Evolution of the Reactor Antineutrino Flux and Spectrum at Daya Bay

Evolution of the Reactor Antineutrino Flux and Spectrum at Daya Bay

F. P. An,1A. B. Balantekin,2H. R. Band,3M. Bishai,4S. Blyth,5,6D. Cao,7G. F. Cao,8J. Cao,8Y. L. Chan,9J. F. Chang,8 Y. Chang,6H. S. Chen,8Q. Y. Chen,10S. M. Chen,11Y. X. Chen,12Y. Chen,13J. Cheng,10Z. K. Cheng,14J. J. Cherwinka,2 M. C. Chu,9 A. Chukanov,15J. P. Cummings,16Y. Y. Ding,8 M. V. Diwan,4M. Dolgareva,15J. Dove,17D. A. Dwyer,18 W. R. Edwards,18R. Gill,4 M. Gonchar,15G. H. Gong,11H. Gong,11M. Grassi,8 W. Q. Gu,19 L. Guo,11 X. H. Guo,20 Y. H. Guo,21Z. Guo,11R. W. Hackenburg,4S. Hans,4,*M. He,8K. M. Heeger,3Y. K. Heng,8A. Higuera,22Y. B. Hsiung,5

B. Z. Hu,5 T. Hu,8 E. C. Huang,17H. X. Huang,23X. T. Huang,10Y. B. Huang,8 P. Huber,24 W. Huo,25G. Hussain,11 D. E. Jaffe,4K. L. Jen,26X. P. Ji,27,11X. L. Ji,8J. B. Jiao,10R. A. Johnson,28D. Jones,29L. Kang,30S. H. Kettell,4A. Khan,14 S. Kohn,31M. Kramer,18,31K. K. Kwan,9M. W. Kwok,9T. J. Langford,3K. Lau,22L. Lebanowski,11J. Lee,18J. H. C. Lee,32 R. T. Lei,30 R. Leitner,33J. K. C. Leung,32C. Li,10D. J. Li,25F. Li,8 G. S. Li,19Q. J. Li,8S. Li,30S. C. Li,24W. D. Li,8 X. N. Li,8X. Q. Li,27Y. F. Li,8Z. B. Li,14H. Liang,25C. J. Lin,18G. L. Lin,26S. Lin,30S. K. Lin,22Y. -C. Lin,5J. J. Ling,14

J. M. Link,24L. Littenberg,4 B. R. Littlejohn,34J. L. Liu,19J. C. Liu,8C. W. Loh,7 C. Lu,35H. Q. Lu,8J. S. Lu,8 K. B. Luk,31,18 X. Y. Ma,8 X. B. Ma,12Y. Q. Ma,8 Y. Malyshkin,36 D. A. Martinez Caicedo,34K. T. McDonald,35 R. D. McKeown,37,38I. Mitchell,22Y. Nakajima,18J. Napolitano,29 D. Naumov,15E. Naumova,15H. Y. Ngai,32 J. P. Ochoa-Ricoux,36A. Olshevskiy,15H. -R. Pan,5J. Park,24S. Patton,18V. Pec,33J. C. Peng,17L. Pinsky,22C. S. J. Pun,32 F. Z. Qi,8M. Qi,7X. Qian,4R. M. Qiu,12N. Raper,39,14J. Ren,23R. Rosero,4B. Roskovec,33X. C. Ruan,23H. Steiner,31,18 P. Stoler,39J. L. Sun,40 W. Tang,4 D. Taychenachev,15K. Treskov,15K. V. Tsang,18C. E. Tull,18N. Viaux,36B. Viren,4 V. Vorobel,33C. H. Wang,6 M. Wang,10N. Y. Wang,20R. G. Wang,8W. Wang,38,14X. Wang,41Y. F. Wang,8 Z. Wang,11

Z. Wang,8 Z. M. Wang,8 H. Y. Wei,11 L. J. Wen,8 K. Whisnant,42C. G. White,34 L. Whitehead,22T. Wise,3 H. L. H. Wong,31,18S. C. F. Wong,14E. Worcester,4C.-H. Wu,26Q. Wu,10W. J. Wu,8D. M. Xia,43J. K. Xia,8Z. Z. Xing,8 J. L. Xu,8Y. Xu,14T. Xue,11C. G. Yang,8H. Yang,7L. Yang,30M. S. Yang,8M. T. Yang,10Y. Z. Yang,14M. Ye,8Z. Ye,22

