New Results of the DANSS Experiment Taking into Account the Absolute Antineutrino Counting Depending on Distance

Abstract

The DANSS detector, i.e., a scintillation detector with a sensitive volume of 1 m³, is installed at the Kalinin nuclear power plant under the reactor core on a mobile stage. The distance from the detector center to the reactor center is varied from 10.9 to 12.9 m. The detector records about 5000 events of inverse beta decay per day a background level from cosmic muons of the order of two percent. The analysis on the search for sterile neutrino taking into account the count rate of antineutrino events is described. The final ratio of the observed rate of absolute DANSS counting to that predicted based on the Huber and Mueller model was 0.98 ± 0.04. New results on the search for sterile neutrino based on 7 million of antineutrino events are presented. When using the conservative estimate of 7% for the total systematic uncertainty in the absolute count rate, the limits in the parameter space of the hypothetical sterile neutrino are determined. In particular, for high (≳10 eV²) parameters $\Delta m_{{41}}^{2}$, the values of ${{\sin }^{2}}2{{\theta }_{{ee}}} > 0.26$ are excluded at the 90% confidence level.

1 INTRODUCTION

Highly segmented scintillation detector of antineutrino DANSS [1] is arranged at the fourth power unit of the Kalinin nuclear power plant (KNPP) under the reactor core on an elevating stage. The distance between detector and reactor centers varies from 10.9 to 12.9 m. One of the main objectives of the DANSS experiment is the search for neutrino oscillations in the hypothetical sterile neutrino. The reactor antineutrino is detected using the inverse beta decay (IBD) reaction: ${{\tilde {\nu }}_{e}} + p \to {{e}^{ + }} + n$ in which almost the total antineutrino energy after subtracting the reaction threshold of 1.8 MeV is transferred to the positron.

The primary results on the search for the sterile neutrino in the DANSS experiment [2] were based on a comparison of the observed and predicted ratio of spectra of detected positrons. The ratio of the spectrum measured in the bottom detector position to the spectrum measured in the top detector position was compared to the curve predicted for various values of the parameters $\Delta m_{{41}}^{2}$, ${\text{si}}{{{\text{n}}}^{2}}2{{\theta }_{{ee}}}$. In this case, the normalization of each spectrum was not fixed, i.e., an analysis depended exclusively on the ratio of spectra shapes. Since the relative detector efficiency (the ratio of absolute efficiencies for various positions) showed good temporal stability, information about relative counts was introduced to the analysis, which made it possible to significantly expand the sensitivity range [3] in comparison with the sensitivity range in the case of analysis based on only the relative spectral shape [4]. In this paper, we consider the analysis on the search for sterile neutrino taking into account absolute count rates of antineutrino events per day. The used statistics was 7 million IBD events, from which 5 million were included into the oscillation analysis. The DANSS results on the previous statistics are presented in [5].

2 ABSOLUTE COUNT RATES OF ANTINEUTRINO EVENTS IN THE DANSS EXPERIMENT

Absolute count rates ${{\tilde {\nu }}_{e}}$ can be described by the expression

$$\frac{{dN(t)}}{{dt}} = {{N}_{p}}\int\limits_{{{E}_{{{\text{th}}}}}}^{{{E}_{{\max }}}} {\int\limits_{{{V}_{{{\text{detector}}}}}} {\int\limits_{{{V}_{{{\text{reactor}}}}}} {\varepsilon ({{E}_{\nu }})\frac{1}{{4\pi {{L}^{2}}}}\sigma ({{E}_{\nu }})\frac{{{{d}^{2}}\phi ({{E}_{\nu }},t)}}{{dEdt}}P(L,{{E}_{\nu }})dEd{{V}_{{{\text{detector}}}}}d{{V}_{{{\text{reactor}}}}},} } } $$

(1)

where ${{N}_{p}}$ is the number of protons in the sensitive detector volume, $\varepsilon$ is the detector efficiency, L is the distance between the ${{\tilde {\nu }}_{e}}$ production point in the reactor core and the IBD detection point in the detector (the distribution of the fission points in the reactor core is taken into account in this case), $\sigma ({{E}_{\nu }})$ is the IBD reaction cross section. The term ${{d}^{2}}\phi (E,t){\text{/}}dEdt$ describes the ${{\tilde {\nu }}_{e}}$ spectrum:

$$\frac{{{{d}^{2}}\phi (E,t)}}{{dEdt}} = \frac{{{{W}_{{{\text{th}}}}}}}{{\langle {{E}_{{{\text{fis}}}}}\rangle }}\sum {{f}_{i}} \cdot {{s}_{i}}(E),$$

