Fuel-composition dependent reactor antineutrino yield and spectrum at RENO

We report a fuel-dependent reactor electron antineutrino ($\overline{\nu}_e$) yield using six 2.8\,GW$_{\text{th}}$ reactors in the Hanbit nuclear power plant complex, Yonggwang, Korea. The analysis uses $850\,666$ $\overline{\nu}_e$ candidate events with a background fraction of 2.0\% acquired through inverse beta decay (IBD) interactions in the near detector for 1807.9 live days from August 2011 to February 2018. Based on multiple fuel cycles, we observe a fuel $U^{235}$ dependent variation of measured IBD yields with a slope of $(1.51 \pm 0.23) \times 10^{-43}$~cm$^2$/fission and measure a total average IBD yield of $(5.84 \pm 0.12) \times 10^{-43}$~cm$^2$/fission. The hypothesis of no fuel-dependent IBD yield or identical spectra of fuel isotopes is ruled out at 6.6\,$\sigma$. The observed IBD yield variation over $^{235}$U isotope fraction does not show significant deviation in the slope from the Huber-Mueller prediction at 1.3\,$\sigma$. The measured fuel-dependent variation determines IBD yields of $(6.15 \pm 0.19) \times 10^{-43}$~cm$^2$/fission and $(4.18\pm 0.26) \times 10^{-43}$~cm$^2$/fission for two dominant fuel isotopes $^{235}$U and $^{239}$Pu, respectively. The measured IBD yield per $^{235}$U fission shows the largest deficit relative to a reactor model prediction. Reevaluation of the $^{235}$U IBD yield per fission may mostly solve the reactor antineutrino anomaly while $^{239}$Pu is not completely ruled out as a possible source of the anomaly. We also report a 2.7\,$\sigma$ significant hint of correlation between the 5\,MeV excess in observed IBD spectrum and the reactor fuel isotope fraction of $^{235}$U.

We report a fuel-dependent reactor electron antineutrino (νe) yield using six 2.8 GW th reactors in the Hanbit nuclear power plant complex, Yonggwang, Korea. This analysis uses an event sample acquired through inverse beta decay (IBD) interactions in identically designed near and far detectors for 1807.9 live days from August 2011 to February 2018. Based on multiple fuel cycles, we observe a fuel dependent variation in the IBD yield of (6.08 ± 0.18) × 10 −43 cm 2 /fission for 235 U and (4.10 ± 0.26) × 10 −43 cm 2 /fission for 239 Pu while a total average IBD yield per fission (y f ) is (5.78 ± 0.11) × 10 −43 cm 2 /fission. The hypothesis of no fuel dependent IBD yield or identical spectra of fuel isotopes is ruled out at 6.7 σ. The measured IBD yield per 235 U fission shows the largest deficit relative to a reactor model prediction. Reevaluation of the 235 U IBD yield per fission may mostly solve the reactor antineutrino anomaly. We also report a hint of correlation between the 5 MeV excess in observed IBD spectrum and the reactor fuel isotope fraction of 235 U.
A definitive measurement of the smallest neutrino mixing angle θ 13 is a tremendous success in neutrino physics during the last decade [1,2]. The measurement has been achieved by comparing the observed ν e fluxes with detectors placed at two different distances from the reactors. As reactor ν e experiments suffer from large reactor related uncertainties of the expected ν e flux and energy spectrum [3][4][5][6][7], identical detector configuration is essential to cancel out the systematic uncertainties. The Reactor Antineutrino Anomaly (RAA), ∼6 % deficit of measured ν e flux compared to the prediction, is an intriguing mystery in current neutrino physics research and needs to be understood [4][5][6][8][9][10][11]. There have been numerous attempts to explain this anomaly by incorrect inputs to the fission β spectrum conversion, deficiencies in nuclear databases, underestimated uncertainties of reactor ν e model, and the existence of sterile neutrinos [3,[12][13][14][15]. Moreover, all of ongoing reactor ν e experiments have observed a 5 MeV excess in the IBD prompt spectrum with respect to the expected one [8,9,16,17]. This suggests that reactor ν e model is not complete at all.
