Measurement of the Reactor Antineutrino Flux and Spectrum at Daya Bay
F. P. An,1A. B. Balantekin,2 H. R. Band,3 M. Bishai,4 S. Blyth,5,6 I. Butorov,7D. Cao,8 G. F. Cao,9J. Cao,9 W. R. Cen,9 Y. L. Chan,10J. F. Chang,9L. C. Chang,11Y. Chang,6H. S. Chen,9Q. Y. Chen,12S. M. Chen,13Y. X. Chen,14Y. Chen,15 J. H. Cheng,11J. Cheng,12Y. P. Cheng,9J. J. Cherwinka,2 M. C. Chu,10J. P. Cummings,16J. de Arcos,17 Z. Y. Deng,9 X. F. Ding,9 Y. Y. Ding,9 M. V. Diwan,4J. Dove,18E. Draeger,17D. A. Dwyer,19W. R. Edwards,19S. R. Ely,18R. Gill,4 M. Gonchar,7G. H. Gong,13H. Gong,13M. Grassi,9W. Q. Gu,20M. Y. Guan,9L. Guo,13X. H. Guo,21R. W. Hackenburg,4 R. Han,14S. Hans,4M. He,9K. M. Heeger,3Y. K. Heng,9A. Higuera,22Y. K. Hor,23Y. B. Hsiung,5B. Z. Hu,5L. M. Hu,4 L. J. Hu,21T. Hu,9W. Hu,9E. C. Huang,18H. X. Huang,24X. T. Huang,12P. Huber,23G. Hussain,13D. E. Jaffe,4P. Jaffke,23
K. L. Jen,11S. Jetter,9 X. P. Ji,25,13X. L. Ji,9 J. B. Jiao,12R. A. Johnson,26L. Kang,27 S. H. Kettell,4S. Kohn,28 M. Kramer,19,28K. K. Kwan,10M. W. Kwok,10T. Kwok,29T. J. Langford,3K. Lau,22L. Lebanowski,13J. Lee,19R. T. Lei,27 R. Leitner,30K. Y. Leung,29J. K. C. Leung,29C. A. Lewis,2D. J. Li,31F. Li,9 G. S. Li,20Q. J. Li,9S. C. Li,29W. D. Li,9 X. N. Li,9X. Q. Li,25Y. F. Li,9 Z. B. Li,32H. Liang,31 C. J. Lin,19G. L. Lin,11P. Y. Lin,11S. K. Lin,22J. J. Ling,32,18,4 J. M. Link,23L. Littenberg,4B. R. Littlejohn,26,17D. W. Liu,22H. Liu,22J. L. Liu,20J. C. Liu,9S. S. Liu,29C. Lu,33H. Q. Lu,9
J. S. Lu,9 K. B. Luk,28,19Q. M. Ma,9 X. Y. Ma,9 X. B. Ma,14Y. Q. Ma,9 D. A. Martinez Caicedo,17K. T. McDonald,33 R. D. McKeown,34,35 Y. Meng,23I. Mitchell,22J. Monari Kebwaro,36Y. Nakajima,19J. Napolitano,37D. Naumov,7 E. Naumova,7 H. Y. Ngai,29Z. Ning,9J. P. Ochoa-Ricoux,38A. Olshevski,7 H.-R. Pan,5 J. Park,23S. Patton,19V. Pec,30
J. C. Peng,18L. E. Piilonen,23L. Pinsky,22C. S. J. Pun,29F. Z. Qi,9 M. Qi,8X. Qian,4 N. Raper,39B. Ren,27J. Ren,24 R. Rosero,4B. Roskovec,30X. C. Ruan,24B. B. Shao,13H. Steiner,28,19G. X. Sun,9J. L. Sun,40W. Tang,4D. Taychenachev,7
K. V. Tsang,19C. E. Tull,19 Y. C. Tung,5 N. Viaux,38B. Viren,4V. Vorobel,30C. H. Wang,6 M. Wang,12N. Y. Wang,21 R. G. Wang,9 W. Wang,32,35 W. W. Wang,8 X. Wang,41Y. F. Wang,9 Z. Wang,13Z. Wang,9 Z. M. Wang,9 H. Y. Wei,13 L. J. Wen,9K. Whisnant,42C. G. White,17L. Whitehead,22T. Wise,2H. L. H. Wong,28,19S. C. F. Wong,10,32E. Worcester,4
Q. Wu,12D. M. Xia,9,43J. K. Xia,9 X. Xia,12Z. Z. Xing,9 J. Y. Xu,10J. L. Xu,9 J. Xu,21Y. Xu,25T. Xue,13J. Yan,36 C. G. Yang,9L. Yang,27M. S. Yang,9 M. T. Yang,12M. Ye,9 M. Yeh,4 B. L. Young,42G. Y. Yu,8Z. Y. Yu,9S. L. Zang,8
L. Zhan,9 C. Zhang,4 H. H. Zhang,32J. W. Zhang,9Q. M. Zhang,36Y. M. Zhang,13Y. X. Zhang,40Y. M. Zhang,32 Z. J. Zhang,27Z. Y. Zhang,9 Z. P. Zhang,31J. Zhao,9 Q. W. Zhao,9Y. F. Zhao,14Y. B. Zhao,9 L. Zheng,31W. L. Zhong,9
L. Zhou,9 N. Zhou,31H. L. Zhuang,9 and J. H. Zou9 (Daya Bay Collaboration)
1
Institute of Modern Physics, East China University of Science and Technology, Shanghai, China 2
University of Wisconsin, Madison, Wisconsin, USA 3
Department of Physics, Yale University, New Haven, Connecticut, USA 4
Brookhaven National Laboratory, Upton, New York, USA 5
Department of Physics, National Taiwan University, Taipei, Taiwan 6
National United University, Miao-Li, Taiwan
7Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia 8
Nanjing University, Nanjing, China 9Institute of High Energy Physics, Beijing, China 10
Chinese University of Hong Kong, Hong Kong, China 11Institute of Physics, National Chiao-Tung University, Hsinchu, Taiwan
12
Shandong University, Jinan, China
13Department of Engineering Physics, Tsinghua University, Beijing, China 14
North China Electric Power University, Beijing, China 15Shenzhen University, Shenzhen, China 16
Siena College, Loudonville, New York, USA
17Department of Physics, Illinois Institute of Technology, Chicago, Illinois, USA 18
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA 19Lawrence Berkeley National Laboratory, Berkeley, California, USA
20
Shanghai Jiao Tong University, Shanghai, China 21Beijing Normal University, Beijing, China 22
Department of Physics, University of Houston, Houston, Texas, USA 23
Center for Neutrino Physics, Virginia Tech, Blacksburg, Virginia, USA 24
25School of Physics, Nankai University, Tianjin, China 26
Department of Physics, University of Cincinnati, Cincinnati, Ohio, USA 27Dongguan University of Technology, Dongguan, China 28
Department of Physics, University of California, Berkeley, California, USA 29Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong, China
30
Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 31University of Science and Technology of China, Hefei, China
32
Sun Yat-Sen (Zhongshan) University, Guangzhou, China
33Joseph Henry Laboratories, Princeton University, Princeton, New Jersey, USA 34
California Institute of Technology, Pasadena, California, USA 35College of William and Mary, Williamsburg, Virginia, USA
36
Xi’an Jiaotong University, Xi’an, China
37Department of Physics, College of Science and Technology, Temple University, Philadelphia, Pennsylvania, USA 38
Instituto de Física, Pontificia Universidad Católica de Chile, Santiago, Chile
39Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York, USA 40
China General Nuclear Power Group, China
41College of Electronic Science and Engineering, National University of Defense Technology, Changsha, China 42
Iowa State University, Ames, Iowa, USA 43Chongqing University, Chongqing, China (Received 18 August 2015; published 12 February 2016)
This Letter reports a measurement of the flux and energy spectrum of electron antineutrinos from six 2.9 GWthnuclear reactors with six detectors deployed in two near (effective baselines 512 and 561 m) and one far (1579 m) underground experimental halls in the Daya Bay experiment. Using 217 days of data, 296 721 and 41 589 inverseβ decay (IBD) candidates were detected in the near and far halls, respectively. The measured IBD yield is (1.55 0.04) ×10−18cm2GW−1day−1or (5.92 0.14) ×10−43 cm2fission−1. This flux measurement is consistent with previous short-baseline reactor antineutrino experiments and is0.946 0.022 (0.991 0.023) relative to the flux predicted with the Huber-Mueller (ILL-Vogel) fissile antineutrino model. The measured IBD positron energy spectrum deviates from both spectral predictions by more than 2σ over the full energy range with a local significance of up to ∼4σ between 4–6 MeV. A reactor antineutrino spectrum of IBD reactions is extracted from the measured positron energy spectrum for model-independent predictions.