(2)

where ${{W}_{{{\text{th}}}}}$ is the reactor thermal power (data are presented by the KNPP), $\langle {{E}_{{{\text{fis}}}}}\rangle$ is the average energy yield per fission, and ${{E}_{i}}$ is the average energy yield for each fissing fuel component [6]:

$$\langle {{E}_{{{\text{fis}}}}}\rangle = \sum {{E}_{i}} \cdot {{f}_{i}},$$

(3)

${{f}_{i}}$ are fission fractions and ${{s}_{i}}$ is the ${{\tilde {\nu }}_{e}}$ spectrum per fission.

The term $P(L,{{E}_{\nu }})$ is the probability of the reactor antineutrino to retain its flavor (do not oscillate to the hypothetical sterile neutrino). The oscillations related to the values of $\Delta {{m}^{2}}$ for three currently known neutrino states are negligible at given distances.

The sensitive detector volume consists of scintillation counters (strips) 100 × 1 × 4 cm³ in size, made of polystyrene with added scintillating dyes. Furthermore, each strip contains a reflecting (insensitive) layer with added gadolinium for capturing IBD neutrons. The number of protons in the sensitive volume was calculated based on information about geometrical characteristics of scintillation counters and their chemical composition. The uncertainty in the number of protons is about 2%, and is mostly caused by nonideal geometrical characteristics. This was found by selective measurements of strip sizes. In the analysis with consideration of relative counts, the contributions to the detector efficiency, which can behave differently for different positions ere already considered [3]. The dead time is calculated directly from the detector count in the current position and for the studied time interval of statistics acquisition. Correlated backgrounds slightly differ in different positions. For each detector position, the correlated background corresponding to a given position was subtracted from IBD spectra. The main contribution is made by the background from cosmic rays, i.e., 1% of the IBD count in the up position, which is determined by the number of events with signals in the cosmic veto system. The analysis also considered the background of fast neutrons (0.3%) and the background of IBD events from neighboring KNPP reactors (0.5%). The total correlated background is only 1.8% of the total IBD count. Therefore, even if we use a very conservative estimate of 30% in the background uncertainty, the contribution of this uncertainty to the absolute count rate will be 0.5%. In the analysis, the detector nonideality associated with faulty channels whose number sometimes varied was taken into account. The detector efficiency is corrected by the factors calculated directly from the number of idle channels in the corresponding period. During several operation years, IBD counts correlate well with the reactor power taking into account the normalization performed by several points at the beginning of the statistics acquisition [7]. This indicates good temporal stability of the relative efficiency. Since the rest contribution to the absolute efficiency is also made by such characteristics as the number of protons or the efficiency of selection criteria, which are independent of time, it can be concluded about the temporal stability of the absolute efficiency. The absolute detector efficiency is estimated using Monte Carlo simulation with the Geant4 library system. Simulation makes it possible to completely reproduce selection criteria of IBD events and to estimate the absolute efficiency based on the initial number of events laid to the model.

