improved measurement of the reactor antineutrino flux and ...33charles university, faculty of...

Chinese Physics C Vol. XX, No. X (201X) XXXXXX

Improved Measurement of the Reactor Antineutrino Flux andSpectrum at Daya Bay

F. P. An1 A. B. Balantekin2 H. R. Band3 M. Bishai4 S. Blyth5,6 D. Cao7 G. F. Cao8

J. Cao8 W. R. Cen8 Y. L. Chan9 J. F. Chang8 L. C. Chang10 Y. Chang6 H. S. Chen8

Q. Y. Chen11 S. M. Chen12 Y. X. Chen13 Y. Chen14 J.-H. Cheng10 J. Cheng11

Y. P. Cheng8 Z. K. Cheng15 J. J. Cherwinka2 M. C. Chu9 A. Chukanov16

J. P. Cummings17 J. de Arcos18 Z. Y. Deng8 X. F. Ding8 Y. Y. Ding8 M. V. Diwan4

M. Dolgareva16 J. Dove19 D. A. Dwyer20 W. R. Edwards20 R. Gill4 M. Gonchar16

G. H. Gong12 H. Gong12 M. Grassi8 W. Q. Gu21 M. Y. Guan8 L. Guo12 R. P. Guo8

X. H. Guo22 Z. Guo12 R. W. Hackenburg4 R. Han13 S. Hans4*

M. He8 K. M. Heeger3

Y. K. Heng8 A. Higuera23 Y. K. Hor24 Y. B. Hsiung5 B. Z. Hu5 T. Hu8 W. Hu8

E. C. Huang19 H. X. Huang25 X. T. Huang11 P. Huber24 W. Huo26 G. Hussain12

D. E. Jaffe4 P. Jaffke24 K. L. Jen10 S. Jetter8 X. P. Ji27,12 X. L. Ji8 J. B. Jiao11

R. A. Johnson28 D. Jones29 J. Joshi4 L. Kang30 S. H. Kettell4 S. Kohn31

M. Kramer20,31 K. K. Kwan9 M. W. Kwok9 T. Kwok32 T. J. Langford3 K. Lau23

L. Lebanowski12 J. Lee20 J. H. C. Lee32 R. T. Lei30 R. Leitner33 C. Li11 D. J. Li26

F. Li8 G. S. Li21 Q. J. Li8 S. Li30 S. C. Li32,24 W. D. Li8 X. N. Li8 Y. F. Li8

Z. B. Li15 H. Liang26 C. J. Lin20 G. L. Lin10 S. Lin30 S. K. Lin23 Y.-C. Lin5

J. J. Ling15 J. M. Link24 L. Littenberg4 B. R. Littlejohn18 D. W. Liu23 J. L. Liu21

J. C. Liu8 C. W. Loh7 C. Lu34 H. Q. Lu8 J. S. Lu8 K. B. Luk31,20 Z. Lv35

Q. M. Ma8 X. Y. Ma8 X. B. Ma13 Y. Q. Ma8 Y. Malyshkin36 D. A. Martinez Caicedo18

K. T. McDonald34 R. D. McKeown37,38 I. Mitchell23 M. Mooney4 Y. Nakajima20

J. Napolitano29 D. Naumov16 E. Naumova16 H. Y. Ngai32 Z. Ning8 J. P. Ochoa-Ricoux36

A. Olshevskiy16 H.-R. Pan5 J. Park24 S. Patton20 V. Pec33 J. C. Peng19 L. Pinsky23

C. S. J. Pun32 F. Z. Qi8 M. Qi7 X. Qian4 N. Raper39 J. Ren25 R. Rosero4

B. Roskovec33 X. C. Ruan25 H. Steiner31,20 G. X. Sun8 J. L. Sun40 W. Tang4

D. Taychenachev16 K. Treskov16 K. V. Tsang20 C. E. Tull20 N. Viaux36 B. Viren4

V. Vorobel33 C. H. Wang6 M. Wang11 N. Y. Wang22 R. G. Wang8 W. Wang38,15

X. Wang41 Y. F. Wang8 Z. Wang12 Z. Wang8 Z. M. Wang8 H. Y. Wei12 L. J. Wen8

K. Whisnant42 C. G. White18 L. Whitehead23 T. Wise2 H. L. H. Wong31,20

S. C. F. Wong15 E. Worcester4 C.-H. Wu10 Q. Wu11 W. J. Wu8 D. M. Xia43 J. K. Xia8

Z. Z. Xing8 J. Y. Xu9 J. L. Xu8 Y. Xu15 T. Xue12 C. G. Yang8 H. Yang7

L. Yang30 M. S. Yang8 M. T. Yang11 M. Ye8 Z. Ye23 M. Yeh4 B. L. Young42

Z. Y. Yu8 S. Zeng8 L. Zhan8 C. Zhang4 H. H. Zhang15 J. W. Zhang8 Q. M. Zhang35

X. T. Zhang8 Y. M. Zhang12 Y. X. Zhang40 Y. M. Zhang15 Z. J. Zhang30 Z. Y. Zhang8

Z. P. Zhang26 J. Zhao8 Q. W. Zhao8 Y. B. Zhao8 W. L. Zhong8 L. Zhou8 N. Zhou26

H. L. Zhuang8 J. H. Zou8

(Daya Bay Collaboration)

1Institute of Modern Physics, East China University of Science and Technology, Shanghai

∗ Now at: Department of Chemistry and Chemical Technology, Bronx Community College, Bronx, New York 10453, USA

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2University of Wisconsin, Madison, Wisconsin 53706, USA3Department of Physics, Yale University, New Haven, Connecticut 06520, USA

4Brookhaven National Laboratory, Upton, New York 11973, USA5Department of Physics, National Taiwan University, Taipei

6National United University, Miao-Li7Nanjing University, Nanjing

8Institute of High Energy Physics, Beijing9Chinese University of Hong Kong, Hong Kong

10Institute of Physics, National Chiao-Tung University, Hsinchu11Shandong University, Jinan

12Department of Engineering Physics, Tsinghua University, Beijing13North China Electric Power University, Beijing

14Shenzhen University, Shenzhen15Sun Yat-Sen (Zhongshan) University, Guangzhou

16Joint Institute for Nuclear Research, Dubna, Moscow Region17Siena College, Loudonville, New York 12211, USA

18Department of Physics, Illinois Institute of Technology, Chicago, Illinois 60616, USA19Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

20Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA21Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai Laboratory for Particle Physics and Cosmology,

Shanghai22Beijing Normal University, Beijing

23Department of Physics, University of Houston, Houston, Texas 77204, USA24Center for Neutrino Physics, Virginia Tech, Blacksburg, Virginia 24061, USA

25China Institute of Atomic Energy, Beijing26University of Science and Technology of China, Hefei

27School of Physics, Nankai University, Tianjin28Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA

29Department of Physics, College of Science and Technology, Temple University, Philadelphia, Pennsylvania 19122, USA30Dongguan University of Technology, Dongguan

31Department of Physics, University of California, Berkeley, California 94720, USA32Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong

33Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic34Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544, USA

35Xi’an Jiaotong University, Xi’an36Instituto de F́ısica, Pontificia Universidad Católica de Chile, Santiago, Chile

37California Institute of Technology, Pasadena, California 91125, USA38College of William and Mary, Williamsburg, Virginia 23187, USA

39Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA40China General Nuclear Power Group

41College of Electronic Science and Engineering, National University of Defense Technology, Changsha42Iowa State University, Ames, Iowa 50011, USA

43Chongqing University, Chongqing

Abstract: A new measurement of the reactor antineutrino flux and energy spectrum by the Daya Bay reactor

neutrino experiment is reported. The antineutrinos were generated by six 2.9 GWth nuclear reactors and detected

by eight antineutrino detectors deployed in two near (560 m and 600 m flux-weighted baselines) and one far (1640 m

flux-weighted baseline) underground experimental halls. With 621 days of data, more than 1.2 million inverse beta

decay (IBD) candidates were detected. The IBD yield in the eight detectors was measured, and the ratio of measured

to predicted flux was found to be 0.946±0.020 (0.992±0.021) for the Huber+Mueller (ILL+Vogel) model. A 2.9 σdeviation was found in the measured IBD positron energy spectrum compared to the predictions. In particular, an

excess of events in the region of 4-6 MeV was found in the measured spectrum, with a local significance of 4.4 σ. A

reactor antineutrino spectrum weighted by the IBD cross section is extracted for model-independent predictions.

Key words: antineutrino flux, energy spectrum, reactor, Daya Bay

PACS: 14.60.Pq, 29.40.Mc, 28.50.Hw, 13.15.+g

1 Introduction

Since the discovery of the neutrino in 1956 at theSavannah River reactor power plant by Cowan, Reinesand collaborators [1], reactor antineutrinos have played

a crucial role in the development of the standard modelof particle physics [2], and in the exploration of neu-trino oscillation. Near the beginning of this century,the CHOOZ and Palo Verde experiments attempted tomeasure the neutrino mixing angle θ13 using reactor an-

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tineutrinos at ∼1 km baselines and obtained upper lim-its [3–5]. In 2003, the KamLAND experiment observedterrestrial neutrino oscillations with a flux-average base-line of 180 km [6], confirming the large mixing angle(LMA) solution to the solar neutrino problem. In 2012,the Daya Bay experiment reported the first observationof a non-zero θ13 [7] with more than 5 σ significance,consistent with the results from T2K [8], MINOS [9],Double CHOOZ [10] and RENO [11] experiments. Thediscovery of a non-zero θ13 opened the way to deter-mining the neutrino mass hierarchy and searching forCP violation in neutrino oscillation experiments. In thefuture, reactor neutrino experiments at ∼km baselineswill continue to improve the precision of θ13 measure-ments, while reactor neutrino experiments at baselinesof ∼50 km [12, 13] are aiming to determine the neu-trino mass hierarchy and precisely measure the neutrinomixing angle θ12 and the mass-squared splittings ∆m

221

and ∆m232. In addition, reactor neutrino experimentsat baselines of ∼10 m will probe physics beyond thethree-neutrino framework through the search for short-baseline neutrino oscillation [14–17]. A recent review ofreactor neutrino oscillation experiments can be found inRef. [18].