M. Yeh,4 B. L. Young,42Z. Y. Yu,8 S. Zeng,8 L. Zhan,8 C. Zhang,4 C. C. Zhang,8H. H. Zhang,14 J. W. Zhang,8 Q. M. Zhang,21R. Zhang,7 X. T. Zhang,8 Y. M. Zhang,11 Y. X. Zhang,40 Y. M. Zhang,14Z. J. Zhang,30Z. Y. Zhang,8

Z. P. Zhang,25 J. Zhao,8 L. Zhou,8 H. L. Zhuang,8 and J. H. Zou8

(Daya Bay Collaboration)

1_{Institute of Modern Physics, East China University of Science and Technology, Shanghai} 2

University of Wisconsin, Madison, Wisconsin 53706

3_{Wright Laboratory and Department of Physics, Yale University, New Haven, Connecticut 06520} 4

Brookhaven National Laboratory, Upton, New York 11973

5_{Department of Physics, National Taiwan University, Taipei} 6

National United University, Miao-Li

7_{Nanjing University, Nanjing} 8

Institute of High Energy Physics, Beijing

9_{Chinese University of Hong Kong, Hong Kong} 10

Shandong University, Jinan

11

Department of Engineering Physics, Tsinghua University, Beijing

12

North China Electric Power University, Beijing

13

Shenzhen University, Shenzhen

14

Sun Yat-Sen (Zhongshan) University, Guangzhou

15

Joint Institute for Nuclear Research, Dubna, Moscow Region

16

Siena College, Loudonville, New York 12211

17

Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

18

Lawrence Berkeley National Laboratory, Berkeley, California 94720

19

Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai Laboratory for Particle Physics and Cosmology, Shanghai

20

Beijing Normal University, Beijing

21

Department of Nuclear Science and Technology, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an

22

Department of Physics, University of Houston, Houston, Texas 77204

23

China Institute of Atomic Energy, Beijing

24

Center for Neutrino Physics, Virginia Tech, Blacksburg, Virginia 24061

25

University of Science and Technology of China, Hefei

26_{Institute of Physics, National Chiao-Tung University, Hsinchu} 27

School of Physics, Nankai University, Tianjin

28_{Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221} 29

Department of Physics, College of Science and Technology, Temple University, Philadelphia, Pennsylvania 19122

30_{Dongguan University of Technology, Dongguan} 31

Department of Physics, University of California, Berkeley, California 94720

32_{Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong} 33

Charles University, Faculty of Mathematics and Physics, Prague

34_{Department of Physics, Illinois Institute of Technology, Chicago, Illinois 60616} 35

Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544

36_{Instituto de Física, Pontificia Universidad Católica de Chile, Santiago} 37

California Institute of Technology, Pasadena, California 91125

38_{College of William and Mary, Williamsburg, Virginia 23187} 39

Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180

40_{China General Nuclear Power Group, Shenzhen} 41

College of Electronic Science and Engineering, National University of Defense Technology, Changsha

42_{Iowa State University, Ames, Iowa 50011} 43

Chongqing University, Chongqing (Received 6 April 2017; published 19 June 2017)

The Daya Bay experiment has observed correlations between reactor core fuel evolution and changes in the reactor antineutrino flux and energy spectrum. Four antineutrino detectors in two experimental halls were used to identify 2.2 million inverse beta decays (IBDs) over 1230 days spanning multiple fuel cycles for each of six 2.9 GWthreactor cores at the Daya Bay and Ling Ao nuclear power plants. Using detector

data spanning effective239Pu fission fractions F239from 0.25 to 0.35, Daya Bay measures an average IBD

yield¯σfofð5.90  0.13Þ × 10−43cm2=fission and a fuel-dependent variation in the IBD yield, dσf=dF239,

ofð−1.86  0.18Þ × 10−43cm2=fission. This observation rejects the hypothesis of a constant antineutrino flux as a function of the239Pu fission fraction at 10 standard deviations. The variation in IBD yield is found to be energy dependent, rejecting the hypothesis of a constant antineutrino energy spectrum at 5.1 standard deviations. While measurements of the evolution in the IBD spectrum show general agreement with predictions from recent reactor models, the measured evolution in total IBD yield disagrees with recent predictions at 3.1σ. This discrepancy indicates that an overall deficit in the measured flux with respect to predictions does not result from equal fractional deficits from the primary fission isotopes235U,