In commercial nuclear reactor power plants, almost all (> 99%)ν e 's are produced through thousands of β-decay branches of fission fragments from 235 U, 239 Pu, 238 U, and 241 Pu. The ν e flux calculation is based on the inversion of spectra of the β-decay electrons of the thermal fissions which were measured in 1980s at ILL [10,11]. The reactor ν e models using these measurements as inputs have large uncertainties [5][6][7]. Therefore, reevaluation of reactor ν e model and precise measurements of the neutrino flux and spectrum are essential to understand the RAA. Recently, Daya Bay collaboration reported an observation of correlation between the reactor core fuel evolution and changes in the reactor ν e flux and energy spectrum [18]. The collaboration concluded that the 235 U fuel isotope may be the primary contributor to the RAA. In this letter, we report an observation of a fuel dependent variation of the reactor ν e flux and spectrum using 1807.9 days of Reactor Experiment for Neutrino Oscillation (RENO) near detector data. We also present a hint of correlation between the 5 MeV excess and the reactor fuel isotope fraction of 235 U.  (near detector) and 1383 m (far detector) from the reactor array center. The near (far) detector is under 120 (450) meters of water-equivalent rock overburden. The detectors with hydrocarbon liquid scintillator (LS) provide free protons as a target. Coincidence between a prompt positron signal and a delayed signal of gammas from neutron capture by Gadolinium (Gd) provides a distinctive IBD signature. Further details of the RENO detectors and ν e data analysis are found in Ref. [9].
The data used in this analysis are taken through IBD interactions in the near detector for 1807.9 live days from August 2011 to February 2018. For the near detector data, we excluded a period of January to December 2013 because of detection inefficiency caused by an electrical noise coming from an uninterruptible power supply. We measure the reactor ν e flux as a function of an effective fission fraction F i (t) given by where f i,r (t) is the fission fraction of i-th isotope in the r-th reactor, W th,r (t) is the r-th reactor thermal power, p r (t) is the mean survival probability of ν e from the r-th reactor, and L r is the distance between the near detector and the r-th reactor. An average ν e energy produced by a reactor is average energy released per fission. The upper panel of Fig. 1 shows time variation of the effective fission fraction of 235 U viewed by the near detector. The effective fission fraction is obtained from the daily thermal power and fission fraction data of each reactor core, provided by the Hanbit nuclear power plant. A total average IBD yield is measured to be y f = (5.78 ± 0.11) × 10 −43 cm 2 /fission with average effective fission fractions F 235 , F 238 , F 239 , and F 241 of 0.573, 0.073, 0.299, and 0.055, respectively. For examining fuel dependent variation of reactor ν e yield and spectrum, eight groups of equal data size are sampled according to the eight different values of the 235 U fission fraction. A time-averaged effective fission fraction (F i,j ) of the i-th isotope in the j-th data group is calculated as, . ( The time-averaged effective fission fractions of the four isotopes in each group are shown as a function of timeaveraged fission fraction of 235 U (F 235 ) in the lower panel of Fig. 1. An average IBD yield per fission of the j-th data group (y f,j ) is given by, where an instantaneous IBD yield per fission (y i ) is calculated as is the IBD reaction cross section, and φ i (E ν ) is the reactor ν e spectrum [5][6][7]. We use the IBD cross section in Ref. [7,19] and a neutron lifetime of 880.2 s in the calculation [20]. The IBD yield y i of a fissile isotope is sensitive to its reactor ν e spectrum because the IBD cross section increases with the ν e energy. A model-independent IBD yield of y f,j is determined by counting the number of events in each data group using the following relationship. (4) where N j is the number of IBD events in the j-th group, N p is the number of target protons, P r (t) is the mean survival probability, and d (t) is the detection efficiency including the signal loss due to timing veto requirements. The IBD yield of an isotope per fission is determined by matching the observed N j with its corresponding value of y f,j for each data group. No fission-fraction dependent IBD yield expects a flat distribution of y f as a function of F 235 . Fig. 2 shows a measured distribution of y f as a function of F 235 or F 239 for the eight data groups. We observe a clear correlation between y f and F 235 , indicating dependence of the IBD yield per fission on the isotope fraction of 235 U. A linear function is used for a fit to the eight data points. The red solid line shows the best fit with χ 2 /NDF= 4.60/6. The horizontal line represents an expected distribution for no fuel dependent IBD yield if the reactor ν e spectra from the four isotope fissions are identical. This result rules out no fuel-dependent variation of the IBD yield per fission at 6.7 σ confidence level, corresponding to the p-value of 2.3 × 10 −11 . Therefore, we conclude that the variation of the y f as a function of F 235 comes from unequal IBD yields among different isotope fissions because of their different ν e energy spectra. The blue dotted line represents the predicted IBD yield per fission after scaling the Huber-Mueller model [5][6][7] by −7.2% with χ 2 /NDF= 5.89/7. The slightly smaller slope of the best-fit result compared to the scaled model prediction may indicates that the model overestimates contribution of the 235 U isotope to the IBD yield.