DOI:10.1103/PhysRevLett.116.061801
Reactor antineutrino experiments have played a key role in developing the picture of neutrinos in the Standard Model of particle physics. They provided the first exper-imental observation of (anti)neutrinos[1], confirmed neu-trino oscillation as the solution to the solar neuneu-trino problem [2], provided the first detection of geoneutrinos [3], and discovered the nonzero neutrino mixing angleθ13 [4,5]. Forthcoming reactor antineutrino experiments are aiming to further explore the nature of neutrinos by determining the neutrino mass hierarchy, precisely meas-uring neutrino mixing parameters, and searching for short-baseline neutrino oscillation[6]. Over the last five decades, reactor antineutrino experiments have measured the flux and spectrum of antineutrinos at various distances from nuclear reactors ranging from ∼10 m to several hundred kilometers. These measurements were found to be in good agreement[7]with predictions derived from the measure-ments of theβ spectra at ILL[8–10]and Vogel’s theoretical calculation [11] when considering the effect of three-neutrino oscillation. In 2011, reevaluations of the reactor antineutrino flux and spectrum with improved theoretical treatments were carried out [12,13], and determined the
flux to be higher than the experimental data. This discrep-ancy is commonly referred to as the“reactor antineutrino anomaly” [14] and may be a sign of new physics or insufficient fissile antineutrino modeling. Precision mea-surements by modern reactor antineutrino experiments can shed light on this issue and probe the physics under-lying current reactor antineutrino predictions. An accurate determination of the reactor antineutrino spectrum can also provide valuable input to next-generation single-detector reactor antineutrino experiments[15].
This Letter reports measurements of the reactor anti-neutrino flux and spectrum based on 217 days of data from the Daya Bay experiment. The Daya Bay reactor complex consists of three nuclear power plants (NPPs), each hosting two pressurized-water reactors, which are a common type of commercial thermal reactor. The maximum thermal power of each reactor is 2.9 GWth. The data used for this
analysis comprises 338 310 antineutrino candidate events collected in six antineutrino detectors (ADs) in the two near experimental halls (effective baselines 512 m and 561 m) and the one far hall (effective baseline 1579 m). This is the largest sample of reactor antineutrinos, comparable to that
from the BUGEY-4 experiment [16]. A more detailed description of the experimental setup and the data set is given in Ref.[17].
In reactor cores, electron antineutrinos (¯νe) are emitted isotropically from fission products of four primary iso-topes:235U,238U,239Pu, and241Pu. The number of¯νewith
energy E emitted from a reactor at a time t can be predicted using d2ϕðE; tÞ dEdt ¼ WthðtÞ P ifiðtÞei X i
fiðtÞSiðEÞcnei ðE; tÞ þ SSNFðE; tÞ;
ð1Þ
where the sums are over the four primary isotopes, WthðtÞ is
the reactor thermal power, fiðtÞ is the fraction of fissions
due to isotope i, eiis the average thermal energy released per fission, SiðEÞ is the ¯νe energy spectrum per fission, cnei ðE; tÞ is the correction to the energy spectrum due to reactor nonequilibrium effects of long-lived fission frag-ments, and SSNFðE; tÞ is the contribution from spent nuclear fuel (SNF). At Daya Bay, the NPPs monitor the reactor power in real time and simulate the evolution of the fuel composition using the SCIENCE software package
[18,19]. The measured power (0.5% uncertainty[20–22]) and simulated fission fractions (∼5% relative uncertainty [23]) of each core are provided to the Daya Bay Collaboration. The power and fission fractions contributed 0.5% and 0.6% uncertainties to the predicted antineutrino rate, respectively. Simulation of reactor cores based on
DRAGON [24] was constructed to study the correlations among the fission fractions of the four isotopes [25]. The energies released per fission (0.2%–0.5% uncertainty) were from Ref. [26]. Nonequilibrium (30% uncertainty) and SNF (100% uncertainty) corrections were applied following Refs.[12]and[27,28], with∼0.5% and ∼0.3% contributions to the total antineutrino rate, respectively. The 0.9% total uncertainty in antineutrino flux due to reactor power, fission fractions, and nonequilibrium and SNF corrections was treated to be uncorrelated among reactors in the corresponding oscillation analysis [17]. It is con-servatively treated as fully correlated between reactors in this analysis.