239_Pu, 238_{U, and} 241_{Pu. Based on measured IBD yield variations, yields of ð6.17  0.17Þ and}

ð4.27  0.26Þ × 10−43_cm2_{=fission have been determined for the two dominant fission parent isotopes} 235_{U and}239_{Pu. A 7.8% discrepancy between the observed and predicted}235_{U yields suggests that this}

isotope may be the primary contributor to the reactor antineutrino anomaly.

DOI:10.1103/PhysRevLett.118.251801

Electron antineutrinos are produced in commercial nuclear reactor cores as neutron-rich fission fragments of the fission isotopes235U,238U,239Pu, and241Pu beta decay successively toward the isotopic line of stability. The total electron antineutrino flux produced by a reactor core is the sum of thousands of individual beta-decay branches, each producing its unique antineutrino flux and spectrum. Daya Bay has recently reported measurements of this aggregate antineutrino flux and spectrum[1,2]. These measurements confirm the observed discrepancy of ∼6% between the measured reactor antineutrino fluxes of past experiments and reactor model predictions [3,4], also known as the “reactor antineutrino anomaly”[5], and indicate a disagree-ment between the measured and predicted antineutrino energy spectrum in the energy range of 5–7 MeV. Similar results have also been reported by other current reactor

experiments [6,7]. Existing interpretations for these flux and spectrum discrepancies include deficiencies in fission beta spectrum conversion inputs and nuclear databases

[8,8–11]or the existence of sterile neutrinos[12]. If correct, these explanations could have implications for future neutrino experiments[13,14]and nuclear applications[15]. One factor taken into account but not yet directly measured in Daya Bay analyses is the effect of fuel evolution on the observed reactor antineutrino spectrum. Since fission yields and beta-decay branches from each fission parent isotope are not identical, antineutrino fluxes and spectra produced from the various fission isotopes differ[16]. Thus, when a reactor experiences a change in the percent contribution to fission rates from each fission-ing isotope (fission fractions), a measurable change in the reactor antineutrino flux and spectrum may also be

produced. Previous experiments have demonstrated varia-tions in the total reactor antineutrino flux with fuel evolution[17,18]while providing indications that a change in the spectral shape with fuel evolution may be present

[18]. In this Letter, we report the direct observation of a change in the reactor antineutrino flux and spectrum with reactor fuel evolution. This result is then used to determine the reactor antineutrino flux produced by 235U and 239Pu and to perform new tests of reactor antineutrino models.

The Daya Bay reactor neutrino experiment studies the flux of electron antineutrinos produced by six 2.9 GWth commercial reactor cores in two near experimental halls (EH1 and EH2) and one far experimental hall (EH3)[19]. EH3 houses four antineutrino detectors (ADs), while EH1 and EH2 each house two. Only the data acquired with the four ADs in EH1 and EH2 in a period covering 1230 days from 2011 to 2015 were utilized in this analysis. This includes a period of 217 days with only three ADs present in the near halls, before the second AD was installed in EH2. EH1 is situated at a distance of about∼360 m from two cores, while EH2 is∼500 m away from the other four. Antineutrinos were detected via the inverse beta-decay (IBD) reaction, ¯ν_eþ p → eþþ n. An IBD candidate was defined as a time-correlated trigger pair consisting of a prompt eþ candidate with reconstructed energy Ep≈ Eν− 0.8 MeV between 0.7 and 12 MeVand a delayed candidate from neutron capture on gadolinium in the target with 6–12 MeV reconstructed energy[20]. An IBD candidate set was required to be isolated in time from cosmogenic muon activity or any other AD triggers. This selection produced a set of about 1 198 000 and 1 025 000 IBD candidates from EH1 and EH2, respectively.

Accidental time coincidences of uncorrelated triggers, the dominant background in all ADs, contribute a rate of ∼1% the size of the IBD signal. To account for the <10% variations in the rate of this background with time, it was calculated and subtracted week by week for each AD. The remaining backgrounds, which contribute ∼0.5% of IBD candidates, were subtracted assuming no time varia-tion in shape or normalizavaria-tion.

