role for measuring the active-sterile neutrino mixing parameters.


Introduction
The concept of neutrino was first introduced by Pauli in 1930 while explaining the energy spectra of beta particles.Later on, it was first observed by Cowan and Reines via the inverse beta decay (IBD) process using the reactor as a source.The tiny mass of neutrinos is a combination of three mass eigen-states, which is established by several experiments using solar, atmospheric, reactor, and accelerator-based neutrinos.However, the physical origin of their masses is still not understood.Since, neutrinos do not have fixed mass but a quantum mechanical superposition mass eigen-states ( ν 1 , ν 2 , ν 3 ) with each one having distinct mass eigen-value m 1 , m 2 , m 3 , they can change flavor while moving from one place to another, a phenomenon which is known as neutrino flavor oscillation.At present several efforts are going on for the precise determination of neutrinos oscillation parameters.Many experiments are being performed to obtain the better neutrino-nucleus cross-sections.Coherent elastic neutrino-nucleus scattering (CEνNS) is a standard model (SM) process in which low energy neutrinos scatter off the atomic nucleus coherently through the neutralcurrent weak interactions [1].For low-energy neutrinos (< 50 MeV), the CEνNS process has a larger cross-section for neutron-rich targets as compared to other known processes, such as inverse beta decay (IBD) and neutrino-electron scattering [2] used for neutrinos measurements.Further, the CEνNS is a threshold-less process in contrast to IBD.Although, having a larger cross-section, the CEνNS process has not been observed earlier due to the difficulty in measuring the low-energy recoil nuclei.The CEνNS cross-section measurement requires high flux of low energy neutrinos and measurement of low nuclear recoil energies.
There are mainly three possible sources of (anti)neutrinos that could be used to search for CEνNS process namely pion decay at rest (DAR) beam, an intense radioactive source or a nuclear reactor.Recently, the CEνNS cross-section has been measured by COHERENT experiment using the neutrinos produced from the spallation neutron source as a DAR [3,4].The neutrinos produced due to this method has a maximum energy of about 53 MeV.It is quite challenging yet very interesting to measure CEνNS using the neutrinos produced from a nuclear reactor or an intense radioactive source.In the case of reactor ν e s, the average energy is about 3.6 MeV with an endpoint near 10 MeV.Due to the lower neutrino energies as compared to other sources, it is necessary to employ novel detector technologies which can attain sub-keV energy thresholds in detection.In fact, several cryogenic bolometers could be optimized for this purpose.
The measurement of CEνNS cross-section by COHERENT group has opened up a window for probing several aspects related to physics beyond the SM at low energy.At present, several experiments are going on and some are proposed to measure the CEνNS cross-section with the required threshold by using charge-coupled devices (CCDs), metallic superconducting bolometers and Ge-based semiconductor detectors using reactor ν e as a source [2,[5][6][7][8][9][10][11][12].The measurement of CEνNS process can shed light on several fundamental SM physics aspects such as non-standard interactions, neutrino magnetic moment, or the weak mixing angle [13].The CEνNS is a flavor blind process, hence the flavor-independent astronomy with supernova neutrinos becomes feasible, which allows to investigate the interior of dense objects as well as stellar evolution in details [14,15].
In this context, we have proposed to measure the CEνNS process using reactor ν e s in India.Although various fundamental physics aspects of neutrino can be studied in the proposed experiment our initial aim is to find out the possible explanation for an anomalous behavior that has been observed in the measurement of the reactor ν e flux by various reactor groups [2,12,16].The ν e flux recalculated precisely by Mueller et al. [17] shows about 6% deficit in the observed-to-predicted ratio of events at small distance through IBD process, which is known as the "reactor antineutrino anomaly" (RAA) [18].There are two distinct explanations proposed for this discrepancy.One of them is the disappearance of ν e while propagating from the source to detector due to Active-Sterile Neutrino (ASN) oscillations with the mass square difference ∆m 2 ∼ 1 eV 2 .On the other hand the observed discrepancy is likely to be related to the incorrect prediction of antineutrino flux due to incomplete reactor models or uncertainty in nuclear data.The Huber-Muller model utilizes the cumulative β − -spectra [19][20][21] measured at ILL for conversion to antineutrino spectra [17,[22][23][24].Therefore, the related experimental biases may be responsible for the anomaly.Recent measurements indicate that bias in the prediction of 235 U flux may be the likely cause of RAA [25,26].The CEνNS process has an advantage compared to other techniques for finding the possible existence of the sterile neutrino.It is a neutral current process in which neutrinos scatter off the nuclei, and are independent of the neutrino flavor.Therefore, any finding of an oscillation structure would indicate mixing completely with non-active neutrinos.An experiment aiming at the observation of CEνNS could also measure the neutrino rate independently of the uncertainties of the oscillations among different flavor neutrinos.