Reactors are a pure source of electron antineutrinos,ν̄e. Inside a reactor core, fission processes are maintainedby neutrons produced through the fission of 235U nuclei.A portion of the neutrons are captured by 238U nucleiand subsequent beta decays and neutron captures leadto the production of fissile isotopes 239Pu and 241Pu. Thebeta-decay chains of the fission products of these fourisotopes are the main source of ν̄e. On average, aboutsix antineutrinos are released per fission. Before 2011,the prediction of antineutrino flux and spectrum wasbased on the beta spectra measured at ILL Grenoblefor the thermal-neutron induced fission of 235U, 239Pu,and 241Pu [19–21] and the theoretical calculation of Vo-gel for 238U [22], which was shown to be in good agree-ment with available data [23]. In 2011, re-evaluation ofthe reactor antineutrino flux and spectrum [24, 25] withimproved theoretical treatments was carried out, andthe new predicted reactor antineutrino flux was shownto be higher than the experimental data. This discrep-ancy is commonly referred to as the “Reactor Antineu-trino Anomaly” [26]. One possible explanation of thereactor antineutrino anomaly is through neutrino oscil-lation with a frequency corresponding to a mass squareddifference at the eV-scale, by introducing at least oneadditional sterile neutrino. Meanwhile, it was pointedout in Ref. [27] that the uncertainty due to the spectralshape of numerous first forbidden beta decays may belarger, which could largely reduce the significance of theanomaly. In addition to the anomaly of the integratedreactor antineutrino flux, recent results from the current

generation of θ13 experiments have also highlighted thepresence of a spectral anomaly consisting of an excess ofdetected events with respect to predictions in the regionof 4-6 MeV of the reconstructed prompt energy [28–30].This feature is unlikely to be the result of active-sterileneutrino oscillations, and raises further questions on theaccuracy of some existing reactor antineutrino flux andspectrum predictions.

To shed light on these issues and probe the nu-clear physics underlying current reactor antineutrino fluxmodels, it is crucial to compare model predictions withprecision measurements of reactor antineutrino flux andspectrum. While the modeling of the reactor antineu-trino spectrum is less critical for oscillation experimentsemploying relative measurements between multiple de-tectors, an accurate determination of the reactor an-tineutrino spectrum is critical to realize the full potentialof the next-generation single-detector medium-baselinereactor antineutrino oscillation experiments [31].

This article will present Daya Bay’s reactor antineu-trino flux and spectral analyses utilizing the dataset fromits most recent spectral oscillation analysis [32]. Thedataset is comprised of more than 1.2 million antineu-trino candidates collected in eight antineutrino detec-tors (ADs) in two near experimental halls (with flux-weighted baselines of 560 m and 600 m) and one far hall(flux-weighted baseline 1640 m), providing a factor of3.6 times more statistics over the results presented inRef. [29]. This paper also aims to provide detailed de-scription of key inputs to these analyses not describedin previous Daya Bay publications, such as the methodof predicting the flux and spectrum from each Daya Baycore, as well as the method of determining the IBD de-tection efficiencies of the Daya Bay ADs. Finally, a moredetailed description will be provided regarding how theflux and spectrum analyses were carried out, and howthe observed prompt spectra are unfolded into a reactorantineutrino spectrum, which is a useful input for futurereactor antineutrino experiments.

This paper is organized as follows: Sec. 2 summa-rizes in detail the treatment of the reactor antineutrinoflux and spectrum prediction in Daya Bay’s neutrino os-cillation analysis with the full eight-detector configura-tion [32]. Sec. 3 overviews the standard IBD selectionsused by Daya Bay, while Sec. 4 provides an in-depthexplanation of the analysis performed to determine thedetection efficiency of the Daya Bay detectors. The up-dated measurements of the reactor antineutrino flux andthe positron prompt energy spectrum are presented indetail in Sec. 5 and Sec. 6. Based on the measuredprompt energy spectrum, an extracted reactor antineu-trino spectrum weighted by the IBD cross section is pre-sented in Sec. 7. Finally, a summary is given in Sec. 8.

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2 Flux Prediction

2.1 Reactor Description

The Daya Bay nuclear power complex is situated atDaya Bay in southern China, approximately 55 kilome-ters northeast of Hong Kong. As shown in Fig. 1, thenuclear power complex consists of three nuclear powerplants (NPPs): the Daya Bay NPP, the Ling Ao NPP,and the Ling Ao II NPP. Each of them has a pair of reac-tor cores generating 2.9 GW thermal power each, duringnormal operation. The distance between the two cores ineach NPP is about 88 m. The Ling Ao II cores reachedfull power in July 2011 while the other cores were run-ning in commercial operation. The uncertainty of thebaseline measurement is estimated to be 18 mm. Detailsof the baseline measurement are described in [33].

AD6AD4

AD5

AD3

AD1AD2

D2 D1

L1L2

L3L4

Daya Bay NPP

EH2

EH3

LS Hall

EH1

Ling Ao NPP

AD7

Ling Ao-II NPP

AD8

200m

Fig. 1. Layout of the full configuration of the DayaBay experiment with eight antineutrino detectors(ADs) installed in three underground experimen-tal halls (EHs). The dots represent reactor cores,labeled as D1, D2, L1, L2, L3 and L4.

The Daya Bay and Ling Ao NPPs use the FrenchFramatome Advanced Nuclear Power 990 MWe (electricpower) three cooling loop design, and Ling Ao II NPPuses an updated Chinese version (CPR 1000) of 1080-MWe. Each cooling system consists of a primary loopand a secondary loop connected with a steam genera-tor. Figure 2 shows a schematic diagram of one coolingsystem. Inside each reactor core, 157 fuel elements arebonded to socket plates in the water-filled reactor pres-sure vessel. The water absorbs the heat generated by

fissions in the fuel and then circulates through invertedU-shape tubes of the steam generators, which are im-mersed in water of the secondary loops. The heat isthen transferred to the water in the secondary loop andthe water is vaporized into saturated steam, which flowsto the turbine-alternator unit. The cooled water in theprimary loop is then pumped back to the vessel and goesto the next cycle. The water is slightly doped with boricacid, which acts as the thermal neutron absorber. Boronconcentration, controlled by the NPPs, decreases dur-ing the refueling cycle to compensate for the power losscaused by the depletion of fuel, helping to keep the totalpower of the reactor stable at a nominal level.

Primary Loop Secondary Loop

Stea

m G

ener

ator

Reac

tor C

ore

Pumplowdown

Turbine Alternator

Feed Water

Steam

⚡️

Fig. 2. Schematic diagram of the reactor coolingsystem. At Daya Bay, each reactor core is con-nected with 3 cooling systems in parallel.

2.2 Reactor Power Measurements and Monitor-ing Systems

Three different systems, RPN (Nuclear Instrumen-tation System) [34], KME (Test Instrumentation Sys-tem) [35] [36], and KIT/KDO (Centralized Data Pro-cessing System/Test Data Acquisition System) [34, 36],were deployed to monitor the power of the reactor coresin Daya Bay. Table 1 is a summary of the three powermonitoring systems.

Table 1. Power monitoring systems in Daya Bay.‘FP’ stands for ‘Full Power’

System Frequency Uncertainty

KME Weekly/Monthly < 0.5%

KIT/KDO Online |PKIT −PKME |< 0.1%FPRPN Online |PRPN −PKME |< 1.5%FP

The RPN system is used for reactor monitoring andprotection by measuring the neutron flux with four neu-tron detectors placed around the reactor core. The re-actor power is supposed to be proportional to the neu-tron flux. However, as the nuclear fuel burns, the poweras measured by RPN gradually differs by an increasingamount from the actual power due to the change of theisotope content in the core. To guarantee accuracy, theRPN system’s measured powers are compared with the

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more accurate KIT/KDO system every day. Once thedifference exceeds 1.5% of full power, the RPN system isre-calibrated.

The KME and KIT/KDO systems are based on theheat balance method. The KME is the secondary looppower measurement system, and has the best accuracyamong all three systems. This system measures the pa-rameters such as water flow rate, temperature and pres-sure in the secondary loop, and calculates the enthalpyincrease when the water passes through the steam gener-ator. Other heat sources such as pumps in the secondaryloop are also considered. By considering the power of allthree steam generators and heat from other sources, thereactor core thermal power can be calculated as

WR =

3∑i=1

WSGi−W∆Pr , (1)

where WR is the reactor core thermal power, WSGi is thethermal power of the i-th steam generator, and W∆Pr isthe heat input and power loss from the pump systemsand other heat sources.

Daya Bay and Ling Ao reactors are all based onFrench Pressurized Water Reactors (PWRs). For FrenchPWRs, the measurement of nominal thermal power fol-lows a procedure known as BIL100, which is performedon the secondary loop [37]. The predominant term inthe calculation of uncertainty for BIL100 is the uncer-tainty related to mass flow rate of the feed water, whichaccounts for up to 80% of the uncertainty related tothermal power [37]. To minimize this source of uncer-tainty, orifice plates were installed in the secondary loopto precisely measure water flow. The uncertainty of theorifice water flow measurement is typically 0.72% (90%C.L.), and could be improved to 0.4% (90% C.L.) ac-cording to lab tests [38]. For Daya Bay’s KME sys-tem, four benchmark tests were made to compare thecore power result between the KME system and an EDF(Electricite de France)-developed high precision SAPECsystem (EDF’s standardized system for enhanced safetyand performance periodic tests on the PWR fleet), whichhas its own sensors, databases and data processing sys-tems [39]. The tests showed the relative difference be-tween the two systems was 0.031% to 0.065%. The powermeasurement uncertainty of the KME system is esti-mated to be less than 0.25%. This is comparable to theuncertainty estimated for the SAPEC system, which is


ment into the reactor core, defined as

burn-up≡ W ·DMU in

, (2)

where W is the average power of the fuel element, Dis the days since the fuel element begins to burn in thecore, and MU in is the initial uranium mass of the fuelelement. The unit of burn-up is MW · day · tonU−1. Asimilar quantity, cycle burn-up, is used to describe theaging of the whole reactor core in a refueling cycle. Cycleburn-up can also be calculated using Eq. 2, where W , D,and MU in in this case represent the total nuclear powerof the reactor core, the days since the beginning of therefueling cycle, and the initial uranium mass of all thefuel elements in the reactor core.

R P N M L K J H G F E D C B A

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

5

10

15

20

25

30

35

40

45

Fig. 3. An example of the reactor core map of fuelelements with different burn-up (unit: GW ·day ·ton−1) shown in color scale at the end of a refu-eling cycle.