The spectrum of reactor antineutrinos with energy Eν detected by an AD at time t is expected to be

d2NðEν; tÞ dEνdt ¼ NpσðEνÞε X6 r¼1 PðEν; LrÞ 4πL2 r d2ϕrðEν; tÞ dEνdt ; ð1Þ where Np is the number of target protons, σðEνÞ is the IBD reaction cross section,ε is the efficiency of detecting IBDs, Lris the distance between the centers of the AD and the rth core, and PðEν; LrÞ is the survival probability due to neutrino oscillation from core r. The sum in r is taken over the six reactor cores present at Daya Bay. The term d2ϕrðEν; tÞ=dEνdt is the antineutrino spectrum from the rth reactor core: d2ϕrðEν; tÞ dEνdt ¼ Wth;rðtÞ ¯ErðtÞ X i

fi;rðtÞsiðEνÞcnei ðEνÞ þ sSNFðEνÞ; ð2Þ where the index i runs over the four primary fission isotopes (235U, 238U, 239Pu, and 241Pu), WthðtÞ is the reactor thermal power, fiðtÞ is the fraction of fissions from isotope i, ¯ErðtÞ ¼

P

ifi;rðtÞeiis the core’s average energy released per fission due to the average energy release ei from each fission isotope, and siðEνÞ is the ¯νe energy spectrum per fission. All other fission isotopes contribute <0.3% to the total antineutrino flux[2]and are neglected in this analysis. The correction cnei ðEνÞ accounts for reactor nonequilibrium effects of long-lived fission fragments, and sSNFðEνÞ is the contribution from nearby spent nuclear fuel; both of these quantities are treated as time independent, an assumption that has a negligible impact on the analysis.

The evolution of the antineutrino flux and spectrum was studied as a function of the effective fission fractions FiðtÞ viewed by each AD:

FiðtÞ ¼ X6 r¼1 Wth;rðtÞ ¯prfi;rðtÞ L2r¯ErðtÞ

=

X6 r¼1 Wth;rðtÞ ¯pr L2r¯ErðtÞ : ð3Þ The mean survival probability¯p_r, calculated by integrating the flux- and cross-section-weighted oscillation survival probability of antineutrinos from core r over Eν, is treated as time independent. The four effective fission fractions F235, F238, F239, and F241, corresponding to the235U,238U, 239_{Pu, and}241_{Pu isotopes, respectively, sum to unity at all} times for any AD. The definition in Eq. (3) allows the expression of the measured IBD yield per nuclear fissionσ_f as a simple sum of IBD yields from the individual isotopes: σf¼

P

iFiσi. Weekly effective fission fraction values for each detector were produced using thermal power and fission fraction data for each core, which were provided by the power plant and validated by the Collaboration using theAPOLLO2reactor modeling code[2]. The baselines and the mean survival probabilities used are the same as in Ref.[20], while ei values were taken from Ref.[21].

Throughout the Letter, changes in the IBD yield and spectrum per fission will be represented as a function of the effective fission fraction F239, which increases as nearby reactors’ fuel cycles progress. At the beginning of each core’s fuel cycle, when 1=3 (1=4) of the fuel rods in the Daya Bay (Ling Ao) cores are fresh,239Pu fission fractions f239are∼15%. This fraction then rises to ∼40% by the end of the cycle. Effective 239Pu fission fractions F239 are shown for the EH1 and EH2 ADs in Fig.1. The F239values for ADs at the same EH are identical to < 0.1%. Periods of constant positive slope correspond to continuous running and evolution of fuel in the cores, while sharp drops in F239 correspond to the shut-down and start-up of a reactor. For EH1 (EH2),∼80% of the antineutrinos originate from the

two Daya Bay (four Ling Ao) cores. As ADs receive fluxes from multiple cores with differing fuel compositions, variations in the effective fission fractions at an AD are smaller than variations in the fission fractions within a single core. The relationships between F239 and the effective fission fractions of the other fissioning isotopes for the same data set are shown in the bottom panel in Fig. 1. The average effective fission fractions ¯Fi for i ¼ ð235; 238; 239; 241Þ for the combined EH1 and EH2 ADs were (0.571, 0.076, 0.299, 0.054).