To study the ASN oscillations using IBD process, the DANSS collaboration has measured the positron energy spectra at 3 different distances (10.7 m to 12 m ) from the reactor core.From the measurements, a large fraction of the RAA region in the sin 2 2θ 14 − ∆m 2   41   plane that covers the parameter space up to sin 2 2θ 14 < 0.01 [27] are excluded.Similarly, the STEREO [28] collaboration has measured the ν e energy spectrum in six different detector cells covering baselines between 9 and 11 meters from the reactor core of the ILL research reactor.The results based on the current reactor ON data are explained by the null ASN oscillation hypothesis and the best fit of the RAA can be excluded at 97.5% confidence level (C.L.).The reactor ν e spectra measured by PROSPECT collaboration disfavors the RAA best-fit point at 2.2σ C.L. and constraints significant portions of the previously allowed parameter space at 95% C.L. [29].The Neutrino-4 group has measured ν e energy spectra with the segmented detectors at different positions ranging from 6 to 12 meters.Their model-independent analysis exclude the RAA region at C.L. more than 3σ.However, the experiment has observed ASN oscillation at sin 2 2θ 14 = 0.39 and ∆m 2 41 = 7.3 eV 2 at C.L. of 2.8σ [30].To this end, a feasibility study has been carried out to ascertain the ASN mixing sensitivity of various types of the detector by placing them at short baseline (L≤ 30m) through CEνNS channel.
The article is organized as follows.In the following section, a detailed description of antineutrinos produced from the reactor is presented.The CEνNS process and the principle of detection are described in Sec. 3. In Sec. 4, the expected number of events in the detector is estimated.The phenomenon of ASN oscillation at short baseline considering the '3+1' mixing model is described in Sec. 5.The simulation procedure for incorporation of detector response on coherent neutrino discussed in Sec. 6.The sensitivity of the proposed MeV.There are on an average six ν e s produced per fission.In the present work, the parameterization for ν e s energy spectra above 2.0 MeV are considered from Huber-Muller model [17,22], whereas the low energy part of the spectra is considered from Ref. [31,32].The relative contribution of each isotope depends on the types of reactor and its fuel cycle.
In this study, reactors with different core composition are considered as discussed below.
In the beginning, it is planned to perform measurements with detector at 4 m from the reactor core in upgraded Apsara (U-Apsara) research reactor facility in Bhabha Atomic Research Centre (BARC), India.The U-Apsara reactor has a compact core with a height of about 0.64 m and a radius of about 0.32 m which can operate at a maximum thermal power of 3 MW th [33].In future, the same detector setup can be placed at other reactor facilities such as DHRUVA, BARC [34], Proto-type Fast Breeder Reactor (PFBR), IGCAR, Kalpakkam, and VVER, Kudankulam in India [35].The DHRUVA reactor core has radius ∼1.5 m and height ∼3.03 m (defined as an extended source) [34], which can operate at a maximum thermal power of 100 MW th consuming natural uranium as fuel.On the other hand, PFBR is relatively a compact source as compared to DHRUVA with a dimension of about 1 m both in radius and height.The PFBR can operate at a maximum thermal power of 1250 MW th with mixed oxide (MOX, PuO 2 -UO 2 ) as fuel [35].The VVER power reactor has thermal power of 3000 MW th and core has radius ∼1.5 m and height ∼3.03 m (also an extended source).The VVER reactor is a pressurized water reactor and uses 3.92% enriched uranium as a fuel [36].
Due to the their compact size, U-Apsara and PFBR reactors are the ideal sources to utilize the detector set-up for investigating the ASN mixing at short distance.On the other hand, at very close distances there are significant contributions from the reactor related background, which will affect the sterile neutrino measurement sensitivity.The above mentioned reactors are not only different with respect to their sizes and thermal power but also with respect to their fuel compositions as mentioned in Table 1.