The uncertainty in the absolute efficiency calculated by the above method is associated with uncertainties in selection criteria. Here, the most meaning factor is the systematic uncertainty of the detector energy scale, since many IBD selection criteria strongly depend on the energy. The detector energy scale variation of one standard deviation allowed estimation of the efficiency uncertainty as 2%. In this case, the conservative estimate of 2% was used for the systematic uncertainty on the energy scale. Almost all calibration sources used in the DANSS experiment for determining the energy scale are identical with an accuracy better than 1% (except sodium which differs 1.8% from the taken energy scale). The temporal stability of the energy calibration is provided by regular calibration of all detector strips using cosmic muons (once per two days). Furthermore, each 30–40 min the gain and the optical coupling coefficient between cells of silicon photomultipliers (the optical crosstalk coefficient), which are considered in the calculation of the numbers of photoelectrons from the number of triggered cells, are calibrated using noise spectra for each individual silicon photomultiplier (SiPM). Also the SiPM response nonlinearity because of the finite effective number of its cells is corrected. The residual oscillations of the energy scale, associated with the temperature dependence of the SiPM quantum efficiency do not exceed 0.1%, and are much smaller than the used conservative estimate of the energy scale uncertainty of 2%. The distance between the detector and reactor is well known based on the KNPP data and precision measurements of the indoor detector position with respect to the floor and ceiling. The distribution of the fission points within the reactor core is known with an accuracy of several cm and varies in the course of the experiment. Simulation showed that the absolute count in the detector varies by ~ 1% at deviations of the distribution of the fission points within systematic errors. The reactor power is known with an accuracy of 1.5% according to the KNPP data. An analysis of the data on the search for the sterile neutrino included the data obtained only for the total reactor power. The uncertainty in the average energy yield per fission is 0.3%, according to the results of [6]. The data on fission fractions of basic fuel components of come from the KNPP. The fission fractions at the KNPP were calculated by various methods. Various methods for calculating the fission fractions yield a noticeable difference (about 7% in ²³⁹Pu fission fractions and about 3% in ²³⁵U fission fractions); however, since the spectra for various fuel components differ not so much, the total contribution to the absolute count from this uncertainty is ~ 2%.

The main source of systematic uncertainties in the analysis using absolute count rates of IBD events is the uncertainty in the antineutrino flux at a given reactor power which is about 5% according to the conservative estimate [8]. The total systematic uncertainty in the absolute IBD count rate was 4% without regard to the uncertainties in predictions for antineutrino fluxes, and 7% with regard to the uncertainty in predictions for antineutrino fluxes, see Table 1. Figure 1 shows the comparison of the observed and predicted by the Huber and Mueller model [9, 10] IBD counts over more than six years. Each point corresponds to several days of statistics acquisition. The band around the predicted values shows the systematic uncertainty without the uncertainty in antineutrino fluxes (i.e., 4%). The total ratio of the observed absolute DANSS count to the predicted one was 0.98 ± 0.04 taking into account all data for the total reactor power and all detector positions. The data are in agreement with the predictions within systematic errors. Statistical errors in this analysis are negligible. If we consider the data obtained at the Kurchatov Institute [11, 12] as predictions for antineutrino fluxes, the ratio of the observed DANSS count to the predicted one is 1.02 ± 0.04.

Table 1. List of systematic uncertainty sources for analysis with absolute IBD count rates; the uncertainties are estimates of 1σ deviations and are given in percentage according to their contribution to the absolute count rate ${{\tilde {\nu }}_{e}}$

Fig. 1.

Observed and predicted IBD count rates in the DANSS detector for the top, bottom, and middle detector positions over the entire data acquisition time. Each point reflects the count rate measured for several days with a specific statistical error. The solid curve shows the predicted counts. The predicted counts disregard oscillations to the hypothetical sterile state, and the model of antineutrino fluxes is based on the Huber and Mueller studies [9, 10]. The illustrated systematic uncertainties do not include uncertainties in the predicted antineutrino fluxes.

3 SEARCHES FOR THE STEROLE NEUTRINO WITH REGARD TO INFORMATION ABOUT THE ABSOLUTE COUNT RATE OF ANTINEUTRINO EVENTS

In the model with three active and one sterile neutrino (3 + 1), the probability to survive (to retain their flavor) at short distances ($\sim$10 m) for reactor antineutrinos is described by the following expression

$$P \approx 1 - {{\sin }^{2}}2{{\theta }_{{ee}}}{{\sin }^{2}}\left( {\frac{{1.27\Delta m_{{41}}^{2}L}}{{{{E}_{\nu }}}}} \right),$$

(4)

where $\Delta m_{{41}}^{2} = m_{4}^{2} - m_{1}^{2}$ [eV²] is the difference of squared neutrino intrinsic mass states, ${\text{si}}{{{\text{n}}}^{2}}2{{\theta }_{{ee}}}$ is the mixing parameter, ${{E}_{\nu }}$ [MeV] is the antineurino energy, and L [m] is the distance between the production point and the detection point. For rather high values of the parameter $\Delta m_{{41}}^{2}$ (≳10 eV²), the argument of the second sine in formula (4) has an error exceeding the oscillation period, which leads to averaging the squared sine ${{\sin }^{2}}(1.27\Delta m_{{41}}^{2}L{\text{/}}{{E}_{\nu }})$ to 1/2.