Two fissile antineutrino spectrum models were used for SiðEÞ in Eq.(1)to predict the reactor antineutrino flux
and spectrum. The ILL-Vogel model refers to the conven-tional ILL model[8–10]of235U,239Pu, and241Pu, and the theoretical model of 238U from Vogel [11]. The Huber-Mueller model refers to the recent reevaluation of 235U,
239Pu, and 241Pu from Huber [13], and that of238U from
Mueller et al. [12]. Both sets of isotope spectra and their uncertainties were taken from the original publications. The Huber-Mueller model was chosen as a reference because of its improved theoretical treatments in β-to-antineutrino
conversions, and the information it provides about uncer-tainties and their correlations.
Reactor antineutrinos were detected via inverseβ decay (IBD) reactions in the gadolinium-doped liquid scintillator (GdLS) of the Daya Bay ADs. The total number of detected IBD events T in a given AD was estimated as
T¼X 6 i¼1 NPεIBD 4πL2 i ZZ
PsurðE; LiÞσIBDðEÞ
d2ϕiðE; tÞ dEdt dEdt;
ð2Þ where d2ϕiðE; tÞ=dEdt is the differential antineutrino rate from the ith reactor core given in Eq.(1), σIBDðEÞ is the cross section of the IBD reaction, Liis the distance between
the center of the detector and the ith core[29], PsurðE; LiÞ is
the survival probability due to neutrino oscillation, NP is
the number of target protons[30], andεIBDis the efficiency
of detecting IBD reactions. The cross sectionσIBDðEÞ was
evaluated based on the formalism in Ref. [31]. Physical constants including the neutron lifetime (880.3 1.1 s) were taken from the Particle Data Group[32].
IBD candidates were selected by requiring a time coincidence between a prompt signal from an IBD positron including its annihilation energy, and a delayed signal from an IBD neutron after capturing on Gd, as described in Refs.[4,17]. The energy of interacting antineutrinos, E, is closely related to the prompt energy of the IBD positrons, Eprompt: without detector effects, Eprompt≃ E þ ðMp− Mn−
MeÞ þ 2Me¼ E −0.78 MeV, where Mp, Mn, and Me are the proton, neutron, and electron masses. The reported data set includes 296 721 and 41 589 IBD candidates at the near and far halls, respectively. Corresponding background rates and spectra were estimated in Ref.[17], with about 5470 240 and 1894 43 background events at the near and far halls, respectively.
The relative analysis of IBD rates for sin22θ13 requires estimates of uncertainties that are uncorrelated among ADs while the measurement of flux is dominated by uncertain-ties that are correlated among ADs. A detailed study of the event selection efficiencies was carried out using Monte Carlo (MC) simulation-data comparisons with the Daya Bay simulation framework based on Geant4 [33].
The previous study of efficiencies is described in detail in Ref. [29]. Estimates of each selection efficiency and detector characteristic are summarized in Table I and are briefly described in order below.
Efficiencies of flashing-photomultiplier tube (flasher), capture-time, and prompt-energy selections were deter-mined as described in Ref.[29]utilizing an updated Daya Bay IBD MC simulator. The IBD neutron-Gd capture fraction is dependent on the target’s Gd concentration and on the escape, or “spill-out”, of IBD neutrons from the target. The former has been measured using neutron calibration sources deployed at the detector center, while the latter was estimated with simulation-data comparisons
of source deployments throughout the GdLS volume with a manual calibration system [34]. The efficiency for detecting Gd-capture IBD neutrons, also called the delayed energy cut efficiency, is dependent on the amount of Gd-capture γ energy deposited outside the scintillator and was determined using MC benchmarked to the IBD Gd-capture spectrum from data. Finally, in order to account for contributions from IBD interactions outside the GdLS target, we have applied a spill-in correction determined using simulation-data comparisons of IBD coincidence time and reconstructed position distributions. The updated detector efficiency ε was estimated to be 80.6% with an AD-correlated fractional uncertaintyδε=ε of 2.1%. Application of additional AD-dependent muon veto and multiplicity cut efficiencies, described in detail in Refs. [17,29], produced total detection efficienciesεIBDranging from 64.6% to 77.2%
among ADs. The total correlated uncertainty was dominated by the spill-in correction, whose uncertainty enveloped the individual uncertainties provided by three independent methods and was limited by small biases in position reconstruction. A cross-check of the spill-in effect provided by data-simulation comparisons of neutron sources deployed outside the target volume showed agreement well within this uncertainty.