Coherent Neutrino-nucleus Scattering Measurement
The CEνNS scattering was first proposed by Freedman [1] within the SM.In this process, the low-energy neutrinos scatter off nuclei which carry only energies up to few keV.It is very challenging to measure such low energies (∼ few tens of eV) of recoiling nuclei which requires the uncertainties associated with the relevant measurements are minimized.The differential CEνNS scattering cross-section is given by where A, N, Z are the mass number, number of neutrons and number of protons in the nucleus, respectively.Further, E ν is the incident neutrino energy, T is nuclear recoil energy, is the weak mixing angle and f (q) is the nuclear form factor for a momentum transfer q.For low energy neutrinos (E ν < 50 MeV), the momentum transfer is very small such that q 2 R 2 <1, where R is the radius of the nucleus, f (q) ∼ 1.At small momentum transfers, the scattering amplitude from individual nucleon is in phase and added coherently which leads to the increase of cross-section.The cross-section is proportional to N 2 and sin 2 θ W has been measured to be 0.23867 ± 0.00016 ∼1/4 [37].Although, the scattering cross-section is enhanced by the number of nucleons, it depends on the measurement of very low energies of recoiling nuclei.The recoil energy of nucleus depends on the its mass, which decreases with the increase in the mass of target nuclei.For example, for the neutrino of energy 1 MeV, the maximum recoil energy is about 20 eV and 50 eV for Ge and Si targets, respectively.
The recoil energy of different target nuclei (Si, Ge) considered in this study is shown in Fig. 1 as a function of neutrino energy.It can be observed from Eq. 3.1 that the crosssection is maximum at zero recoil energy and it decreases with the increase of T .Hence, a detector with higher threshold energy for detecting the signal leads to lesser number of events.Therefore, it is very challenging to select the type of detector for the measurement of such cross-section.Because of the low energy of the neutrinos, the recoil energy deposited in the detector is up to a few keV, while the minimum mass needed is ten to hundreds of kilograms.The incoming particle energy can be determined from particle interactions in a target which includes the measurement of ionization, scintillation, and/or the phonon excitation in the material.

Expected Event Rate in Detector
The CEνNS reaction cross section per unit detector mass can be two orders of magnitude larger than for IBD, potentially allowing for detectors in the kilogram range.The expected where M det is the mass of the detector, t is the time duration of data taking, λ 0 is the total neutrino flux and, λ(E ν ) is the neutrino energy spectrum.For a given experimental setup, the detector threshold decides the minimum recoil energy of the nuclei.As the number of neutrinos of higher energy (> 6.0 MeV) is less, we have considered neutrinos with maximum energy about 6.0 MeV for the analysis.It can be noted here that the expected number of events in the detector is estimated by considering the contributions from each stable isotope of the element weighted by its natural abundance.Figure 2 shows the differential event rate dependence of recoil energy for Ge and Si detectors.For a given recoil energy, the number of events increases with the target mass number due to increase in number of neutron.However, the number of events decreases with the increase of recoil energy.So, it is necessary to either increase the target mass or energy of neutrinos for target with lower mass number.As mentioned earlier, the expected number of events also depends on the detector threshold.The number of events expected in the detector of mass 10 kg is mentioned in Table 2. Events are estimated considering the detector is placed at 4m distance from the Apsara-U reactor core for an exposure of 1 year.