Then formula (4) takes the following form

$$P \approx 1 - \frac{1}{2}{{\sin }^{2}}2{{\theta }_{{ee}}}.$$

(5)

Thus, the use of information about absolute count rates per day makes it possible to expand the sensitivity range in the parameter space of the sterile neutrino to larger values of $\Delta m_{{41}}^{2}$. Since, the probability in formula (5) is independent of distance, the analysis with regard to only relative counts and the relative spectral shape did not allow to advance to this range. Exactly in the range of large $\Delta m_{{41}}^{2}$, there is evidence to the existence of the sterile neutrino, obtained in the BEST [13] and Neutrino-4 [14] experiments. To consider information about absolute count rates of antineutrinos, the corresponding term $\chi _{{{\text{abs}}}}^{2}$ is introduced to the test statistics. As a result, ${{\chi }^{2}}$ is defined as follows:

$${{\chi }^{2}} = \mathop {\min }\limits_{\eta ,k} \{ \chi _{{\text{I}}}^{2} + \chi _{{{\text{II}}}}^{2} + \chi _{{{\text{penalty}}}}^{2} + \chi _{{{\text{abs}}}}^{2}\} ,$$

(6)

$$\chi _{{\text{I}}}^{2} = \sum\limits_{i = 1}^N \left( {{{Z}_{1}}\;{{Z}_{2}}} \right) \cdot {{W}^{{ - 1}}} \cdot \left( {\begin{array}{*{20}{c}} {{{Z}_{1}}} \\ {{{Z}_{2}}} \end{array}} \right),$$

(7)

$$\chi _{{{\text{II}}}}^{2} = \sum\limits_{i = 1}^N \frac{{Z_{{1i}}^{2}}}{{\sigma _{{1i}}^{2}}} = \sum\limits_{i = 1}^N \frac{{{{{(R_{{1i}}^{{{\text{obs}}}} - {{k}_{1}} \cdot R_{{1i}}^{{{\text{pre}}}}(\eta ))}}^{2}}}}{{\sigma _{{1i}}^{2}}},$$

(8)

$$\chi _{{{\text{penalty}}}}^{2} = \sum\limits_{j = 1,2} \frac{{{{{({{k}_{j}} - k_{j}^{0})}}^{2}}}}{{\sigma _{{kj}}^{2}}} + \sum\limits_l \frac{{{{{({{\eta }_{l}} - \eta _{l}^{0})}}^{2}}}}{{\sigma _{{\eta l}}^{2}}},$$

(9)

$$\begin{gathered} \chi _{{{\text{abs}}}}^{2} = (({{N}_{{{\text{top}}}}} + {{N}_{{{\text{mid}}}}} + {{N}_{{{\text{bottom}}}}}{{)}^{{{\text{obs}}}}} \\ - {{({{N}_{{{\text{top}}}}} + {{k}_{2}} \cdot \sqrt {{{k}_{1}}} \cdot {{N}_{{{\text{mid}}}}} + {{k}_{1}} \cdot {{N}_{{{\text{bottom}}}}})}^{{{\text{pre}}}}}{{)}^{2}}{\text{/}}\sigma _{{{\text{abs}}}}^{2}, \\ \end{gathered} $$

(10)

where i is the energy bin, ${{Z}_{j}} = R_{j}^{{{\text{obs}}}} - {{k}_{j}} \times R_{j}^{{{\text{pre}}}}(\Delta {{m}^{2}},{\text{si}}{{{\text{n}}}^{2}}2\theta ,\;{\boldsymbol{\eta }})$ for each energy bin, ${{R}_{1}} = {{N}_{{{\text{bottom}}}}}{\text{/}}{{N}_{{{\text{top}}}}}$, ${{R}_{2}} = {{N}_{{{\text{mid}}}}}{\text{/}}\sqrt {{{N}_{{{\text{bottom}}}}} \cdot {{N}_{{{\text{top}}}}}}$, where ${{N}_{{{\text{top}}}}}$, ${{N}_{{{\text{mid}}}}}$, ${{N}_{{{\text{bottom}}}}}$ are the absolute count rates per day for each detector position, the indices ${\text{obs}}$ and ${\text{pre}}$ correspond to observed and predicted values, respectively. $W$ is the covariance matrix, k is the relative efficiency (nominal values $k_{1}^{0} = k_{2}^{0} = 1$), η are other parameters of the systematic uncertainties (nuisance parameters), and σ is the systematic uncertainty. As a systematic uncertainty of absolute counts, the conservative estimate ${{\sigma }_{{{\text{abs}}}}} = 7\%$ was used, which consider both uncertainties associated with the experiment (4%) and uncertainties in the predicted antineutrino spectra (5%).