For determination of y 235 and y 239 simultaneously, a χ 2 with pull parameter terms of systematic uncertainties is constructed using the observed IBD yield per fission and minimized by varying the free parameters of y 235 and y 239 , and pull parameters. The subdominant isotopes of 238 U and 241 Pu are not included in the fitting parameters. We take 10 % for the 238 U yield uncertainty [4] and 5 % for the 241 Pu yield uncertainty [21]. The reactor uncorrelated uncertainties of thermal power, fission fraction, energy per fission and detection efficiency are taken into account in the χ 2 calculation. The χ 2 is given by where y obs,j is the observed IBD yield per fission averaged over the four isotopes in the j-th data group, σ obs,j is the statistical uncertainty of y obs,j , y exp,j is the expected IBD yield per fission averaged over the four isotopes, F j i is the time-averaged effective fission fraction of the i-th isotope for the j-th data group, σ 238 and σ 241 are the uncertainties of y 238 (10%) and y 241 (5%), respectively, σ th , σ f , σ en and σ det are the uncertainties of thermal power (0.5%), fission fraction (0.7%), energy per fission (0.2%) and detection efficiency (1.04%), respectively, ξ 238 and ξ 241 are the pull parameters of y 238 and y 241 , respectively, and ξ th , ξ f , ξ en and ξ det are the pull parameters for thermal power, fission fraction, energy per fission and detection efficiency, respectively.
The best-fit results are y 235 = (6.08 ± 0.18) × 10 −43 cm 2 /fission and y 239 = (4.10 ± 0.26) × 10 −43 cm 2 /fission. Fig. 3 shows the combined mea-surement of y 235 and y 239 . The best-fit value of y 235 is smaller than the prediction from the Huber-Mueller model at 3.5 σ while the best-fit y 239 is consistent with the prediction within 1.2 σ. This indicates that reevaluation of the 235 U IBD yield per fission may mostly solve the RAA.
Following the analysis in Ref. [22] we also perform the combined measurements for all combinations of the four isotopes, total six pairs. The χ 2 of Eq. (5) is used with an added constraint term of (ξ i /σ i ) 2 to restrict the fitted values of y 238 and y 241 within reasonable ranges. Fig. 4 shows allowed regions of each pair of IBD yields per fission. The dot is the best fit of each pair of IBD yields while the crossing lines represent the model predicted yields. The shaded contours are 68.3, 95.5 and 99.7% C.L. allowed regions for each pair of IBD yields. In the fitting results of the six pairs of isotopes, we observe that y 235 is smaller than the prediction at ∼2.5 σ while the IBD yields per fission of the rest isotopes are consistent with the prediction within 1 σ.
The deficit of y 235 relative to the Huber-Mueller prediction could be interpreted by an indication of incorrectly evaluated IBD yield of 235 U fission that may be a major source of the RAA [18,23]. To check this possibility, we perform pseudoexperiments. Pseudodata with IBD yields per fission, y f,j , are produced for various ratios of y 235 and y 239 . For each input of y 235 and y 239 , 1000 pseudodata are produced within statistical and systematic errors of y 238 and y 241 . The obtained best-fit values of y 235 and y 239 , 6.08 and 4.10 ×10 −43 cm 2 /fission, respectively, are used as the inputs of the pseudodata. The means of the best-fit values agree well with the inputs. In addition, pseudoexperiments with y f scaled down by 7.2% from the model prediction are generated by reducing y 235 only. A fit finds a value of y 235 less than the measured value of 6.08×10 −43 cm 2 /fission and 4.5 σ deviation from the model prediction. This does not reproduce the measured y 235 deviation of 3.5 σ by reducing y 235 only. Pseudoexperiments with y f scaled down by 7.2% from the model prediction are also generated by reducing equal fractions of y 235 and y 239 . A fit finds ∼3 σ deviation of y 235 from the model prediction. This is consistent with the obtained best-fit result of data. Thus, we conclude that the RAA can be explained by reevaluation of 239 Pu as well as 235 U.