Neutrino Oscillation Probability at Short Baseline Experiment
The main advantage of considering the CEνNS process for finding the ASN mixing sensitivity is due to its larger cross-section as compared to IBD cross-section.This enables the use of smaller size detectors in the CEνNS measurements.The compact detector will minimize the neutrinos path length uncertainty.In the SM, there are three flavors of active neutrinos (ν e , ν µ , ν τ ).The conversion of flavor to mass eigen-states is expressed using Pontecorvo-Maki-Nakagawa-Sakata (PMNS) [38] unitary matrix.Worldwide several measurements are being carried out to observe the phenomenon of neutrino oscillation and measurements of three generation oscillation parameters [39][40][41][42][43][44][45][46][47].Beyond these three active neutrinos, various experiments are going on to either find out or exclude the existence of a sterile neutrino which has no analogous SM gauge interactions.However, its presence can affect the standard neutrino oscillations.Firstly, a standard neutrino could oscillate into an undetectable sterile neutrino, leading to a reduction of the observed event rate within the detector.Secondly, the mass eigen-state (ν 4 with mass m 4 ) primarily associated with the sterile neutrino would enhance the transformation probability between standard neutrinos, leading to the detection of a neutrino flavor that is not emitted by the source.The experiments looking for a reduction of the interaction rate are called "disappearance" experiments while the ones seeking an enhanced neutrino conversion are called "appearance" experiments.In this case of ASN oscillation, PMNS matrix is expanded to 3+1 from 3 generations, where "3" stands for three active neutrinos and "1" for a sterile neutrino (ν s ).The order of rotation and elements of the mixing matrix is given in Ref. [48].The 3+1 generation oscillation model is reduced to two flavor framework for a small value of mixing angle θ 14 and at a few meters (< 100 m) source to detector distance.Then the ν e survival probability can be approximated as where E ν is the neutrino energy (in MeV), L is the path length (in m) between the source and the detector, and ∆m 2 41 is the squared masses difference (in eV 2 ) between the two neutrino mass eigen-states.The ASN oscillation parameters ∆m 2  41 and sin 2 2θ 14 are represented by where U e4 = sin θ 14 , one of the elements of unitary mixing matrix.The combined analysis of data obtained by NEOS and DANSS collaborations give the present the best-fit values of ASN oscillation parameters as ∆m 2 41 1.30 eV 2 and sin 2 2θ 14 0.049 [49].Similar values are also observed from the global analysis [50].With these values of ASN mixing parameters, experimentally, the possible existence of sterile neutrinos at short baseline can be observed by finding the distortions of the ν e energy spectrum which is otherwise absent in three active neutrino oscillation.

Simulation Procedure
In the present study, the potential of different detectors have been explored for finding the ASN oscillation sensitivity by using the neutrinos produced from various types of reactor facilities as mentioned in Table 1.The energy spectrum of the neutrinos produced from the reactor is different for different isotopes.Therefore, the number of neutrinos produced from the reactor is dependent on not only their thermal power but also on the fuel compositions.The spatial variation of neutrino flux due to the finite-size reactor is considered as a cylindrical shape which can be parameterized as [51], where φ 0 represents the flux at the center of the reactor core taken as the vertex position, R, and H are the physical radius and height of the cylindrical reactor core, respectively, J 0 is the zeroth-order Bessel function of first kind with r (0 ≤ r ≤ R) and z (0 ≤ z ≤ H).
In the analysis, the events are estimated using the reactor antineutrinos flux and CEνNS cross section as already described.The detector response to the recoil energy spectrum is incorporated by assuming a standard Gaussian form with the standard deviation(σ) for the energy resolution given as where T and T m are the simulated true and observed recoil energy of nuclei, respectively.The detector resolution is considered as σ/T ∼ 10%/ √ T .The recoil energy spectrum generated due to neutrino induced events are distributed with variable bin widths such that the minimum number of events in each bin is ≥ 5.The number of events in i-th energy bin after folding the detector resolution is given as 3) The index i corresponds to the measured energy bin and N r i represents the number of reconstructed events, k is summed over the true recoil energies of nuclei and n k is the number of events in k-th true energy bin.Further, K k i is the integral of the detector resolution function over the T bins and which is given as The integration is performed between the lower and upper boundaries of the measured energy (T L i and T H i ) bins.In the present analysis, we have assumed 80% for the detection efficiency, 90% as the fiducial volume of the detector, and 70% reactor duty cycle for a total exposure of 1 year.Both the production point of neutrino inside the reactor core and the interaction point in the detector are generated randomly using a Monte-Carlo method.