Uncertainties in the input reactor data will result in systematic uncertainties in the measured IBD yields and in the reported F239 values. The thermal power of each reactor was determined through heat-balance calculations of the reactor cooling water to a precision of 0.5%, uncorrelated among cores[2]. Dominant uncertainties in this calculation arise from limitations in the accuracy of water flow rate measurements. Since these measurement techniques are independent of the core composition, this uncertainty was treated for a single core as fully correlated at all fission fraction values. Fission fraction uncertainties of δf_i=fi¼ 5% were determined by comparing measurements of iso-topic content in spent nuclear fuel to values obtained by the APOLLO2 reactor modeling code [2,22]. As these compar-isons do not suggest systematic biases in the reported fission fractions for specific burnup ranges, fission fraction uncer-tainties were treated as fully correlated for all F239.

The fuel evolution analysis is particularly sensitive to detection systematics not fully correlated in time. The

stability of the ADs’ performance in time has been well demonstrated[20,23]. Variations in the detector live time due to periodic calibrations, maintenance, or data quality were corrected for in the analysis with a negligible impact on systematic uncertainties. Percent-level yearly time variation in light collection in the ADs has been corrected for in Daya Bay’s energy calibration. Residual time variations in reconstructed energies of the order of 0.2% had a negligible impact on the observed rate and spectrum variations described below. Time-independent uncertainties in the IBD detection efficiency were also included in the analysis; AD-uncorrelated and AD-correlated efficiency uncertainties are 0.13% and 1.9%, respectively[20].

To examine changes in the observed IBD yield and spectrum with reactor fuel evolution, effective fission frac-tions F239were used to group weekly IBD data sets into eight bins of differing fuel composition, resulting in similar statistics in each bin. For the F239bins utilized in this analysis, the effective fission fractions (F235, F238, F239, F241) vary within envelopes of width (0.119, 0.001, 0.092, 0.025), as illustrated in Fig.1. Each bin’s IBD yield per fission, σ_f in cm2=fission, was then calculated based on that bin’s IBD detection rate[2]. Measured IBD yields[24], presented in Fig.2, show a clear downward trend with increasing F239.

The data were then fit with a linear function describing the IBD yield as a function of F239, in terms of the average 239_{Pu fission fraction ¯F}

239 given above: σfðF239Þ ¼ ¯σfþ

dσf

dF239ðF239− ¯F239Þ: ð4Þ The fit parameters are the total F239-averaged IBD yield¯σf and the change in yield per unit 239Pu fission fraction FIG. 1. Top: Weekly effective 239Pu fission fractions F239

[defined in Eq. (3)] for the EH1 and EH2 ADs based on input reactor data. Bottom: Effective fission fractions for the primary fission isotopes versus F239. Each data point represents an

average over periods of similar F239 from the top panel.

FIG. 2. IBD yield per fission,σ_f, versus effective239Pu (lower axis) or235U (upper axis) fission fraction. Yield measurements (black) are pictured with bars representing statistical errors, which lead the uncertainty in the measured evolution, dσf=dF239.

Constant yield (green line) and variable yield (red line) best fits described in the text are also pictured, as well as predicted yields from the Huber-Mueller model (blue line), scaled to account for the difference in total yield ¯σ_f between the data and prediction.

dσf=dF239. This fit determines dσf=dF239¼ ð−1.86  0.18Þ × 10−43 _cm2_{=fission with a χ}2_{=NDF of 3.5=6. The} statistical errors inσ_f values are the leading uncertainty in the measurement, with reactor data systematics also provid-ing a non-negligible contribution; errors arisprovid-ing from assum-ing linear trends in IBD yield with F239 [Eq. (4)] are negligible. The fit also provides a total IBD yield ¯σ_f of (5.90  0.13) ×10−43 cm2=fission with the error dominated by uncertainty in the estimation of the ADs’ IBD detection efficiency. This result was then compared to a constant reactor antineutrino flux model, where dσf=dF239 ¼ 0. This model, depicted by the horizontal green line in Fig. 2, provides a best fit with χ2=NDF ¼ 115=7. The best-fit dσf=dF239 value is incompatible with this constant flux model at 10 standard deviations (σ).