To extract the rate of IBD interactions at Daya Bay, the θ13-driven oscillation effect must be corrected for in each
detector. A normalization factor R was defined to scale the measured rate to that predicted with a fissile antineutrino spectrum model. The value of R, together with the value of sin22θ13, were simultaneously determined with aχ2similar to the one used in Ref. [4]:
χ2¼X6 d¼1 ½Md− RTdð1 þ ϵDþ P rωdrαrþ ϵdÞ þ ηd2 Mdþ Bd þX r α2 r σ2 r þX6 d¼1 ϵ2 d σ2 d þ η2d σ2 Bd þϵ2D σ2 D ; ð3Þ
where Md is the number of measured IBD events in
the dth detector with backgrounds subtracted, Bd is the
corresponding number of background events, Td is the
number of IBD events predicted with a fissile antineutrino spectrum model via Eq.(2), and ωd
r is the fractional IBD
contribution from the rth reactor to the dth detector determined with baselines and reactor antineutrino rates, σr(0.9%) is the uncorrelated reactor uncertainty,σd(0.2%
[17]) is the uncorrelated detection uncertainty, σBd is the
background uncertainty listed in Ref.[17], andσD(2.1%) is the correlated detection uncertainty, i.e., the uncertainty of detection efficiency in Table I. Their corresponding nui-sance parameters areαr,ϵd,ηd, and ϵD, respectively. The best-fit value of sin22θ13¼ 0.090 0.009 is insensitive to the choice of model. The best-fit value of R is 0.946 0.022 (0.991 0.023) when predicting with the Huber-Mueller (ILL-Vogel) model. Replacing the Huber-Mueller 238U spectrum with the recently measured spectrum in Ref.[35] yields negligible change in R. The uncertainty in R is dominated by the correlated detection uncertaintyσD.
With the oscillation effect for each AD corrected using the best-fit value of sin22θ13 in Eq.(3), the measured IBD yield for each AD is expressed in two ways: the yield per GWth per day, Y, and equivalently, the yield per nuclear fission,σf. These results are shown in the top panel of Fig.1. The measured IBD yields are consistent among all ADs after further correcting for the small variations of fission fractions among the different sites. The average IBD yield in the three near ADs is Y¼ ð1.55 0.04Þ × 10−18 cm2 GW−1 day−1, orσf¼ ð5.92 0.14Þ × 10−43 cm2fission−1. These results
are summarized in Table II along with the flux-weighted average fission fractions in the three near ADs.
A global fit for R was performed to compare with previous reactor antineutrino flux measurements following the method described in Ref. [36]. Nineteen past short-baseline (<100 m) measurements were included using the data from Ref.[14]. The measurements from Chooz[37] and Palo Verde [38] were also included after correcting for the effect of standard three-neutrino oscillations. All measurements were compared to the Huber-Mueller model. All predictions were fixed at their nominal value in the fit. The resulting past global average is Rpastg ¼ 0.942
0.009ðexptÞ 0.025ðmodelÞ. Daya Bay’s measurement of the reactor antineutrino flux is consistent with the past experiments. Including Daya Bay in the global fit, the new average is Rg¼ 0.943 0.008ðexptÞ 0.025ðmodelÞ. The results of the global fit are shown in the bottom panel of Fig.1.