In reactors, electron antineutrinos are emitted pri-marily from the fissions of four isotopes: 235U, 238U,239Pu, and 241Pu. Fissions of other isotopes contributeless than 0.3%. Fissions of 238U are only induced byfast neutrons, while fissions of the other three isotopesare mainly induced by thermal neutrons. Fresh fuel el-ements contain only uranium isotopes. The plutoniumisotopes are gradually generated through neutron cap-tures on 238U and subsequent neutron captures and betadecays of its successor isotopes.

Fuel evolution is a dynamic process related to manyfactors such as power, neutron flux, fuel composition,type and position of fuel elements, and boron concentra-tion. For safe operation of the reactors, NPPs do cal-culations and simulations of the fuel evolution in every

refueling cycle by considering all of the factors above.These detailed simulations are performed by validatedand licensed commercial software. The simulation pack-age used by the Daya Bay NPP is SCIENCE, whichwas developed by CEA, France. It uses the APOLLO2code [40] as the core component. The simulation resultsare provided to the Daya Bay collaboration in a tablewhich uses cycle burn-up as the index. The fission frac-tions are provided by the simulation in the form of fi(β),where fi is the fission fraction of isotope i, and β is thecycle burn-up. Figure 4 shows an example of the fissionfraction evolution as a function of cycle burn-up withina refueling cycle [41].

Burn-up (MWD/TU)0 5000 10000 15000 20000

Fiss

ion

fract

ion

(%)

0

10

20

30

40

50

60

70

80

90

100U235

Pu239

U238

Pu241

Others

Fig. 4. Fission fractions of isotopes in reactor coreD1 as a function of cycle burn-up from a simula-tion of a complete refueling cycle. Other isotopescontribute less than 0.3%.

The APOLLO2 code is widely used for cross sectiongeneration and neutron transport calculations in com-mercial reactor cores. It adopts rigorous methodologyfor its validation, including comparison with the refer-ence calculation using the same nuclear data libraries,and with the experimental measurements [40]. Measure-ments of spent fuel isotopic content were made and com-pared with the results calculated using the APOLLO2code [42]. The comparison shows that the measurement-model deviations are less than 5%. Therefore, the uncer-tainty of the calculated fission fraction is conservativelyestimated to be 5% for each isotope.

The NPPs also provide 3D core simulation results fordifferent burn-up stages, which enable an investigationof the spatial distribution of the antineutrino productioninside the core. The reactor can be considered as a pointsource of ν̄e for the Daya Bay experiment because the fuelelements are symmetrically arranged in the reactor coreas shown in Fig 3. The relative difference between treat-ing the reactor as a point source and as a finite source isnegligible and the variation of the effective fission centerin the reactor is estimated to be 2 cm horizontally. The

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impact on the baselines of the vertical variation of thefission center is negligible. Combined with the 18 mmuncertainty in the baseline measurements, the total un-certainty of the baselines is conservatively estimated tobe 27 mm.

The open source simulation code DRAGON [43]wasalso used to calculate the fission fractions, and to es-timate their uncertainty. The impact of many reactorparameters was taken into account, including power,neutron flux, fuel composition, type and position offuel elements, and boron content. DRAGON was origi-nally developed for CANDU (CANada Deuterium Ura-nium) reactors, but also yields reliable predictions forPWRs [44, 45]. The fission fraction uncertainty of eachisotope was found to be less than 5%, consistent withthe results of APOLLO2 validation. The fission fractionsof four isotopes are correlated with each other because239Pu and 241Pu are gradually produced while 235U iscontinuously consumed and the sum of the fission frac-tions is normalized to be 100%. DRAGON was used tocalculate correlations among fission fractions using thefission fraction data from several cycles of the NPPs.The results are given in Table 2. The correlations wereused as an input when propagating the fission fractionuncertainties to the reactor antineutrino flux uncertainty.

Table 2. Correlation coefficients of fission fractionsfor the four isotopes.

Isotope 235U 238U 239Pu 241Pu235U 1.00 -0.22 -0.53 -0.18238U -0.22 1.00 0.18 0.26

239Pu -0.53 0.18 1.00 0.49241Pu -0.18 0.26 0.49 1.00

2.5 Expected Unoscillated Spectrum

Electron antineutrinos are generated in the reactorsfrom the beta decays of the fission fragments producedby the four isotopes. Each fission isotope produces aunique ν̄e spectrum through its fission and subsequentdecay chains. In principle, using cumulative fission yieldsand beta decay information for each fission production,it is possible to compute the antineutrino spectrum abinitio. However, this requires reliable beta decay infor-mation on more than 1000 isotopes [46], many of whichhave never been observed. The lack of decay informa-tion combined with nuclear structure-related uncertain-ties and the uncertainties of the fission yields, results inan overall 10–20% energy dependent uncertainty in thepredicted antineutrino spectrum.

To improve on the purely ab initio method de-scribed above, several direct measurements were doneat ILL [19–21] in the 1980s to determine the electronenergy spectra from the individual fission isotopes 235U,

239Pu, and 241Pu. In these measurements, foils of iso-tope samples were placed inside the reactor and exposedto thermal neutron fluxes for 1–2 days. A high-precisionelectron spectrometer measured the electrons emitted bythe samples. The observed electron spectrum was thenconverted into an antineutrino spectrum by fitting witha set of hypothetical β-decay branches and adding up theantineutrino spectrum from each fitted branch. The un-certainty of the antineutrino spectrum by this conversionprocess was estimated to be 2.7%. These experiments didnot perform similar measurements for 238U, which onlyfissions with fast neutrons. Theoretical antineutrino fluxcalculations for 238U were carried out by Vogel [22], withoverall uncertainties < 10%. Since 238U only contributesto ∼8% of the total reactor antineutrino flux, the errorintroduced to the total flux is less than 1%. These cal-culations of antineutrino spectra are referred to as theILL+Vogel model.

The prediction of antineutrino spectra from 235U,239Pu, and 241Pu was recently improved [24, 25], wherethe ILL electron spectra were reanalyzed by taking intoaccount several higher-order corrections to the β-decayspectra. The ab initio calculation of the 238U antineu-trino spectrum was updated by Mueller et al. [24]. Thesenew calculations are referred to as the Huber+Muellermodel. The claimed uncertainty of the predicted to-tal flux from the Huber+Mueller model is 2.4%. Boththe ILL+Vogel model and the Huber+Mueller modelare used to calculate the expected antineutrino spec-trum from a single reactor core. A measurement of the238U beta spectrum was performed and the correspond-ing antineutrino spectrum was determined in Ref. [47].Replacing the Mueller 238U antineutrino spectrum withthis measurement only changes the total integrated fluxby 0.2% since 238U only contributes 8% of the total in-tegrated flux.

The total antineutrino spectrum is calculated oncethe time evolution of reactor power and fission fractionsare provided by the Daya Bay NPP,

dφ(Eν)

dEν=∑i

Fi ·dφi(Eν)

dEν, (3)

where i is the index of individual fission isotope inthe reactor fuel, that is 235U, 238U, 239Pu, or 241Pu.dφi(Eν)/dEν is the antineutrino spectrum of the i-th iso-tope per fission, and Fi is the total fission rate of the i-thisotope. The total fission rate is directly related to thetotal thermal power of the reactor core, and can be cal-culated as follows:

Fi =Wth∑jfj ·ej

·fi , (4)

where Wth is the total thermal power of the reactor core,ei is the energy released per fission of the i-th isotope,and fi is the fission fraction of the i-th isotope. The

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term∑

ifi ·ei represents the average energy released per

fission from the four isotopes.The energy released per fission (ei) is defined as the

amount of energy from a fission event that transformsinto heat over a finite time interval [48], which has aslight dependence on the reactor burning history. Theywere calculated by considering the neutron captures inthe reactor and decays of long-lived fission daughters, us-ing typical PWR reactor parameters [48]. The improvedcalculation of the energy released per fission [49] used inthis analysis includes using updated nuclear databases,considering the production yields of fission fragmentsfrom both thermal and fast incident neutrons, and anupdated calculation of the average energy taken away byantineutrinos. This new calculation gives slightly largervalues of ei with smaller uncertainties than in [48], re-sulting in a 0.32% decrease of the calculated antineutrinoflux. The values of ei and their uncertainties are listedin Table 3.

Table 3. Energy released per fission for the fourmain isotopes and their uncertainties. [49]

Isotope Energy per Fission (MeV)235U 202.36 ± 0.26238U 205.99 ± 0.52

239Pu 211.12 ± 0.34241Pu 214.26 ± 0.33

In the Daya Bay experiment, the electron antineutri-nos are detected via the inverse beta decay (IBD) reac-tion: ν̄e+p→ e++n. The expected antineutrino spectrumweighted by the IBD cross section in the detector d fromreactor r is calculated by

Sdr(Eν) =1

4πL2dr

dφ(Eν)

dEν�dNdpσ(Eν), (5)

where Ldr is the distance from reactor r to detector d,�d is the IBD selection efficiency, Ndp is the number oftarget protons, and σ(Eν) is the inverse beta decay crosssection calculated using the formalism in [50], with theupdated neutron lifetime of 880.3±1.1 s taken from PDG2014 [2]. The uncertainty of the cross section is domi-nated by the uncertainty of neutron lifetime. The totalreactor antineutrino spectra for a detector d is the sumof antineutrino spectra from all reactors:

Sd(Eν) =∑r

Sdr(Eν) . (6)

As an example, the expected total antineutrino spectrumat the near site ADs is shown in Fig. 5.

Antineutrino Energy (MeV)2 4 6 8 10 12

see

ann

ota

tio

ns

0

0.5

1

1.5

2

2.5

3

3.5

4 )-4

2 1

0× 2

Cro

ss s

ecti

on

(cm

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

/MeV)5 in near site ADs (10eν(c) Expected

)-42 10× 2(b) IBD cross section (cm

spectra (1/fission/MeV)eν(a) Isotope

(c)

(a)

(b)U238

U235

Pu241

Pu239

Fig. 5. (a) The antineutrino spectra for four iso-topes in Huber+Mueller model.(b) The inversebeta decay (IBD) cross section. (c) The expectedantineutrino spectrum weighted by the IBD crosssection without oscillation in the near site ADs.The error bars are systematic only (see text fordetails).