The RENO collaboration has reported an excess of the observed IBD prompt spectrum at 5 MeV [8,9], also observed by the other ongoing reactor ν e experiments as well [16,17]. The 5 MeV excess is observed to be proportional to the reactor thermal power [9]. Several explanations and suggestions are proposed to understand the origin of the 5 MeV excess [24][25][26][27][28]. There is a suggestion that a particular isotope could be the source of the excess [26], while an analysis disfavors the 239 Pu and 241 Pu isotopes as a single source for the 5 MeV excess [29]. However, there is no clear understanding of the origin of the 5 MeV excess yet.
A possible fuel dependence of the 5 MeV excess is examined by the IBD yield per fission for the events in the 5 MeV region of 3.8 < E p < 7 MeV. The upper panel of Fig. 5 shows a correlation between y f of the 5 MeV region and F 235 . The IBD yield of the 5 MeV region also shows a correlation with F 235 and is consistent with the model prediction scaled by −6.3 %. The lower panel of Fig. 5 shows the ratio of the IBD yield between the 5 MeV region and the total IBD events as a function of F 235 . The expected yield ratio from the model prediction is not constant over F 235 but increases in proportion to the value of F 235 . The measured yield ratio shows a weakly enhanced IBD yield for the 235 U isotope. The χ 2 /NDF is 6.77/6 for the best fit and is 8.92/7 for the scaled model prediction ratio. This demonstrates that the 5 MeV excess contributes to y f more than the total IBD events.
To make a more sensitive study of a fuel dependence of the IBD yield by the 5 MeV excess only, we examine a fraction of the IBD events in the 5 MeV excess with respect to the total observed IBD events. Five groups of equal data size are sampled according to five different values of F 235 . The event rate of the 5 MeV excess is obtained by subtracting the MC predicted event rate from the observed one in the region of 3.8 < E p < 7 MeV. Fig. 6 shows the distribution of 5 MeV excess fractions as a function of F 235 for the five data groups. The horizontal dotted line is the best fit with a zeroth-order polynomial function indicating a constant 5 MeV excess fraction with an average excess fraction of (2.55 ± 0.07) %. The red solid line is the best fit with a first-order polynomial function. We observe a suggestive correlation between the 5 MeV excess fraction and F 235 . The hypothesis of a constant 5 MeV excess fraction is disfavored at 2.6 σ where the χ 2 /NDF is 2.18/3 for the best fit and 8.76/4 for the constant hypothesis. While the current result shows a marginal dependence of the 5 MeV excess fraction on F 235 , further accumulated data may reveal the source of the 5 MeV excess.
In summary, we report a fuel dependent IBD yield and energy spectrum using 1807.9 days of RENO near detector data. We measure an IBD yield per fission of (6.08 ± 0.18) × 10 −43 cm 2 /fission and (4.10 ± 0.26) × 10 −43 cm 2 /fission for the dominant fission isotopes of 235 U and 239 Pu, respectively. A change in the IBD energy spectrum with respect to the effective 235 U fission fraction is observed at 6.7 σ. The measured IBD yield per fission of (5.78±0.11)×10 −43 cm 2 /fission is 7.2% smaller than the Huber-Mueller model prediction and confirms the RAA. The measured IBD yield per 235 U fission is smaller than the Huber-Mueller model prediction at 3.5 σ. This suggests that the RAA can be understood by incorrect estimation of the 235 U IBD yield. We obtain the first hint for a correlation between the 5 MeV excess fraction and the 235 U fission fraction. The correlation indicates that the 5 MeV excess may be associated with the 235 U fission. the BK21 of NRF and Institute for Basic Science grant No. IBS-R017-G1-2018-a00. We gratefully acknowledge the cooperation of the Hanbit Nuclear Power Site and the Korea Hydro & Nuclear Power Co., Ltd. (KHNP). We thank KISTI for providing computing and network resources through GSDC, and all the technical and administrative people who greatly helped in making this experiment possible.