Extending the study from the integrated flux to the energy spectrum, the measured prompt-energy spectra of the three near-site ADs were combined after background subtraction and compared with predictions. The antineu-trino spectrum at each detector was predicted by the procedure described above, taking into account neutrino oscillation with sin22θ13¼ 0.090 and Δm2ee¼ 2.59× 10−3eV2 based on the oscillation analysis of the same TABLE I. Summary of IBD selection efficiencies and their
AD-correlated uncertainties. The uncertainties are given in relative units. Efficiency (ε) Uncertainty (δε=ε) Target protons 0.47% Flasher cut 99.98% 0.01% Capture-time cut 98.70% 0.12% Prompt-energy cut 99.81% 0.10% Gd-capture fraction 84.17% 0.95% Delayed-energy cut 92.71% 0.97% Spill-in correction 104.86% 1.50% Combined 80.6% 2.1%
data [17]. The detector response was determined in two ways. The first method sequentially applied a simulation of energy loss in the inactive acrylic vessels, and analytical models of energy scale and energy resolution. The energy scale model was based on empirical characterization of the
spatial nonuniformity and the energy nonlinearity with improved calibration of the scintillator light yield and the electronics response [39]. The uncertainty of the energy scale was about 1% in the energy range of reactor antineutrinos [39]. The second method used full-detector simulation in which the detector response was tuned with the calibration data. Both methods produced consistent predictions for prompt energies above 1.25 MeV. Around 1 MeV, there was a slight discrepancy due to different treatments of IBD positrons that interact with the inner acrylic vessels. Additional uncertainty below 1.25 MeV was included to cover this discrepancy.
Figure 2 shows the observed prompt-energy spectrum and its comparison with the predictions. The predicted spectra were normalized to the measurement in order to test the agreement between spectral shapes. The spectral uncertainty of the measurement is composed of the stat-istical, detector response and background uncertainties. Between 1.5 and 7 MeV, it ranges from 1.0% at 3.5 MeV to
AD1 AD2 AD3 AD4 AD5 AD6 Model
GW -1 day -1 2 cm -18 10× Y 1.5 1.6 1.7 fission –1 2 cm -43 10× f σ 5.8 6.0 6.2 6.4 Daya Bay (stat.)
Daya Bay w fission–1 fraction corr. (stat.)
Daya Bay near site combined (syst.) Huber – Mueller ILL – Vogel Distance (m) 10 102 103 Data /P rediction 0.6 0.8 1 1.2 Previous data Daya Bay Global average Experiments Unc. σ Model Unc. σ
1-FIG. 1. Top: Rate of reactor antineutrino candidate events in the six ADs with corrections for three-flavor oscillations (closed circles), and additionally for the variation of flux-weighted fission fractions at the different sites (open squares). The average of the three near detectors is shown as a gray line (and extended through the three far detectors as a dotted gray line) with its1σ systematic uncertainty (gray band). The rate predicted with the Huber-Mueller (ILL-Vogel) model and its uncertainty are shown in blue (orange). Bottom: The measured reactor ¯νe rate as a function of the distance from the reactor, normalized to the theoretical prediction with the Huber-Mueller model. The rate is corrected for three-flavor neutrino oscillations at each baseline. The blue shaded region represents the global average and its 1σ uncer-tainty. The 2.7% model uncertainty is shown as a band around unity. Measurements at the same baseline are combined for clarity. The Daya Bay measurement is shown at the flux-weighted baseline (573 m) of the two near halls.
Entries / 250 keV 5000 10000 15000 20000 Data Full uncertainty Reactor uncertainty ILL–Vogel Integrated Ratio to Prediction 0.8 0.9 1 1.1 1.2 (Huber – Mueller)
Prompt Energy (MeV)
2 4 6 8 contribution 2 χ −−42 0 2 4 )i χ∼ ( (1 MeV windows) Local p value 6 − 10 5 − 10 4 − 10 3 − 10 2 − 10 1 − 10 1
FIG. 2. Top panel: Predicted and measured prompt-energy spectra. The prediction is based on the Huber-Mueller model and normalized to the number of measured events. The highest energy bin contains all events above 7 MeV. The gray hatched and red filled bands represent the square root of diagonal elements of the shape-only covariance matrix ( ffiffiffiffiffiffiVii
p
) for the reactor related and the full (reactor, detector, and background) systematic uncertainties, respectively. The error bars on the data represent the statistical uncertainty. Middle panel: Ratio of the measured prompt-energy spectrum to the predicted spectrum (Huber-Mueller model). The blue curve shows the ratio of the prediction based on the ILL-Vogel model to that based on the Huber-Mueller model. Bottom panel: The definedχ2distribution (~χi) of each bin (black dashed curve) and local p values for 1-MeV energy windows (magenta solid curve). See the text for the definitions of these quantities.