Extraction of Active-Sterile Neutrino Mixing Sensitivity
The detector sensitivity to the ASN mixing can be extracted by knowing the neutrino energy spectrum, flux, and its cross-section accurately.Total number of neutrino induced events expected within the detector can be estimated using the procedure mentioned above for a given oscillation hypothesis and it can be compared with the measured one.For this purpose, a statistical analysis between the predicted and measured event distribution by simulation is carried out in order to quantify the sensitivity of the detector to the ASN mixing parameters θ 14 and ∆m 2  41 for a given exposure.The detector response is folded in both simulation predicted as well as the expected events.The sensitivity to the sterile neutrino mixing parameters are extracted by estimating the χ 2 .
The exclusion limit is obtained for each value of ∆m 2 41 by scanning over the various values of sin 2 2θ 14 to determine the boundary of the corresponding χ 2 (e.g.χ 2 = 5.99 for 95.0% confidence limit (C.L.)).The definition of χ 2 is taken from Ref. [52] and given as where, n is the number of energy bins, R ex n , R th n are the number of events obtained from the simulations with oscillation (expected) and without oscillation (theoretically predicted) events, respectively.The theoretically predicted events R th n are calculated considering the reactor ν e flux, the CEνNS cross-section, detection efficiency, and energy resolutions of the detector.The R ex n is estimated by folding the oscillation probability on R th n along with the detector resolution.The R th n carries the information about the systematic uncertainties given by with π i n being the strength of the coupling between the pull variable ξ i and R th n .The χ 2 is minimized with respect to pull variables ξ i and it is estimated by considering four sources of systematic uncertainties.It includes 3.0% normalization uncertainty which arises due to reactor total neutrino flux, number of target atoms, and detector efficiency, uncertainty due to nonlinear energy response of the detector taken as 1.0%, and, uncertainty in the energy calibration given as 0.5%.In addition, the uncorrelated experimental bin-to-bin systematic error of 2.0% is also considered which could result due to the insufficient knowledge of other sources of background.

Active-Sterile Neutrino Mixing Sensitivity
The study of ASN mixing sensitivity has been performed earlier with the ISMRAN detector set-up with the consideration that the detector will be placed at a fixed distance from the reactor core and detection through the IBD process [48,53].The present analysis has been carried out by varying both the reactor and detector related parameters with the neutrinos detected through CEνNS process.The detector to the ASN oscillation parameters are compared by employing ν e s produced from various types of reactors as mentioned in Table 1.

With Different Types of Detector
As compared to the IBD case, there is a wider range of detector materials available in which CEνNS can be measured.While the CEνNS scattering cross section increases with increase in the number of nucleons present in the target material, the recoil energy of the nuclei itself decreases with mass.The ASN mixing sensitivity of the detector has been studied considering commonly used detector materials, such as Germanium (Ge) and Silicon (Si) each having a payload of 10 kg at a given reactor thermal power and reactor core to detector distance, Figure 3 shows the extracted results in sin 2 2θ 14 -∆m 2 41 plane at 95.0 % C.L for an exposure of 1.0 year.Results are presented for different distances between the detector and the core of the reactor based on accessibility conditions of different reactors.We assume recoil energy threshold of 20.0 eV and 50.0 eV for Ge and Si detectors, respectively.Allowed regions for the Gallium anomaly is also depicted in the same figure [54].Figure 3(a) shows the sensitivity by placing the detectors at 4 m from Apsara-U research reactor core.Figure 3(b) shows the sensitivity of the detector by positioning it at 7.0 m and 13.0 m from DHRUVA reactor core.Figure 3(c) shows the sensitivity of the detector at PFBR reactor which is at a distance of 25.0 m from the detector, and Figure 3(d) shows the sensitivity for the detectors placed at 30 m from the VVER power reactor core.The shape of the sensitivity curve in the region of low values ∆m 2 41 (∆m 2 41 1.0 eV 2 ) shows a linear dependence between sin 2 2θ 14 and ∆m 2  41 in the logarithmic scale.This may happen as typical neutrino oscillation lengths are much larger as compared to the size of the detector, and the ν e survival probability mentioned in Eq. 5.1 is approximately given by P νeνe (E ν , L) ≈ 1 − C sin 2 2θ 14 × ∆m 2 41 2 , where C is a constant.In the region with higher ∆m 2  41 values, the systematic uncertainties related to the neutrino source dominate over the statistical uncertainties.The detector energy resolution flattens the high frequency oscillation-induced deformations significantly, resulting in the gradual decrease of the shape discriminating power.This leads to event distribution due to with and without oscillation which overlaps except for constant normalization factor.It is also observed that, placing the detector at a distance in the range of 15-30 m in case of PFBR and VVER reactors, more parts of the region can be excluded in the sin 2 2θ 14 -∆m 2  41 plane.Also the maximum sensitivity of the detector shifts to lower value of ∆m 2 41 (∼ 0.03 eV 2 ) due to the increase in source to detector distance.It is observed that the ASN mixing sensitivity of the Ge detector is better as compared to Si detector for values of ∆m 2 41 ≤ 1.0 eV 2 .For higher ∆m 2 41 > 1.0 eV 2 , both the detectors have almost similar sensitivity to the mixing angle sin 2 2θ 14 .Both Si and Ge detectors exclude the allowed region of the GALLIUM experiment at C.L. of 2σ.