2.6 Non-equilibrium Effect and Spent NuclearFuel Correction

In the ILL measurements, fissile samples were ex-posed to the thermal neutron flux for only 1–2 days.The rate of beta decays from some long-lived fission frag-ments did not reach equilibrium with their productionrates. When using converted antineutrino spectra fromthe ILL measurements, this non-equilibrium effect needsto be corrected, since the long-lived fission fragments ac-cumulate in the reactor core and their beta decays con-tribute to the total antineutrino flux.

After burning in the core, the nuclear fuel is removedfrom the reactor and stored as spent nuclear fuel (SNF)in a cooling pool near the reactor core. The long-livedisotopes in the SNF will decay and act as another sourceof antineutrinos.

The total neutrino spectrum is then modified:

Sν =SILL+Sneq+SSNF (7)

where SILL is the expected antineutrino spectrum withILL measurement-based models, Sneq is the contributionfrom the non-equilibrium effect and SSNF is the contri-bution from the spent fuel.

The non-equilibrium correction is a function of an-tineutrino energy, the burn-up and irradiation history ofnuclear fuel [24]. Taking into account the information ofthe refueling history of reactors provided by the ChinaGeneral Nuclear Power Corporation, the cumulative con-tribution of the non-equilibrium effect at Daya Bay andLing Ao reactors was calculated. On average, the effect

010201-8


contributed ∼0.6% additional IBD events, which is illus-trated in Fig. 6. The uncertainty of the non-equilibriumeffect is taken to be 30% from the estimation in Ref. [24].

The contribution of SNF can be evaluated by usingthe cumulative yields and spectra of the known long-livedfission fragments. The candidate isotopes were selectedfrom the fission products with the condition that theyhave a half-life longer than 10 hours and either the iso-tope or its daughter nuclei undergoes beta decay withend point energy larger than the IBD reaction threshold(1.8 MeV). The antineutrino spectra of these candidateisotopes were calculated based on their beta decay pro-cess. The cumulative yields of the SNF were calculatedwith the input from the refueling history and SNF inven-tory information provided by the China General NuclearPower Corporation. The calculated SNF antineutrinospectrum is illustrated in Fig. 6. The contribution to thetotal number of IBD events is ∼ 0.3%, which is consis-tent with previous calculations [51, 52]. The uncertaintyis conservatively estimated to be 100% after the investi-gation on the uncertainty of the SNF inventory historyinformation. We neglect an additional low energy cor-rection [53] which has a smaller effect than SNF.

Antineutrino Energy (MeV)2 3 4 5 6 7 8 9 10

Rat

io

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Spent nuclear fuel

Non-equilibrium

Fig. 6. The ratio of calculated antineutrino spec-trum the non-equilibrium effect (red) and spentnuclear fuel (blue) to that from the four fissileisotopes in reactor core. The drop at 3 MeV isdue to the end point energy of 144Pr beta decay,which contributes the most with its mother nu-clide 144Ce to SNF antineutrinos.

2.7 Systematic Uncertainties of the PredictedReactor Antineutrino Spectrum

The systematic uncertainties of the predicted reac-tor antineutrino spectrum can be categorized as eithercorrelated or uncorrelated among different reactor cores.The list of systematic uncertainties, and their values forthe integrated reactor antineutrino flux, are shown in Ta-ble 4. The combined correlated uncertainty is taken tobe 2.7% from the ILL+Vogel model (or 2.4% from the

Huber+Mueller model). The correlated uncertainties arecommon for all reactor cores, therefore they are irrele-vant in the neutrino oscillation analysis where only therelative rate and spectrum between the near and the fardetectors are compared. The combined uncorrelated un-certainty is 0.9%, as a square root of the quadratic sum ofthe uncorrelated items, including power, energy/fission,fission fraction, spent fuel, and non-equilibrium in Ta-ble 4.

Table 4. Summary of the systematic uncertaintiesof the predicted integrated reactor antineutrinoflux associated with a single reactor core.

uncertainty

power 0.5%

energy/fission 0.2%

isotope spectrum 2.7%

IBD cross section 0.12%

fission fraction 0.6%

baseline negligible

spent fuel 0.3%

non-equilibrium 0.2%

Antineutrino Energy (MeV)2 3 4 5 6 7 8 9 10

Unc

erta

inty

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Bin Uncorrelated

Bin Correlated

Fission FractionSpent Fuel

Non-equilibrium

Fig. 7. The systematic uncertainties of the pre-dicted reactor antineutrino spectrum from eachenergy-dependent component. The bin uncorre-lated/correlated uncertainty (see text for details)is the average value of the four primary isotopes,weighted by their fission fractions.

Some uncertainties are dependent on antineutrino en-ergy, and can induce fluctuations in the energy spectrum,while the others only impact the integrated antineutrinoflux. The contribution from each energy-dependent com-ponent is broken down and shown in Fig. 7. The energy-dependent uncertainties can be further categorized ascorrelated or uncorrelated between energy bins. Theisotope antineutrino spectra of 235U, 239Pu, and 241Puare converted from the respectively measured beta de-cay spectra. The uncertainties of these spectra have bothbin-to-bin correlated and uncorrelated components. The

010201-9


bin-to-bin correlated uncertainty is induced by the elec-tron to antineutrino spectrum conversion models. Thebin-to-bin uncorrelated uncertainty is induced by the sta-tistical uncertainty of the measured beta decay spectra.The antineutrino spectrum of 238U is based on theoreticalcalculation, and its uncertainty is bin-to-bin correlated.

The size of the total uncertainty is shown as the errorbars on the predicted antineutrino spectrum in Fig. 5.

3 Inverse Beta Decay Event Selection

After production in the six Daya Bay reactor cores asdescribed above, ν̄e are detected in identically designedDaya Bay antineutrino detectors (ADs). Each AD con-sists of three nested cylindrical vessels. The inner acrylicvessel (IAV) with a thickness of 11 mm is filled with0.1% gadolinium-doped liquid scintillator (GdLS), whichconstitutes the primary antineutrino target. The outeracrylic vessel surrounding the target is filled with un-doped LS, increasing the efficiency of detecting gammarays produced in the target. The outermost stainlesssteel tank is filled with mineral oil. A total of 192 8-inchphotomultiplier tubes (PMTs) are radially positioned inthe mineral-oil region of each AD. Specular reflectors aredeployed directly above and below the outer acrylic ves-sel. Three automated calibration units (ACUs) capa-ble of deploying radioactive sources into the AD alongthree vertical z-axes are located on the top of each AD’souter tank [54]. At each site, ADs are submerged intwo-zone water Cherenkov muon detection systems, com-posed of inner and outer water shields (IWS and OWS),in three experimental halls, as shown in Fig. 1. A moredetailed description of all detector systems can be foundin [33, 55].

For the first seven months of Daya Bay data-takingfrom December 2011 until July 2012, six ADs were de-ployed and utilized for data analysis, two at the DayaBay near site, one at the Ling Ao near site, and threeat the Far Site. For the additional 13 months of thedata to be used in this publication, from October 2012to November 2013, the full eight-AD detector deploy-ment was utilized, with two ADs at each near site andfour ADs at the Far Site. During a special calibrationperiod in Summer 2012, one ACU was temporarily re-moved to facilitate deployment of a Manual CalibrationSystem, which was capable of deploying an articulatingacrylic arm down the AD’s center axis, allowing for full-volume calibration of the GdLS volume at a variety ofvertical Z-positions and radial R-positions with a PuCneutron/gamma source.

A series of cuts are applied to the data to selecthigh purity time-coincident trigger pairs in the AD thatmatch the characteristics of IBD signals: a prompt en-ergy deposition from ionization and annihilation of theIBD positron, followed by an energy deposition from Gd-

capture of the IBD neutron 30 µs later on average. Theselection process and various cuts have been described indetail in a previous Daya Bay publication [41], and haveremained unchanged for this analysis. We briefly list thesequence of IBD selection cuts below.

• Flasher Cut: Spurious single triggers caused byPMT light emission are efficiently removed usinglight collection topology cuts described in [41].

• Capture Time Cut: Candidate trigger pairs are se-lected by requiring time-coincident triggers be sep-arated by 1–200 µs.

• Prompt Energy Cut: The prompt trigger in thetime-coincident pair must have an energy of 0.7–12 MeV.

• Delayed Energy Cut: The delayed trigger in thetime-coincident pair must have an energy of 6–12 MeV.

• Muon Veto Cut: Candidate pairs are rejected iftheir delayed signals occur (i) within a (-2 µs,600 µs) time window with respect to a water shieldmuon trigger with a PMT multiplicity >12 eitherin the inner or outer water shield, or (ii) withina (0, 1000 µs) time window with respect to trig-gers in the same AD with an energy ranging from20 MeV to 2.5 GeV, or (iii) within a (0, 1 s) timewindow with respect to triggers in the same ADwith an energy above 2.5 GeV.

• Multiplicity Cut: To remove ambiguities in the IBDpair selection when multiple triggers are in time-coincidence, candidate pairs are removed if thereis an additional candidate with E > 0.7 MeV inthe interval 200 µs before the prompt-like signal,200 µs after the delay-like signal, or between theprompt-like and delayed-like signals.

Total IBD candidate event rates after applying thesecuts are listed in Table 5. Due to the near-identical re-sponse of the Daya Bay ADs, the efficiencies of mostIBD selection cuts are the same for all detectors. Muonveto efficiency (�µ) and multiplicity cut efficiencies (�m)are dependent on muon fluxes and intrinsic backgroundlevels, which vary among different sites and ADs.

Backgrounds from accidental coincidences, fast neu-trons, cosmogenic 8He/9Li production, AD-intrinsic al-pha radioactivity, and AmC neutron calibration sourcesremain in the sample of IBD candidates and have beenestimated using a variety of techniques described in de-tail in previous publications [32, 41]. Background rateestimates remain unchanged for this analysis.

010201-10


Table 5. Summary of signal and backgrounds. Rates are corrected for the muon veto and multiplicity cut efficienciesεµ · εm. Rate differences between detectors at the same site result from differences in fluxes between detectorlocations.