Observed IBD yields were compared to those predicted by recent reactor antineutrino models, generated according to Eqs.(1)and(2). Among many available models[9,25–27], 235_U, 239_{Pu, and} 241_{Pu antineutrino spectrum per fission} predictions from Huber [3] and 238U predictions from Mueller et al. [4]were used to enable a direct comparison to the reactor antineutrino anomaly. The predicted total IBD yield¯σ_f, (6.22  0.14) ×10−43 cm2=fission, differs from the measured ¯σ_f by 1.7σ. This 5.1% deficit is consistent with previous measurements reported by Daya Bay[1,2], as well as with the∼6% deficit observed in global fits of past reactor experiments. The predicted dσf=dF239 from the Huber-Mueller model, (−2.46  0.06Þ × 10−43 _cm2_{=fission, is} rep-resented in Fig.2after scaling by the 5.1% difference in the predicted and measured¯σ_ffrom this analysis. This predicted dσf=dF239differs from the measurement by3.1σ, indicating additional tension between the flux measurements and models beyond the established differences in total IBD yield ¯σ_f. In particular, it suggests that the fractional differ-ence between the predicted and measured antineutrino fluxes may not be the same for all fission isotopes. If the measured fractional yield deficits from all isotopes are equal, the ratio of the slope dσf=dF239to the total yield ¯σfwill be identical for the measurement and prediction. These ratios, −0.31  0.03 and −0.39  0.01, respectively, are incom-patible at2.6σ confidence level.

The evolution of Daya Bay’s IBD yield pictured in Fig.2

was also used to measure the individual IBD yields of235U and239Pu. For each F239bin a in Fig.2, the measured IBD yield can be described as

σa f¼ X i Fa iσi; ð5Þ where Fa

i are the effective fission fractions for each isotope andσ_i is the IBD yield from that isotope. Measurements from all bins can be summarized with the matrix equation

σf ¼ Fσ; ð6Þ

where σ_f is an eight-element vector of the measured IBD yields,σ is a vector containing the IBD yields of the four fission isotopes, and F is an 8 × 4 matrix containing fission fractions for the data in each F239bin. This matrix equation was used to construct aχ2test statistic:

χ2_{¼ ðσ}

f− FσÞ⊤V−1ðσf− FσÞ; ð7Þ which allows a scan over the fullσ parameter space. The matrix V is a covariance matrix containing the previously discussed statistical, reactor, and detector uncertainties and their correlation between measurementsσ_f.

In order to break the degeneracy from contributions of the two minor fission isotopes 241Pu and 238U, weak constraints were applied to these isotopes’ IBD yields. This was accomplished in Eq.(7)by adding termsðσ_i− ˆσ_iÞ2=ϵ2i for 238U and 241Pu, where ˆσ_i and ϵ_i are theoretically predicted IBD yields and assigned uncertainties, which were treated as fully uncorrelated. Values forˆσ_iwere taken from Ref. [4] for 238U (10.1 × 10−43 cm2=fission) and Ref. [3] for 241Pu (6.05 × 10−43 cm2=fission). Values ϵi were set at 10% of the model-predicted yield, significantly higher than the quoted Huber-Mueller uncertainties, in order to reduce the potential bias to the fit.

The IBD yields from 235U and 239Pu, σ₂₃₅ and σ₂₃₉, were found to be (6.17  0.17) and (4.27  0.26) ×10−43cm2=fission, respectively. Allowed regions and one-dimensionalΔχ2 profiles forσ₂₃₅ and σ₂₃₉ are shown in Fig.3. The measurement is currently limited in precision by the AD-correlated uncertainty in Daya Bay’s detection efficiency and by the statistical uncertainty in the measure-mentsσ_f. The 10% uncertainties assigned toσ_238;241provide a subdominant contribution to the uncertainty inσ₂₃₅ and σ239. Thisσ235is 7.8% lower than the Huber-Mueller model value of (6.69  0.15) ×10−43 cm2=fission, a difference significantly larger than the 2.7% measurement uncertainty. A measuredσ₂₃₅ yield deficit has also been reported using global fits to antineutrino data from reactors of varying fission fractions[28]. The measuredσ₂₃₉value is consistent with the predicted value of (4.36  0.11) ×10−43 cm2=fission within the 6% uncertainty of the measurement.