With Different Mass of the Detector
The expected number of events decreases with a decrease in the target mass number.So to enhance the sensitivity of the detector it is required to increase the neutrino flux, exposure time, or the target mass.At a given reactor power, in order to increase the CEνNS interaction rate the actual target mass number of the detector is more critical.Hence, it is a good idea to increase the detector mass although handling of detector is bit cumbersome.Taking into account the backgrounds, it is observed that CEνNS detectors offer a mass advantage of one order of magnitude assuming that measurements of eV-scale recoil thresholds are feasible and a signal-to-background ratio of about 1 can be achieved in the experiment [55].Figure 4 shows the ASN mixing sensitivity in sin 2 2θ 14 -∆m 2  41 plane at 95% C.L. for an exposure of 1 yr for different mass of the detector.Figure 4(a) shows for Si detector and Fig. 4(b) for Ge detector with masses 10 kg, 50 kg and 100 kg.It can be noted here that, sensitivities are extracted considering a threshold of 100 eV and 20 eV for silicon and germanium detector, respectively.At a given detector mass at higher ∆m 2   41   the sensitivity in sin 2 2θ 14 is more as compared to lower ∆m 2  41 .The sensitivity improves in all regions of sin 2 2θ 14 with increase in detector mass as the number of expected events increases.It can be seen that the Ge detector excludes both allowed regions of GALLIUM experiment.

With Various Types of Detector Threshold
As mentioned earlier, the recoil energy of nuclei decreases with increases of mass number of the detector.Hence, low threshold detectors, such as Ge and Si can perform nuclear recoil discrimination down to eV scale energy threshold.Such detectors will be more useful if we can observe the recoil energies as low as few 10s of eV.For CEνNS cross-section, as given in Eq. 3.1, the nuclear recoil energy T is the relevant observable.For a given neutrino energy there is a limit to the maximum recoil energy.The cross-section is maximum for lower values of T , therefore, the total number of observed event rate sensitivity depends on the low-energy threshold for nuclear recoil T min .The study has been performed to find out the impact of detector threshold on ASN mixing sensitivity.We have considered both Si and Ge detectors of mass 10 kg placed at 4m from Apsara-U reactor core.Figure 5 shows the sensitivity in sin 2 2θ 14 -∆m 2 41 plane at 95 % C.L for different threshold energies.The sensitivity of the detector at lower ∆m 2  41 is better at lower detector threshold.However, for ∆m 2 41 ≥ 1.0 eV 2 , the detector threshold has minimal impact on ASN mixing sensitivity.

With Different Resolution of Detector
The sensitivity of detector to the neutrino mixing parameters such as angle and squared mass difference depends on its resolution and efficiency.In order to study the effect of energy resolution, we have considered Ge detector of mass 10 kg placed at 4m distance from Apsara-U reactor core.The detector resolution is varied from σ/E = 3%-10%/ √ E for extracting its sensitivity to the upper limit for the ASN mixing angle θ 14 .Figure 6 shows the sensitivity to ASN mixing parameters in the ∆m 2  41sin 2 2θ 14 plane.It is observed that the detector has better ASN mixing sensitivity for resolution of σ/E = 3%/ √ E. It is observed that for ∆m 2 41 < 1.0 eV 2 , ASN mixing sensitivity is independent of detector resolution whereas for higher ∆m 2 41 ≥ 1.0 eV 2 , the ASN mixing sensitivity improves for the detector resolution.At higher ∆m 2  41 , the oscillation frequency is more and hence to have better sensitivity a detector with very good energy resolution is necessary.