EH1 EH2 EH3

EH1-AD1 EH1-AD2 EH2-AD1 EH1-AD2 EH3-AD1 EH3-AD2 EH3-AD3 EH3-AD4

IBD candidates 304459 309354 287098 190046 40956 41203 40677 27419

DAQ live time(days) 565.436 565.436 568.03 378.407 562.451 562.451 562.451 372.685

εµ 0.8248 0.8218 0.8575 0.8577 0.9811 0.9811 0.9808 0.9811

εm 0.9744 0.9748 0.9758 0.9756 0.9756 0.9754 0.9751 0.9758

Accidentals(per day) 8.92±0.09 8.94±0.09 6.76±0.07 6.86±0.07 1.70±0.02 1.59±0.02 1.57±0.02 1.26±0.01Fast neutron(per AD per day) 0.78±0.12 0.54±0.19 0.05±0.01

9Li/8He(per AD per day) 2.8±1.5 1.7±0.9 0.27±0.14Am-C correlated 6-AD(per day) 0.27±0.12 0.25±0.11 0.27±0.12 0.22±0.10 0.21±0.10 0.21±0.09Am-C correlated 8-AD(per day) 0.20±0.09 0.21±0.10 0.18±0.08 0.22±0.10 0.06±0.03 0.04±0.02 0.04±0.02 0.07±0.03

13C(α, n)16O(per day) 0.08±0.04 0.07±0.04 0.05±0.03 0.07±0.04 0.05±0.03 0.05±0.03 0.05±0.03 0.05±0.03IBD rate(per day) 657.18±1.94 670.14±1.95 594.78±1.46 590.81±1.66 73.90±0.41 74.49±0.41 73.58±0.40 75.15±0.49

4 Event Selection Efficiencies

In order to estimate the total number of inverse betadecay interactions in each AD, the efficiencies of all sig-nal selection cuts must be estimated. All cut efficien-cies have been estimated in previous Daya Bay publi-cations [32, 41]. Many of these efficiencies remain un-changed in this analysis, and are only briefly describedhere. A few key efficiencies common to all detectors havebeen recalculated with respect to those reported in [41]utilizing new comparisons between data and Monte Carlo(MC) simulation. The improved data-constrained detec-tion efficiencies and systematics will be described belowin detail. The recalculation and application of these keyefficiencies and systematics result in a robust measure-ment of the overall reactor νe flux from Daya Bay. Sincethese key systematics for detector efficiencies are largelycorrelated among all Daya Bay detectors, this reanalysisdoes not affect the previous measurement of oscillationparameters reported by Daya Bay.

To produce improved efficiency determinations, a va-riety of new MC samples were generated utilizing anupdated version of Daya Bay’s simulation frameworkNuWa, which is based on the Geant4 simulation pack-age [56] and the Gaudi framework [57]. A few key MCimprovements with respect to the version utilized to pro-duce previous efficiency estimates in [41] are briefly high-lighted. Models used to generate the spectrum of gam-mas released by neutron capture on Gd were alteredbased on new Daya Bay and bench-top datasets. Thesealterations, which affect the efficiency in detecting neu-tron captures on Gd, will be described in further detailbelow. Adjustment was also made to the model describ-ing the thermalization and scattering of neutrons at allenergies. This adjustment will also be described in fur-ther detail below, as it has a small impact on the capturetime cut and on the position distribution of IBD events.

4.1 Flasher Cut Efficiency

Spontaneous light emission from the Daya Bay PMTbases can mimic particle interactions of various energies.Flasher triggers can be rejected using charge topologycuts, as described in detail in [41]. The IBD signal effi-ciency of these cuts is estimated to be 99.98%.

4.2 Capture Time Cut Efficiency

To be selected as an IBD signal the time separationbetween the trigger pair must be within a (1µs, 200µs)range. As described in [41], the vast majority of signalevents meet this criterion, with 98.70% passing this cutin the most recent Daya Bay MC simulations. An uncer-tainty of 0.12% is assigned to this cut by noting small dif-ferences in trigger coincidence time distributions betweenAmC, AmBe, and PuC fast neutron source deploymentsand MC.

4.3 Muon Veto Cut Efficiency

Cuts are applied to reject coincident triggers corre-lated in time with muons traversing the water pools orADs. The characteristics and performance of these cutsare described in [41]. Total signal efficiencies for thesecuts depend on the muon flux at each site and are around82%, 86%, and 98% at EH1, EH2, and EH3, respectively,as shown in Table 5. Muon veto cut efficiencies are calcu-lated based on the actual number of muon vetos enforcedin the dataset, and thus have negligible uncertainties.

4.4 Multiplicity Cut Efficiency

Some trigger coincidences containing more than twotriggers are also rejected to avoid ambiguities in identi-fying the true IBD prompt-delayed pair. The definitionsof these multiplicity cuts are described in [41], and havean efficiency of 97.5% for all ADs, within 0.1%. Multi-plicity cut efficiencies are calculated on-the-fly and havenegligible associated uncertainty.

010201-11


4.5 Prompt Energy Cut Efficiency

While the 0.7 MeV prompt energy cut is significantlybelow the 1 MeV annihilation gamma energy, a smallproportion of events (0.2%) deposit most of their energyin the non-scintillating inner acrylic vessel and fall belowthe threshold. The efficiency is 99.81%± 0.10% deter-mined by the most recent Daya Bay MC data which isconsistent with that cited in [41].

4.6 Delayed Energy Cut: Gd Capture Fraction

Inefficiency in detection of neutrons from IBD inter-actions in the target GdLS region is the result of threeprimary physical processes:

• Capture on hydrogen in the target, producing a sin-gle 2.2 MeV gamma well below the applied 6 MeVthreshold.

• Capture on hydrogen outside the target where noGd is present, producing the same 2.2 MeV gamma(spill-out effect).

• Deposition of significant neutron-Gd (nGd) cap-ture gamma energy outside the scintillating detec-tor region, producing a detected delayed energy be-low the applied 6 MeV threshold.

We choose to describe and quantify each of these contri-butions to the delayed energy cut efficiency separately inthis analysis to produce robust and transparent efficiencyand uncertainty estimates fully constrained by data. Webegin by describing our estimates of inefficiency from thefirst two of these processes, collectively described as theGd capture fraction.

4.6.1 Gd Concentration and AD-Center Gd CaptureFraction

The keV-range kinetic energy neutrons created inIBD interactions in the GdLS thermalize in the detec-tor and capture principally on either H or Gd nuclei.Because of their low capture energy (2.2 MeV), neutron-hydrogen (nH) captures are completely excluded fromthe IBD signal by the 6 MeV cut used in this analysis.Determining the Gd capture fraction is vital in deter-mining the predicted reactor antineutrino flux. This Gdcapture fraction is physically determined by the Gd con-centration in the GdLS, which is ∼0.1% by weight. TheGd capture fraction resulting from the Gd concentrationcan be measured largely independently of spill-out effectsby looking at AD-center Gd capture events from variousnon-IBD (i.e., from calibration)datasets.

The AD-center Gd capture fraction was first mea-sured utilizing muon spallation neutrons. This datasetwas obtained by selecting all AD non-flasher triggerswithin a time window of 20-300 µs after traversal of theAD by a muon, which is identified by an AD trigger

with more than 3000 photoelectrons (∼20 MeV). Trig-gers from events other than neutron captures are then re-moved from the sample by subtracting a similar datasetoccurring 520-800 µs after a muon traversal. AD centerevents are then selected by removing all events havingreconstructed positions R> 0.8 m or |Z|> 0.8 m, wherethe position reconstruction follows the second methoddescribed in [55]. The background-subtracted spallationneutron capture spectrum for all four near ADs is shownin Fig. 8, along with the background spectrum.

Delayed Energy (MeV)1 2 3 4 5 6 7 8 9 10

Eve

nts

/30

keV

1

10

210

310

410

510Data, Background-Subtracted

Background

Fig. 8. The background-subtracted spallation neu-tron capture spectrum and associated backgroundspectrum in all near-site ADs combined for thefull Daya Bay dataset. The main contribution tothe background at low energy is natural radioac-tivity.

The Gd capture fraction for this dataset can be cal-culated using the following definition:

FGd =NGd

NGd+NH

=N(6−12 MeV)

N(6−12 MeV)+N(1.7−2.7 MeV). (8)

Low-energy cuts ∼30% below the nH and nGd peak val-ues were chosen to exclude roughly similar proportions ofthe nH and nGd low-energy tails from the calculation ofthis metric. By this definition, the Gd capture fractionfor a specific dataset is determined independently of anyMC inputs.

For this dataset, we obtain a Gd capture fraction of85.4%, as seen in Table 6, with a statistical uncertainty of


µs), relative length (few-µs difference in signal and back-ground window length), or in start time (from 20µs to40µs for signal, for example), FGd is altered by < 0.1%.As AD-center position cuts are varied from the nomi-nal 0.8 m to either 0.5 m or 1.0 m, FGd is altered by0.3%. We also note that fractional contributions of tar-get spallation neutron capture on other isotopes, such ascarbon, are below 0.1%, negligible in the scope of the ef-ficiency analysis. Adding the uncertainties quadratically,we obtain a Gd capture fraction of 85.4% ± 0.4% fromspallation neutrons.

The Gd capture fraction has also been measured bydeploying AmC, AmBe, and PuC neutron calibrationsources at the centers of the two ADs at the Daya BayNear Site (EH1) during a period of special calibrationruns coincident with installation of the final two DayaBay detectors at the other experimental halls [54, 58].These neutron sources produce time-correlated triggers,with proton recoils and excitation gammas forming theprompt signal, and the subsequent neutron capture form-ing the delayed signal. The neutron kinetic energy rangesand excitation gamma energies for various prompt en-

ergy ranges for these sources are listed in Table 6. Someexcited states with low neutron energies closer to thatof ∼keV-scale IBD neutrons, such as the second excitedstate of 16O produced by the PuC (α,n) reaction, areeasily separable from other calibration source decays ex-hibiting higher neutron kinetic energies. This is becauseminimally quenched de-excitation gammas from theseexcited states produce a much higher prompt energythan the highly-quenched prompt proton recoils gener-ated by energetic neutrons produced in the ground state.Meanwhile, other excited states produce either a varietyof neutron kinetic energies (AmBe), or have prompt ener-gies indistinguishable from the ground state. Daya Bay’sstandard gamma-less AmC sources produce no transi-tions to excited states, since alphas in these sources aremoderated with thin gold foils [59]. For all sources, re-moval of uncorrelated triggers was accomplished by sub-tracting a set of accidental coincidences formed by ran-domly ordering in time that calibration run’s single trig-gers according to the calculated singles rate for that run.As the sources were deployed at the detector center, cutson reconstructed position were not utilized.