By applying additional constraints onσ_fin Eq.(7), these σ235 and σ239 results were tested for consistency with hypotheticalσ_f values representing differing sources of the reactor antineutrino anomaly. If the anomaly is produced solely via incorrect predictions of235U, the measuredσ₂₃₅ should deviate from its predicted value while σ_238;239;241 remain at their predicted values; enforcement of this addi-tional constraint in Eq. (7) produced a best fit higher by Δχ2_{=NDF ¼ 0.17=1 (two-sided p value 0.68). A similar} test of239Pu as the sole source of the anomaly yielded a best-fit value higher by Δχ2=NDF ¼ 10.0=1 (p value 0.000 16). Requiring all isotopes in Eq.(7) to exhibit an equal fractional deficit with respect to prediction, the best

fit was found to be higher byΔχ2=NDF ¼ 7.9=1 (p value 0.0049). Thus, the hypothesis that 235U is primarily responsible for the reactor antineutrino anomaly is favored by the Daya Bay data, with the equal deficit and239Pu-only deficit hypotheses disfavored at the 2.8σ and 3.2σ con-fidence levels, respectively.

To investigate changes in the antineutrino spectrum with reactor fuel evolution, observed IBD spectra per fission, S, were examined, whereσ_f¼P_jSj, the sum of IBD yields in all prompt energy bins. For each F239 bin depicted in Fig.4, the measured Sjvalues were compared to the F239 -averaged IBD yield per fission value ¯Sj. The ratio Sj= ¯Sjis plotted against F239in Fig.4for four different Epbins. The common negative slope in Sj= ¯Sj visible in all prompt energy ranges indicates an overall reduction in the reactor antineutrino flux with increasing F239, as demonstrated in Fig.2. In addition, the trends in Sj= ¯Sjwith F239in Fig.4 differ for each energy bin, indicating a change in the spectral shape with fuel evolution. In particular, the content of higher-energy bins decreases more rapidly than lower-energy bins as F239 increases.

To quantify the statistical significance of these trends, a χ2_{fit similar to that of Eq.(4)was applied to each of the} four energy ranges in Fig.4:

SjðF239Þ ¼ ¯Sjþ dSj

dF239ðF239− ¯F239Þ: ð8Þ If no change in the spectrum shape is observed, ð1=¯SjÞðdSj=dF239Þ values in Fig. 4 should be identical for all energy ranges. The best-fitð1=¯S_jÞðdS_j=dF239Þ value for this scenario is −0.31  0.03, with a χ2=NDF of 57.1=27. If a change in the spectrum shape is present, each energy range may exhibit an independent ð1=¯SjÞðdSj=dF239Þ value. Best-fit ð1=¯SjÞðdSj=dF239Þ val-ues for this scenario, given in the subpanels in Fig. 4, produce aχ2=NDF of 22.6=24. The Δχ2=NDF between the best-fit alternative and null hypotheses is 34.5=3, corre-sponding to the rejection of the hypothesis of no change in the spectral shape at5.1σ significance.

Measured changes in the IBD spectrum with F239were also compared to that predicted by the Huber-Mueller model. To allow a direct comparison to the measured IBD spectrum per fission, antineutrino spectra predicted by the Huber-Mueller model were processed with a detector response matrix to obtain predicted spectra in terms of IBD prompt energy Ep[20]. This comparison is shown in Fig.5, where the best-fit slopes in IBD yield per fission ð1=¯SjÞðdSj=dF239Þ are plotted for six prompt energy ranges for the data as well as for the Huber-Mueller model. The trend of the measured spectral evolution described by the best-fitðdS_j=dF239Þ values is similar to that of the Huber-Mueller model. This result generally demonstrates the validity of recent theoretical studies describing antineu-trino-based monitoring of reactor fissile content [29,30]. FIG. 4. Relative IBD yield per fission versus effective239Pu (lower axis) or 235U (upper axis) fission fraction for different prompt energy Epranges. The observed slopesð1=SÞðdS=dF239Þ

are listed in each panel. FIG. 3. Combined measurement of235U and239Pu IBD yields

per fissionσ₂₃₅ and σ₂₃₉. The red triangle indicates the best fit σ235andσ239, while green contours indicate two-dimensional1σ,