Sensitivity of Detector in Presence of Background
The ASN mixing sensitivity has been obtained with the inclusion of backgrounds considering Ge detector which will be placed in the above ground conditions at 4.0m distance from Apsara-U reactor.At the experimental site, the reactor related background such as neutron and gamma together with the cosmogenic background such as muon induced neutrons that can not be completely eliminated even with the shielding will contaminate the actual signal.Several groups have performed the measurement with the Ge detectors operated in above-ground low-background environments and provided the background level.The energy dependent background level due to neutron and gamma are considered from the Ref. [7].In this study a signal to background ratio 1.0 is considered.While estimating the χ 2 , an associated 10% systematic uncertainty is therefore considered due to these backgrounds.Figure 7 shows the comparison of Ge detector sensitivity with and without the inclusion of backgrounds.It is observed that with the contribution of both backgrounds, the ASN mixing angle sensitivity is further reduced as compared the case with no back- ground.Therefore better background reduction techniques have to be employed for the measurement with required sensitivity.

Summary
The study on neutrinos provides the avenues for exploring several phenomena of physics beyond the standard model.At present, several experiments are going on to measure various fundamental properties of neutrinos emanating from different sources.An experimental program has been proposed at the research reactor U-Apsara for the measurement of CEνNS.We have studied active-sterile neutrino mixing sensitivity with Si, and Ge detectors in the context of CEνNS measurements at reactors with different core configuration and sizes available in India.The analysis has been carried out for determining the activesterile neutrino mixing sensitivity considering an exposure of 1 year and detectors with varying masses, detection thresholds and resolutions.The region in sin 2 2θ 14 -∆m 2  41 plane is constrained considering a single detector which will be placed at a fixed position with respect to the reactor core.It is found that the ASN oscillation at 95% confidence level with sin 2 2θ 14 ≥ 0.09 at ∆m 2 41 = 1.0 eV 2 can be observed with the Ge detector of mass 10 kg for an exposure of 1-yr.The Ge detector can exclude a large portion of the favored nonzero ASN mixing parameters region obtained from GALLIUM experiment.The sensitivity improves by placing the detector at PFBR or VVER reactor facilities.

Figure 1 .
Figure 1.Recoil energy of Si and Ge nuclei as a function of energy of the neutrino.

Figure 2 .
Figure 2. Differential event rate variation with recoil energy using Si and Ge detectors.

Figure 3 .
Figure 3.The comparison of ASN mixing sensitivity at 95 % C.L. for the Ge and Si detectors placed at fixed distances of 4 m, 13 m, 25 m, and 30 m from the U-Apsara, DHRUVA, PFBR and VVER reactors, respectively.

Figure 4 .
Figure 4.The comparison of ASN mixing sensitivity at 95 % C.L. for different detector mass of the Ge and Si detectors placed at fixed distances of 4 m, 13 m, 25 m, and 30 m from the U-Apsara, DHRUVA, PFBR and VVER reactors, respectively.

Figure 5 .
Figure 5.The comparison of ASN mixing sensitivity at 95 % C.L. for different detector threshold for the Si(left panel) and Ge (right panel) detectors placed at 4 m from the U-Apsara reactor facility.

GeFigure 6 .
Figure 6.The comparison of ASN mixing sensitivity at 95 % C.L. for different resolution of Ge detector placed at 4 m from the U-Apsara reactor facility.

Figure 7 .
Figure 7.The comparison of ASN mixing sensitivity at 95 % C.L. of Ge detector in presence of background placed at 4m from the U-Apsara reactor facility.

Table 1 .
Reactor details nuclear reactor is an intense source of electron ν e s.There are two processes primarily by which ν e s are produced from the reactor, namely the beta decay of fission fragments of mainly four isotopes 235 U, 238 U, 239 Pu and 241 Pu and the neutron capture process on the 238 U.The antineutrinos produced from the beta decay of fission fragments have energy up to about 10 MeV and those produced from neutron capture have energy less than 2 A

Table 2 .
Expected events with different detectors placed at 4m from Apsara-U reactor