Table 6. Characteristics and AD-center nGd capture fractions for neutron calibration sources with varying promptErec categories. Prompt signals are provided by muons (spallation neutrons), proton recoils (calibration sourcedecaying to ground states), excitation gammas (calibration source decaying to excited states), or IBD positrons(IBD MC). Results for spallation neutrons are the average of all ADs, while results for calibration sources arethe average of the two EH1 ADs, where all of the differing neutron sources were deployed. Measured Gd capturefractions are consistent within the associated systematic uncertainty range of 0.4%.

Data Set Erec,prompt (MeV) KEn (MeV) Eγ (MeV) FGd (%) σstat (%)

Spallation Neutron - 0-100+ - 85.4


the source deployment in data and MC.Resultant FGd values from extended runs of these

three sources are shown in Table 6, with delayed spectrafrom each source shown in Figure 9. While neutron cap-ture tail shapes from the different sources deviate slightlyfrom one another, likely due to differing source packag-ing material and optical properties, values of FGd from allsources agree to within 0.3%. These source FGd valuesare also consistent within 0.4% between data and MCfor all source types and neutron energy ranges. Similarvariations of energy and timing cuts applied to the spal-lation neutron dataset above produce


Gd capture fraction, but as a benchmark of the agree-ment between full-volume Gd capture fractions betweenMC and data. An additional check on this analysis us-ing interpolated values between all available PuC MCSdeployment positions yields differences of up to 0.7% be-tween data and MC for all PuC neutron kinetic energies.

After performing these benchmark comparisons be-tween MC and data, the precision of the MC-reportedfull-volume Gd capture fraction is estimated as the max-imum difference between these reported MC and datavalues above, 0.7%. Adding quadratically the approxi-mate 0.4% uncertainty in the AD-center Gd capture frac-tion, we obtain a predicted Gd capture fraction of 84.17± 0.80%. The difference from early Daya Bay publica-tions (83.8 ± 0.8%) is caused by the improved Geant4neutron thermalization models on which this analysis isbased, which produce a lower rate of IBD neutron spill-out.

R [mm]200 400 600 800 1000 1200 1400

Gd

Cap

ture

Fra

ctio

n

0.83

0.84

0.85

0.86

MCS Data

MCS MC

Z = 0 mm Scan

Z [mm]-1500 -1000 -500 0 500 1000 1500

Gd

Cap

ture

Fra

ctio

n

0.8

0.82

0.84

0.86

MCS Data

MCS MC

R = 200 mm Scan

Fig. 10. Variation in the Gd capture fraction FGdreported by a MCS-deployed PuC source as afunction of R (top) and Z (bottom) position in thedetector. For the Z scan, MCS runs at R=200 mmwere utilized. For the R scan, MCS runs atZ=0 cm (AD middle) were utilized. A drop inthe Gd capture fraction is clearly visible near thetarget boundary. Despite small visible differences,data and MC yield similar integrated full-volumeGd capture fractions within 0.6%.

4.7 Delayed Energy Cut: Gd Capture DetectionEfficiency

Of the 84.17% of target IBD neutrons capturing onGd, a small percentage will have delayed reconstructedenergy below the 6 MeV delayed energy cut. This ineffi-ciency arises as a portion of gammas from some Gd cap-tures exit the scintillating region of the detector beforedepositing their energy. In order to properly estimatethe predicted reactor antineutrino flux, this Gd capturedetection efficiency must be properly estimated. As withthe full-volume Gd capture fraction, the Gd capture de-tection efficiency is determined using MC, since the fulltail of the IBD delayed energy signal is obscured in databy nH captures and accidental backgrounds.

The shape of the Gd capture tail, and therefore theGd capture detection efficiency, is dependent on themodel used to describe the gamma energies releasedby a nGd capture. The excited states of 158Gd and156Gd, the products of neutron capture on 157Gd and155Gd, are numerous, making a first-principles determi-nation and modelling of de-excitation pathways imprac-tical. Instead, the Daya Bay MC produces nGd capturegammas by performing an energy-conserving samplingof previously-measured Gd-capture gamma spectra. Thealgorithm that performs this sampling is tuned to ensurethat the energy conservation requirement does not biasaggregate sampled gamma spectra relative to the inputspectrum. In previous publications [7, 41], Daya Bayutilized nGd gamma spectrum models based on earlyspectroscopic measurements [60], shown in top panel ofFig. 11, which do not sufficiently reproduce the IBD ex-tended nGd tail shapes now visible in Daya Bay’s high-statistics datasets, pictured in middle panel of Fig. 11.This gamma model is referred to in this paper as the“M13A,Old” model

We investigated additional nGd gamma models to ob-tain a better description of the data. It was found thatnGd gamma spectra included in Geant4 libraries [56],shown in bottom panel of Fig. 11, produced reason-able agreement with observed data once energy conser-vation in gamma emission, not present in Geant4 by de-fault, was implemented. This model is referred to asthe “M14A,Geant” model in this paper. Another well-matching model, called “M14A,Caltech”, was generatedthrough direct measurement of nGd gamma productionin a small cell of Daya Bay GdLS using a benchtop HPGedetector setup at Caltech. In both new “M14A,Geant”and “M14A,Caltech” models, the total contribution ofhigh-energy gammas is lower than in early spectroscopicmeasurements.

Figure 11 shows the combined IBD nGd capture spec-tra from all Daya Bay detectors and from the varioustested MC models. The nGd tail is clearly visible withhigh statistical precision above 3.0 MeV, and provides a

010201-15


direct constraint on the delayed energy cut inefficiencyabove this energy. The two MC models provide a bound-ing envelope around the observed spectrum when ap-proaching the low-energy region where the nH peak ob-scures the true nGd tail shape. The delayed energy cutinefficiency from this low energy region is estimated bythe relative contribution from these new MC nGd cap-ture models. The data-constrained portion of the tailfrom 3–6 MeV provides a 6.6% inefficiency, while thelow-energy MC-constrained portion below 3.0 MeV con-tributes 0.4% and 0.9% for the different models.

Energy (MeV)0 1 2 3 4 5 6 7 8

Entr

ies/

0.02

MeV

0

0.005

0.01

0.015

0.02

0.025

0.03

M13A, Old

M14A, Geant

M14A, Caltech

Energy (MeV)0 5 10

Even

ts/0

.1 M

eV

210

310

410

Data

MC13A, Old

MC14A, Geant

MC14A, Caltech

data

Energy (MeV)0 5 10

En

trie

s/0.

1 M

eV

10

210

310

410

M13A, Old

M14A, Geant

M14A, Caltech

g4mc

Fig. 11. Top: Models of produced nGd capturegamma spectra utilized in the previous (red)or current (blue and green) efficiency estimates.Middle: Erec distribution of the IBD delayed sig-nal for data and MC utilizing these nGd gammamodels. Bottom: The spectrum of IBD nGd de-layed signals from MC for these models. These

distributions are used to compute the expectednGd capture detection efficiency for Daya Bay.

The total estimated nGd detection efficiency usingthe “M14A,Geant” model is 92.71%. A conservative100% uncertainty is assigned to the total contributionbelow 3 MeV due to the lack of direct data constraints.The 0.5% difference in the low-energy contribution fromthe data-enveloping MC models provides good motiva-tion for this choice. Further uncertainty contributionsfrom statistical and other systematics, such as the MC-data difference in energy scale near the GdLS-LS bound-aries, are negligible in comparison.

This Gd capture detection efficiency estimate,92.71%, differs from previous estimates, 90.9%, in [7]by 1.8%, a ∼3 σ change with respect to previous sys-tematic uncertainty estimates. As previously mentioned,this difference stems from improved modelling of the nGdgamma spectrum in the updated Daya Bay MC simula-tions. Due to the limited available statistics, previousuncertainty estimates were made using comparisons be-tween the previous MC model and data only in a narrowhigher-energy window (6-7 MeV) bordering the nGd tailregion. In contrast, the updated efficiency estimate is di-rectly constrained by data with


4.9 Spill-in Effects

When calculating the total number of expected Gdcapture detections, one must take into account IBD neu-trons generated outside the GdLS that are captured inthe GdLS. This process, termed as the spill-in effect, ef-fectively increases the size of the target volume. As withthe spill-out effect, the size of the spill-in effect and thenet increase in effective target volume is calculated us-ing MC simulation of IBD neutrons in the detector. Thecalculated value of the effective target size in the defaultDaya Bay MC due to spill-in is 104.9%.

The spill-in correction obtained by the MC is depen-dent on the choice of neutron scattering models. DayaBay’s default MC for neutron scattering includes inelas-tic scattering of thermal neutrons below 4 eV wheremolecular effects due to hydrogen bonds and their en-ergy transfer with neutrons must be considered. Thisis in contrast to “free-gas” models of neutron scatteringwhich forego this detailed modelling at low energies. Inits G4NDL3.13 physics library, Geant4 has inherited sev-eral neutron thermal scattering models and parametersfrom the Evaluated Nuclear Data Files (ENDF/B-VI)database [61] for a variety of moderators such as waterand polyethylene. As database entries are unavailable forthe primary Daya Bay target materials GdLS, acrylic,and mineral oil, ENDF models for water and polyethy-lene were used to describe each of these target materialsin the MC. Variations between these different models in-dividually for each Daya Bay target material produced 3.5 MeV on the promptevent energy to suppress the accidental back-ground in data.

The IBD coincidence time distributions have beencompared between data and MC. Since spill-in eventsoriginate in the LS, they tend to have longer coincidencetimes and contribute heavily to the tail of the IBD coin-cidence time distribution. This relation was determinedwith a MC IBD event dataset by calculating both thespill-in fraction and the fraction of signal events withgreater than 50 µs coincidence time for subsets of eventsin common reconstructed position bins, and the result is

010201-17


shown in top of Fig. 13. The coincidence time peak-to-tail ratios in each Rp bin were computed for both dataand MC with a requirement of > 3.5 MeV on the promptevent energy, shown in bottom of Fig. 13. The differencebetween data and MC at the boundary of GdLS regionreflects the spill-in difference. According to the relationbetween capture time distortion (peak-to-tail ratio) andthe fraction of spill-in event, the spill-in fraction is eval-uated for the data. The relative contribution of spill-in events was found to agree between data and MC towithin 0.5% of the total event sample for a wide varietyof systematic variations including coincidence time taildefinitions, and assumed position reconstruction biases.