TABLE II. Average IBD yields (Y andσf) of the near halls, flux normalization with respect to different fissile antineutrino model predictions, and flux-weighted average fission fractions of the near halls. IBD Yield Y (cm2GW−1 day−1) ð1.55 0.04Þ × 10−18 σf (cm2fission−1) ð5.92 0.14Þ × 10−43 Data/Prediction R (Huber-Mueller) 0.946 0.022 R (ILL-Vogel) 0.991 0.023
Average Fission Fractions
6.7% at 7 MeV, and above 7 MeV, it is larger than 10%. Agreement between a prediction and the data was quanti-fied with theχ2 defined as
χ2¼X i;j ðNobs i − N pred i ÞV−1ij ðNobsj − N pred j Þ; ð4Þ
where NobsðpredÞi is the observed (predicted) number of events at the ith prompt-energy bin and V is the covariance matrix that includes all statistical and shape-only system-atic uncertainties. The systemsystem-atic uncertainty portion of the covariance matrix V was estimated using simulated data sets with randomly fluctuated detector response, background contributions, and reactor-related uncertain-ties, while the statistical uncertainty portion was calculated analytically. A comparison to the Huber-Mueller model yielded a χ2=NDF, where NDF is the number of degrees of freedom, of 43.0=24 in the full energy range from 0.7 to 12 MeV, corresponding to a2.6σ discrepancy. The ILL-Vogel model showed a similar level of discrepancy from the data at2.4σ.
The ratio of the measured to predicted prompt-energy spectra is shown in the middle panel of Fig. 2. A discrepancy is apparent around 5 MeV. Two approaches were adopted to evaluate the significance of local discrep-ancies. The first was based on theχ2contribution of each energy bin, which is evaluated by
~χi¼ Nobs i − N pred i jNobs i − N pred i j ffiffiffiffiffiffiffiffiffiffiffiffiffi X j χ2 ij s ;
whereχ2ij≡ ðNobsi − Npredi ÞV−1ij ðNobsj − Npredj Þ: ð5Þ As shown in the bottom panel of Fig.2, there is a larger contribution around 5 MeV. In the second approach, the significance of deviations are conveyed with p values calculated within local energy windows. A free-floating nuisance parameter for the normalization of each bin within a chosen energy window was introduced to the fitter that was used in the neutrino oscillation analysis [17]. The overall normalization was unconstrained in the fit. The difference in the minimumχ2before and after introducing these nuisance parameters was used to evaluate the p value of the deviation from the theoretical prediction within each window. The p values within 1-MeV energy windows are shown in the bottom panel of Fig. 2. The p value for a 2-MeV window between 4 and 6 MeV reached a similar minimum of 5.4 × 10−5, which corresponds to a 4.0σ deviation. The ILL-Vogel model showed a similar level of discrepancy between 4 and 6 MeV.
The number of events in excess of the predictions in the 4–6 MeV region was estimated to comprise approximately 1%–2% of all events in both the near and far detectors. This excess is approximately 10% of events within the 4–6 MeV region. This discrepancy was found to be time independent and correlated with reactor power, therefore disfavoring
hypotheses involving unknown backgrounds. The hypoth-esis that the excess was due to detector response was disfavored given that no discrepancy was observed in the
12B spectrum[17]. A similar excess was observed in other
reactor antineutrino experiments[40,41]. A recent ab initio calculation of the antineutrino spectrum showed a similar deviation from previous predictions in the 4–6 MeV region and identified prominent fission daughter isotopes as a potential explanation[42]. A number of tentative explan-ations based on the nuclear physics ofβ decays and fission yields have been put forward and are under active inves-tigation; for examples, see Refs. [42–46]. These studies suggest an increased uncertainty in both the yields and spectra of the fissile antineutrino models, which may also account for the discrepancy.
From the measured IBD prompt spectrum at Daya Bay, we have obtained a reactor antineutrino spectrum of IBD reactions that can be used to make model-independent predictions of reactor antineutrino flux and spectra [47]. The spectrum was obtained by first summing the prompt-energy spectra of the three near site ADs weighted with their target mass relative to the average target mass of all near-site ADs, ¯M: ScombinedðEpromptÞ ¼
P3
i¼1SiðEpromptÞ ¯M=Mi.