2σ, and 3σ allowed regions. Contours utilize theoretically predicted IBD yields for the subdominant isotopes 241Pu and

238_{U as indicated in the lower left panel. Predicted values and1σ}

allowed regions based on the Huber-Mueller model are also shown in black. The top and side panels show one-dimensional Δχ2 _{profiles forσ}

The data suggest slightly better agreement inðdS_j=dF239Þ with the Huber-Mueller model above 4 MeV prompt energy than below, emphasizing the possibility of disagreements in the evolution of both the flux and the spectrum. Increased statistics are required in order to investigate the possible isotopic origin of the excess in the observed antineutrino flux from 4–6 MeV prompt energy[1,6,7], a topic discussed recently in the literature[10,28,31–33].

In summary, the evolution of Daya Bay’s detected IBD yield and energy spectrum has been measured using 2.2 million IBD candidates detected over 1230 days of data taking. A total IBD yield ¯σ_f of (5.90  0.13) ×10−43 cm2=fission was measured with average effective fission fractions F235, F238, F239, and F241of 0.571, 0.076, 0.299, and 0.054, respectively. A change in the IBD yield dσf=dF239 of ð−1.86  0.18Þ × 10−43 cm2=fission was observed over a range of effective 239Pu fission fractions from 0.25 to 0.34. These yield measurements were used to calculate IBD yield per fission values of (6.17  0.17) and (4.27  0.26) ×10−43cm2=fission for the dominant fission isotopes235U and239Pu, respectively. A change in the IBD energy spectrum with the effective 239Pu fission fraction was also observed at the5.1σ confidence level.

These observations were compared to the Huber-Mueller reactor antineutrino model. While the measured evolution of the IBD energy spectrum is generally consistent with this model, measured ¯σ_fand dσf=dF239values are incom-patible with predictions at the 1.7σ and 3.1σ confidence levels. These discrepancies indicate issues in modeling the reactor antineutrino flux. One can invoke a model including only eV-scale sterile neutrino oscillations to explain the observed deficit in ¯σ_f. Such a model requires an equal fractional flux deficit from all fission isotopes and a ratio

of dσf=dF239to¯σfunchanged from the prediction, which is incompatible with Daya Bay’s observation at 2.6σ. A comparison of the measured and predicted235U and239Pu IBD yields instead indicates a preference for an incorrect prediction of the 235U flux as the primary source of the reactor antineutrino anomaly. Improvement in Daya Bay’s measurements of σ₂₃₅ and σ₂₃₉ can be achieved with increased statistics and with a reduction of the AD-correlated IBD detection efficiency systematic uncertainty. Future short-baseline experiments at highly enriched uranium reactors[34–36]may also provide the capability to probe this apparent overprediction via precise new measurements of the235U antineutrino flux.

Daya Bay is supported in part by the Ministry of Science and Technology of China, the U.S. Department of Energy, the Chinese Academy of Sciences, the CAS Center for Excellence in Particle Physics, the National Natural Science Foundation of China, the Guangdong provincial government, the Shenzhen municipal government, the China General Nuclear Power Group, Key Laboratory of Particle and Radiation Imaging (Tsinghua University), the Ministry of Education, Key Laboratory of Particle Physics and Particle Irradiation (Shandong University), the Ministry of Education, Shanghai Laboratory for Particle Physics and Cosmology, the Research Grants Council of the Hong Kong Special Administrative Region of China, the University Development Fund of The University of Hong Kong, the MOE program for Research of Excellence at National Taiwan University, National Chiao-Tung University, and NSC fund support from Taiwan, the U.S. National Science Foundation, the Alfred P. Sloan Foundation, the Ministry of Education, Youth, and Sports of the Czech Republic, the Joint Institute of Nuclear Research in Dubna, Russia, the National Commission of Scientific and Technological Research of Chile, and the Tsinghua University Initiative Scientific Research Program. We acknowledge Yellow River Engineering Consulting Co., Ltd., and China Railway 15th Bureau Group Co., Ltd., for building the underground laboatory. We are grateful for the ongoing cooperation from the China General Nuclear Power Group and China Light and Power Company.

*_{Department of Chemistry and Chemical Technology, Bronx}

Community College, Bronx, NY 10453, USA.

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