Spill-in Fraction0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Co

inci

den

ce T

ime

Pea

k-to

-tai

l Rat

io

1

1.5

2

2.5

3

3.5

4

]2 [m2pR0 0.5 1 1.5 2 2.5 3 3.5

Co

inci

den

ce T

ime

Pea

k-to

-tai

l Rat

io

1

1.5

2

2.5

3

3.5

4Data

MC

Fig. 13. Top: Points show the relation be-tween true spill-in percentage and coincidencetime peak-to-tail ratio in Monte Carlo simulationfor event groupings at common Rp,rec. The peak-to-tail ratio compares IBD events in the (1,50)and (50,200) µs capture time regions. A curveis fitted to infer the spill-in fraction for the IBDcandidate dataset. Bottom: The coincidence timepeak-to-tail ratio in different bins along the ra-dius. The spill-in percentage in each bin of datais predicted with the relation of spill-in and peak-to-tail ratio obtain from MC.

To provide a conservative estimate of the inaccuracyof the IBD spill-in percentage reported by MC, the max-imum MC-data difference observed in any of these stud-ies, 1.0%, is used as the uncertainty in the spill-in con-tribution to the efficiency estimate.

4.10 Target protons

The uncertainty in the number of target protons is in-cluded with the detection efficiency uncertainties as theIBD rate is proportional to the number of target protons.The number of target protons in the GdLS is calculatedas

Np =M ·FH ·NA ·I1H/mH , (10)

where M is the mass of GdLS in the target, FH is themass fraction of hydrogen in GdLS, NA is the Avogadroconstant, I1H is the isotope abundance of

1H in natrualhydrogen, and mH is the atomic mass of hydrogen.

The target mass was precisely measured during thedetector filling and monitored during the data taking.The uncertainty of the target mass is 3.0 kg [33], cor-responding to 0.015% of the 20 ton target mass. Thehydrogen mass fraction of FH = 12.02± 0.11% was ob-tained from the combination of two sets of independentcombustion measurements, one of which is tabulated inRef. [33]. The combined fractional uncertainty in Npis 0.92%. The previous reported uncertainty in Np of0.47% [29] was incorrect.

4.11 Efficiency Summary

Calculated detection efficiencies and their related un-certainties are listed in Table 7. The detection efficiencycommon to all detectors is �=80.6%. Including the effi-ciencies that vary among detectors, as given in Table 5,total detection efficiencies range from 64.6% to 77.2%.The total systematic uncertainty of detection efficienciesis δ�/�=1.93%.

Table 7. Summary of the detection efficiencies andsystematic uncertainties. Muon veto and multi-plicity cut efficiencies vary between sites and havenegligible uncertainty.

Source � δ�/�

Target protons - 0.92%

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%

nGd detection efficiency 92.71% 0.97%

Spill-in correction 104.86% 1.00%

Combined 80.60% 1.93%

010201-18


5 Measurement of Reactor AntineutrinoFlux

Naively, the reactor antineutrino flux can be mea-sured directly using the Daya Bay near-site data. How-ever, due to the relatively large size of θ13, even at thenear sites (360–500 m baselines) there is an approxi-mately 1–2% deficit of the antineutrino flux caused byneutrino oscillations. Therefore, far-site data are re-quired in order to extract the value of θ13 independentof other experiments. In this section, we describe twomethods to measure the reactor antineutrino flux fromthe Daya Bay experiment. In the first method, the datafrom all ADs are fit based on neutrino oscillation the-ory and a reference reactor antineutrino flux model. Thevalue of sin2 2θ13 and the flux normalization R are simul-taneously obtained from the fit, the latter being the mea-sured reactor antineutrino flux. In the second method,we use the measured value of sin2 2θ13 and the near-sitedata only. The measured reactor antineutrino flux isthen expressed in a model-independent way in terms ofσf (cm

2/fission) and Y (cm2/day/GWth). Finally, wecombine our measurement with the past short-baselineexperiments to obtain a global average value, and com-pare it with different model predictions.

5.1 Measurement of sin2 2θ13 and Flux Normal-ization R

The IBD event candidates are selected as described inSec. 3. Figure 14 shows the daily averaged rates of IBDcandidate events per AD in the three experimental hallsas a function of time. The expected backgrounds aresubtracted and the detection efficiencies are corrected inthe figure. The measured IBD rates are highly correlatedwith the reactor operations.

IBD

Rat

e (/d

ay/A

D)

400

500

600

700

800

900EH1

DataNo OscillationBest Fit

IBD

Rat

e (/d

ay/A

D)

300400500600700800 EH2

01/2012 04/2012 07/2012 10/2012 12/2012 04/2013 07/2013 10/2013

IBD

Rat

e (/d

ay/A

D)

405060708090

100110

EH3

Fig. 14. Daily averaged rates of IBD candidateevents per AD in the three experimental hallsas a function of time. The discontinuity fromJuly 2012 to Oct 2012 corresponds to the periodwhen the last two ADs were installed. The dottedcurves represent no-oscillation predictions based

on reactor antineutrino flux analyses and detec-tor simulation. The predictions incorporated thebest-fit normalization parameter (R). The ratespredicted with the best-fit sin2 2θ13 are shown asthe red solid curves.

Figure 15 shows the integrated rate of the detectedν̄e signals at each AD, divided by the no-oscillation pre-dictions. A signal deficit of about 6% at the far hallrelative to the near halls is observed, indicating the sizeof the oscillation driven by θ13. A normalization factorR was defined to scale the signal predicted by a reac-tor model. The value of R, together with the value ofsin2 2θ13, was simultaneously determined with a χ

2 con-structed similarly as in Ref. [7] using only the integratedrate information,

χ2 =

8∑d=1

[Md−R ·Td(1+�D+∑

rωdrαr+�d)+ηd]

2

Md+Bd

+

6∑r=1

α2rσ2r

+

8∑d=1

(�2dσ2d

+η2dσ2B,d

)+�2Dσ2D

, (11)

where Md is the number of measured IBD events in the d-th detector with backgrounds subtracted, Bd is the corre-sponding number of background events, Td is the numberof IBD events predicted by a reactor model with neutrinooscillations, and ωdr is the fractional IBD contributionfrom the r-th reactor to the d-th detector determined bybaselines and reactor antineutrino fluxes. σr (0.9%) isthe uncorrelated reactor uncertainty, σd (0.2%) is the un-correlated detection uncertainty, σB,d is the backgrounduncertainty listed in Ref. [32], and σD (1.93%) is thecorrelated detection uncertainty, i.e. the uncertainty ofdetection efficiency in Table 7. Their corresponding nui-sance parameters are αr, �d, ηd, and �D, respectively.

We use the rate-only fit in this analysis in order to fixthe reference reactor model to its nominal value. Thusthe obtained normalization R can be directly comparedwith other experiments. Fixing the reactor model doesnot affect the oscillation result due to the relative mea-surement between far and near detectors. If we add thespectral information, we would need to include and in-flate the model uncertainty in the fit in order not tobias the oscillation result. Consequently, even thoughwe would obtain a more precise value of sin2 2θ13, thebest-fit flux of the reference reactor model would devi-ate from its nominal value, making the comparison withother experiments impractical.

The minimization of the rate-only χ2 defined inEq. 11 yields χ2/NDF = 5.7/6. The best-fit value ofsin2 2θ13 = 0.085± 0.006 is insensitive to the choice ofreactor models. The uncertainty in sin2 2θ13 is statisti-cally dominated. The 0.9% reactor related uncertainty,

010201-19


treated as uncorrelated in the oscillation analysis in orderto avoid a bias of the sin2 2θ13 fit, is conservatively addedquadratically to the uncertainty of R, effectively treatingit as correlated among reactors in the rate measurement.The best-fit result of R is 0.946± 0.020 (0.992± 0.021)when compared with the Huber+Mueller (ILL+Vogel)model. Replacing the Mueller 238U spectrum with themeasured spectrum in Ref. [47] yields an R increasedslightly by 0.002. The contributions to the uncertaintyin R are summarized in Table 8. The uncertainty is dom-inated by the detection uncertainty σD.

Effective Baseline [km]0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

exp

ecte

d / N

de

tecte

dN

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

Daya Bay

Ling Ao

Far Hall

reactorσ

Fig. 15. Ratio of the detected to expected non-oscillation ν̄e signals at the 8 ADs located in threeexperimental halls as a function of the effectivebaseline, which is determined for each detector byequating the multicore oscillated flux to an effec-tive oscillated flux from a single baseline. A 6%signal deficit at the far hall relative to the nearhalls is observed, indicating the size of the θ13-driven oscillation. The oscillation survival prob-ability at the best-fit value is given by the redcurve. In addition, there is a 5% normalizationdeficit when compared with the Huber+Muellermodel prediction. The uncertainty of the modelprediction is shown as the gray band around unity.Two far hall points are displaced by 50 m for vi-sual clarity.

Table 8. Summary of contributions to the total un-certainty of the reactor antineutrino flux measure-ment.

Uncertainty

statistics 0.1%

oscillation 0.1%

reactor 0.9%

detection efficiency 1.93%

Total 2.1%

The best-fit oscillation curve is shown in Fig. 15. Dis-regarding the normalization, the measurement is con-sistent within the three-neutrino paradigm. On theother hand, the normalization is inconsistent with theHuber+Mueller model prediction within the model un-certainties. We will further discuss the implication inSec. 5.3.

5.2 Measurement of IBD Yield

In this subsection, we express the measurement intwo model-independent ways: the IBD yield per nuclearfission (σf ), and the IBD yield per GWth per day (Y ).

σf for each AD is determined by solving the followingequation:

Md =

6∑r=1

N fr4πL2dr

σdfNTd P

drsur�

Dd , (12)

where N fr is the predicted number of fissions from therth reactor core, which is calculated based on Wr (av-erage thermal power of rth core), f isor (average fissionfraction of rth core for each isotope) and Eiso (mean en-ergy release per fission for each isotope), integrated overthe live time of the detector:

N fr =

∫Wr∑4

iso=1f isor E

isodt. (13)

Ldr is the distance between the dth detector and the rthreactor core. NTd is the total number of target protonsin the GdLS of each AD. The total detection efficiency,�Dd , is different for each AD because of different effectsof muon veto and multiplicity cuts on each AD. P drsur isthe survival probability given an AD-core pair, calcu-lated using the best-fit value of sin2 2θ13 from the rate-only analysis described in the previous subsection. Dueto the relatively large size of θ13, even at the near sitesthere are on average about 1.5% rate deficits, as shownin Fig. 15. The values of σdf for all ADs, from Eq. 12, aresummarized in Table 9. Similar to the normalization R,the uncertainty in σdf (summarized in Table 9 as σexp) isdominated by the correlated detection uncertainty σD.