Detector response effects were then removed by unfolding the combined prompt spectrum ScombinedðEpromptÞ to an
antineutrino spectrum of IBD reactions, ScombinedðEÞ.
Finally, oscillation effects were removed and each bin of the antineutrino spectrum was normalized to cm2fission−1MeV−1 using the thermal power WthðtÞ and
fission fraction fiðtÞ information of each core. The reactor
antineutrino spectrum is expressed as
SreactorðEÞ ¼ ¯P ScombinedðEÞ
surðEÞ ¯NP· Ftotal
; ð6Þ
where ¯PsurðEÞ is the flux-weighted average of the survival
probabilities PsurðE; Li;dÞ from the six reactors (i) to the three
detectors (d), ¯NPis the number of target protons in ¯M, and
Ftotal is the total number of fissions from the sum of the
fissions of the six reactors to the three detectors weighted withεIBD;d=4πL2i;d. Correcting the unfolded spectrum with
an average survival probability resulted in a negligible bias (<0.01%).
Detector response effects were removed with the sin-gular value decomposition (SVD) unfolding method[48]. Statistical and systematical uncertainties are naturally propagated in the SVD method. The bias of unfolding was estimated by using detector response matrices con-structed from the two different detector response models and by using a variety of input antineutrino spectra which covered the uncertainties of the two models and those estimated in Ref.[42]. The bin-to-bin bias between 2.2 and 6.5 MeV was about 0.5%, which was a few times smaller than the statistical uncertainty. The bias outside this region was about 4% and increased with energy due to the
decrease of events. The bias values were assigned as addi-tional uncertainties to the unfolded spectrum. Unfolding performed with the Bayesian iteration method [49,50] produced consistent results. Between 2 and 7.5 MeV, the spectral uncertainty of the unfolded spectrum ScombinedðEÞ
ranges from 1.1% at 4.25 MeV to 9.3% at 7.5 MeV, and around 10 MeV is more than 20% due to low statistics. The obtained reactor antineutrino spectrum and its correlation matrix are shown in the top panel of Fig. 3. Between 2 and 7.5 MeV, the uncertainty of the diagonal elements ranges from 2.7% at 4.25 MeV to 10.4% at 7.5 MeV. The bottom panel of Fig.3is the ratio of the extracted reactor antineutrino spectrum to the prediction using the fissile antineutrino spectra of the Huber-Mueller model and the average fission fractions listed in TableII. The integral of the ratio is equal to the flux normalization factor R given in TableII. The integral of the spectrum is equal to the yield σfgiven in TableII. The discrepancy between 5 and 7 MeV
corresponds to the discrepancy between 4 and 6 MeV in the IBD prompt-energy distribution in Fig.2.
In summary, the Daya Bay experiment collected more than 330 000 antineutrino events in the data-taking period with six antineutrino detectors. The measured IBD yield is ð1.55 0.04Þ × 10−18 cm2 GW−1 day−1 or ð5.92 0.14Þ × 10−43cm2fission−1. This flux
measure-ment is consistent with the global average of previous
short baseline experiments and is0.946 0.022 ð0.991 0.023Þ times the prediction using the Huber-Mueller (ILL-Vogel) fissile antineutrino model. In addition, the measured and predicted spectra are discrepant with a significance of∼4σ in the 4–6 (5–7) MeV region of the IBD prompt (antineutrino) energy spectrum. Investigation of the discrepancy strongly disfavors explanations involv-ing detector response or an unknown background. A reactor antineutrino spectrum was extracted from the measurement at Daya Bay, enabling model-independent predictions of reactor antineutrino spectra.
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 (CAS), 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, Laboratory Directed Research and Development Program of Institute of High Energy Physics, 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, Laboratory Directed Research and Development Program of Berkeley National Laboratory and Brookhaven National Laboratory, the Ministry of Education, Youth, and Sports of the Czech Republic, Charles University in Prague, the Joint Institute of Nuclear Research in Dubna, Russia, the NSFC-RFBR joint research program, the National Commission of Scientific and Technological Research of Chile. We acknowledge Yellow River Engineering Consulting Co., Ltd., and China Railway 15th Bureau Group Co., Ltd., for building the underground laboratory. We are grateful for the ongoing cooperation from the China General Nuclear Power Group and China Light and Power Company.
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