The best point in the parameter space of the sterile neutrino, obtained in the DANSS experiment, has the values $\Delta m_{{41}}^{2} = 0.34$ eV², ${{\sin }^{2}}2{{\theta }_{{ee}}} = 0.07$, and $\chi _{{4\nu }}^{2} - \chi _{{3\nu }}^{2} = 9.8$, which corresponds to the significance ($\sim 2.3\sigma$). Thus, the DANSS experiment did not detect statistically significant evidences in favor of the existence of the sterile neutrino.

The exclusion area in the space of parameter $\Delta m_{{41}}^{2}$, ${{\sin }^{2}}2{{\theta }_{{ee}}}$ is shown in Fig. 2. Cyan color indicates the regions corresponding to the analysis without regard to absolute count rates of the antineutrino events in the DANSS. Crimson color designates the regions obtained with regard to information about the absolute count rate of antineutrino events. Such an analysis made it possible to significantly expand the experimental sensitivity to the region of higher values of the parameter $\Delta m_{{41}}^{2}$. As a result of, the best point obtained in the Neutrino-4 experiment ($\Delta m_{{41}}^{2} = 7.3$ eV², ${\text{si}}{{{\text{n}}}^{2}}2{{\theta }_{{ee}}} = 0.36$), as well as a significant part of the preferred parameters of the sterile neutrino, obtained in the BEST experiment. As predictions for antineutrino spectra, the Huber and Mueller model is used [9, 10]. When using the predictions for the antineutrino spectra, based on the results of the Kurchatov Institute [11, 12], even a more stringent limit to the parameter ${\text{si}}{{{\text{n}}}^{2}}2{{\theta }_{{ee}}}$ appears. The result obtained depends on the model for neutrino spectra; however, the conservative estimate of 5% was used in the analysis for this uncertainty.

Fig. 2.

Exclusion area of the parameters $\Delta m_{{41}}^{2}$, ${{\sin }^{2}}2{{\theta }_{{ee}}}$ at the 90% confidence level, obtained by the Gaussian CL_s method. Cyan color corresponds to the analysis without regard to information about the absolute count rate of IBD events; crimson color corresponds to the analysis with regard to the absolute IBD count rate. Dashed lines are corresponding boundaries of sensitivity ranges. Gray areas are the preferred parameters obtained in the BEST experiment; the marker designates the best point obtained in the Neutrino-4 experiment.

4 CONCLUSIONS

The estimates of the main systematic uncertainties in the count rate of antineutrino events in the DANSS detector were obtained at various distances from the reactor. The total systematic uncertainty was 7%. The observed and predicted using the Huber and Mueller model count rates of antineutrino events over six years were compared. The total ratio of the observed absolute DANSS count to the predicted one was 0.98 $\pm$ 0.04 with regard to the data acquired in all detector positions (without regard to the systematic uncertainty in the predictions for antineutrino spectra).

The exclusion area in the parameter space of the sterile neutrino in the DANSS experiment was obtained in the case of the consideration of absolute count rates of antineutrino events at various distances from the reactor using a conservative estimate of 7% for the systematic uncertainty of the absolute count rate. The exclusion area was obtained using the Huber and Mueller predictions for the antineutrino spectra from the reactor. For large (≳ 10 eV²) parameters $\Delta m_{{41}}^{2}$, the values of the parameter ${\text{si}}{{{\text{n}}}^{2}}2{{\theta }_{{ee}}} > 0.26$ are excluded with a 90% confidence level. The use of the absolute count rates of the DANSS detector allowed exclusion of the best point $\Delta m_{{41}}^{2}$ = 7.3 eV², ${\text{si}}{{{\text{n}}}^{2}}2{{\theta }_{{ee}}} = 0.36$ obtained in the Neutrino-4 experiment. Furthermore, almost the entire region of acceptable parameters obtained in the BEST experiment is excluded for rather large parameter $\Delta m_{{41}}^{2}$.