Theoretically, σf represents the IBD cross sectionconvolved with the reactor antineutrino spectra from allfission isotopes, and integrated over energy:

σf =

4∑iso=1

fiso

∫Siso(Eν)σ(Eν)dEν (14)

Given a reactor model that predicts the antineutrinospectrum Siso(Eν) for each of the four main fission iso-topes 235U, 238U, 239Pu and 241Pu, and the fission frac-tions fiso determined by NPP operations and simula-tions, σf can be theoretically calculated and comparedwith the model-independent measurement. The ratios ofthe measurement versus the Huber+Mueller model pre-diction (RH+M), and versus the ILL+Vogel model pre-diction (RI+V) for each AD are summarized in Table 9.

Alternatively, we can define Yd ≡ σdfN fr /Wr as theIBD yield per GW thermal power per day. The aboveexpression approaches a common value Y after averag-ing multiple fuel burnup cycles, since all the reactor cores

010201-20


have the same average fuel composition. During the 6-AD data taking period, none of the reactor cores hadcompleted a burnup cycle. The differences in fuel compo-sition cause about 2% variations in measured IBD yield(top panel of Fig. 16). These core-to-core variations canbe corrected using known values of the fission fractions

given by Table 9. On the other hand, all the reactor coreshad roughly one full cycle during the 6-AD and 8-ADdata taking period. Therefore measurements from eightdetectors give the same value (within statistical fluctua-tion), and core-to-core variations are negligible (bottompanel of Fig. 16).

Table 9. Tabulated results of the flux measurement from each AD. σf is the measured cross section in units of10−43cm2/fission. Y is the IBD yield in units of 10−18cm2/GW/day. RH+M and RI+V are the ratios of measuredflux with respect to Huber-Mueller and ILL-Vogel model predictions, respectively. σexp is the total fractionalexperimental uncertainty of the flux measurement. 235U, 238U, 239Pu, 241Pu are the flux-weighted fission fractionsof each fission isotope. L is the flux-weighted baseline for each AD. Psur is the average ν̄e survival probability ateach AD. See the text for more details.

σdf ·1043 Y ·1018 RH+M RI+V σexp 235U 238U 239Pu 241Pu Ld Psur

(cm2/fission) (cm2/GW/day) (%) (m)

EH1-AD1 5.907 1.531 0.945 0.991 2.1 0.564 0.076 0.303 0.056 566 0.985

EH1-AD2 5.912 1.536 0.946 0.992 2.1 0.564 0.076 0.303 0.056 561 0.986

EH2-AD1 5.925 1.538 0.948 0.994 2.1 0.557 0.076 0.312 0.055 594 0.983

EH2-AD2 5.894 1.529 0.944 0.990 2.1 0.552 0.076 0.315 0.057 598 0.983

EH3-AD1 5.819 1.521 0.940 0.986 2.2 0.559 0.076 0.310 0.055 1635 0.934

EH3-AD2 5.858 1.540 0.946 0.992 2.2 0.559 0.076 0.310 0.055 1636 0.934

EH3-AD3 5.842 1.536 0.944 0.990 2.2 0.559 0.076 0.310 0.055 1640 0.934

EH3-AD4 5.907 1.554 0.956 1.002 2.2 0.552 0.076 0.315 0.057 1641 0.934

Table 9 further summarizes a few characteristic pa-rameters calculated for each AD, including the averagefission fraction f isod , flux-weighted baseline Ld and aver-age survival probability P dsur. These parameters can betrivially obtained in the case of a single reactor core, butrequire clear definitions in the multi-core case of DayaBay. The average fission fraction f isod is defined as fol-lows:

f isod =

∑6r=1

βdr ·f isor∑6r=1

βdr, βdr =

N frL2dr

(15)

where βdr is the flux-weighting factor calculated from Nfr

and Ldr (see Eq. 12 for definition). We note that the av-erage fission fractions for the two newly installed ADs(EH2-AD2 and EH3-AD4) are slightly different from theADs at the same site, because they are seeing different re-actor core histories with respect to other detectors. Theflux-weighted baseline Ld is defined as

1

L2d=

∑6r=1

N fr ·1/L2dr∑6r=1

N fr. (16)

Finally, the average survival probability P dsur is calcu-lated as follows:

P dsur =

∑6r=1

NdrPdrsur∑6

r=1Ndr(17)

where Ndr is the predicted number of IBD events at thedth AD from the rth reactor core without oscillation, andP drsur is the average survival probability given an AD-corepair as defined in Eq. 12.

EH

1-A

D1

EH

1-A

D2

EH

2-A

D1

EH

2-A

D2

EH

3-A

D1

EH

3-A

D2

EH

3-A

D3

EH

3-A

D4

Mo

del

)-1

day

-1 G

W2

cm

-18

10

×Y

( 1.5

1.6

1.7 6-ADDaya Bay (stat.)Daya Bay w/ corr. (stat.)Daya Bay Combined (syst.)Huber + MuellerILL + Vogel

EH

1-A

D1

EH

1-A

D2

EH

2-A

D1

EH

2-A

D2

EH

3-A

D1

EH

3-A

D2

EH

3-A

D3

EH

3-A

D4

Mo

del

)-1

day

-1 G

W2

cm

-18

10

×Y

(

1.5

1.6

1.7 8-ADDaya Bay (stat.)Daya Bay w/ corr. (stat.)Daya Bay Combined (syst.)Huber + MuellerILL + Vogel

Fig. 16. Yield Y for the IBD events in the 6-ADonly (top) and 8-AD only (bottom) period withcorrections of 3-flavor oscillations (closed circles),and additional corrections due to the variationsof flux-weighted fission fractions at different sites(open squares). The horizontal line is the averageyield of the near detectors, and the gray band isits 1σ systematic uncertainty. The rate predictedby the Huber+Mueller (ILL+Vogel) model andits uncertainty are shown in blue (orange) region.

The measured IBD yields for each AD are plotted in

010201-21


Fig. 16. The yields are consistent among all ADs aftercorrecting for the small variations of fission fractions atthe different sites. The results are summarized in Ta-ble 10.

Table 10. The average IBD yields (Y and σf ) ofthe near halls, the flux normalization with re-spect to different reactor model predictions, andthe flux-weighted average fission fractions of thenear halls.

IBD Yield

Y ( cm2/GW/day) (1.53±0.03)×10−18

σf (cm2/fission) (5.91±0.12)×10−43

Data / Prediction

R (Huber+Mueller) 0.946±0.020 (exp.)R (ILL+Vogel) 0.992±0.021 (exp.)

235U : 238U : 239Pu : 241Pu 0.561 : 0.076 : 0.307 : 0.056

5.3 Comparison with Past Reactor Experiments

Recently, there was great interest in the so-called“reactor antineutrino anomaly”, which arises from re-evaluations of the reactor ν̄e flux that resulted in anincrease of the predicted ν̄e flux in the Huber+Muellermodel [24, 25]. Combining the new predictions with there-analysis of the past experimental data at baselines 10-100 m suggests a ∼4-6% deficit between the measuredand the predicted reactor ν̄e flux [26, 62]. In this subsec-

tion, our measurement is compared with the past reactorneutrino experiments.

A global fit was performed for the past reac-tor neutrino experiments. Nineteen short-baseline(


To calculate the global average independent of themodel uncertainty used by the past measurements, wefollow the method described in Ref. [62] by first remov-ing σmodel from both uncertainties, and define:

σexperr =√σ2err−σ2model

σexpcor =√σ2cor−σ2model. (18)

σexperr and σexpcor now represent experimental uncertainties

only. We then build a covariance matrix V exp such that

V expij = Robsi ·σ

expi,cor ·Robsj ·σ

expj,cor, (19)

where Robsi is the “ratio” column in Table 11 correctedby the “Psur” column for the θ13-oscillation effect. R

obsi

represents the observed rate from each measurement.We then calculate the best-fit average ratio Rpastg by

minimizing the χ2 function defined as:

χ2(Rpastg ) = (Rpastg −Ri) ·(V

expij )

−1(Rpastg −Rj), (20)

where V −1 is the inverse of the covariance matrix V . Thisprocedure yields the best-fit result Rpastg = 0.942±0.009,where the error is experimental only.

Since we now use the Huber+Mueller model as thereference model, we re-evaluate the model uncertaintyusing the correlated and uncorrelated uncertainty com-ponents given by Ref. [24, 25]. Using the weighted av-erage fission fraction from all experiments (235U : 238U: 239Pu : 241Pu = 0.642 : 0.063 : 0.252 : 0.0425), themodel uncertainty is calculated to be 2.4%, and the finalresult becomes:

Rpastg = 0.942±0.009 (exp.)±0.023 (model) (21)

Finally, we compare the Daya Bay result with thepast global average. In the previous subsection, we ob-tained the Daya Bay measured reactor antineutrino fluxwith respect to the Huber+Mueller model prediction:RDYB = 0.946±0.020(exp.). This result is consistent withthe past global average Rpastg = 0.942±0.009(exp.). If weinclude the Daya Bay result in the global fit, the newaverage is Rg = 0.943±0.008(exp.)±0.023(model). Theresults of the global fit and the Daya Bay measurementare shown in Fig. 17.

The consistency between Daya Bay’s measurementand past experiments suggests that the origin of the “re-actor antineutrino anomaly” is from the theoretical side.Either the uncertainties of the theoretical models thatpredict the reactor antineutrino flux are underestimatedor more intriguingly, there exists an additional neutrinooscillation that suppresses the reactor antineutrino fluxwithin a few meters from the reactor. Such an oscillationwould imply the existence of one or more eV-mass-scalesterile neutrinos. To investigate this tantalizing possibil-ity, future short baseline (10 m) experiments are requiredto observe the L/E dependence of such an oscillation.

Distance (m)10 210 310

Dat

a / P

red

icti

on

0.6

0.8

1.0

1.2

Previou

improved measurement of the reactor antineutrino flux and ...33charles university, faculty of...

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