New Measurement of Antineutrino Oscillation with
the Full Detector Configuration at Daya Bay
F. P. An,1A. B. Balantekin,2H. R. Band,3M. Bishai,4S. Blyth,5,6I. Butorov,7G. F. Cao,8J. Cao,8W. R. Cen,8Y. L. Chan,9 J. F. Chang,8L. C. Chang,10Y. Chang,6H. S. Chen,8Q. Y. Chen,11S. M. Chen,12Y. X. Chen,13Y. Chen,14J. H. Cheng,10
J. Cheng,11Y. P. Cheng,8 J. J. Cherwinka,2 M. C. Chu,9 J. P. Cummings,15J. de Arcos,16Z. Y. Deng,8 X. F. Ding,8 Y. Y. Ding,8 M. V. Diwan,4 E. Draeger,16D. A. Dwyer,17 W. R. Edwards,27,17 S. R. Ely,18R. Gill,4 M. Gonchar,7 G. H. Gong,12H. Gong,12M. Grassi,8 W. Q. Gu,19M. Y. Guan,8 L. Guo,12X. H. Guo,20R. W. Hackenburg,4 R. Han,13 S. Hans,4M. He,8K. M. Heeger,3Y. K. Heng,8A. Higuera,21Y. K. Hor,22Y. B. Hsiung,5B. Z. Hu,5L. M. Hu,4L. J. Hu,20 T. Hu,8W. Hu,8E. C. Huang,18H. X. Huang,23X. T. Huang,11P. Huber,22G. Hussain,12D. E. Jaffe,4P. Jaffke,22K. L. Jen,10 S. Jetter,8 X. P. Ji,24,12X. L. Ji,8 J. B. Jiao,11R. A. Johnson,25L. Kang,26S. H. Kettell,4M. Kramer,17,27 K. K. Kwan,9 M. W. Kwok,9 T. Kwok,28T. J. Langford,3K. Lau,21L. Lebanowski,12J. Lee,17R. T. Lei,26R. Leitner,29K. Y. Leung,28 J. K. C. Leung,28C. A. Lewis,2D. J. Li,30F. Li,8G. S. Li,19Q. J. Li,8S. C. Li,28W. D. Li,8X. N. Li,8X. Q. Li,24Y. F. Li,8
Z. B. Li,31H. Liang,30C. J. Lin,17G. L. Lin,10 P. Y. Lin,10S. K. Lin,21J. J. Ling,4,18J. M. Link,22L. Littenberg,4 B. R. Littlejohn,25,16D. W. Liu,21H. Liu,21J. L. Liu,19J. C. Liu,8S. S. Liu,28C. Lu,32H. Q. Lu,8J. S. Lu,8K. B. Luk,27,17
Q. M. Ma,8 X. Y. Ma,8 X. B. Ma,13Y. Q. Ma,8 D. A. Martinez Caicedo,16K. T. McDonald,32R. D. McKeown,33,34 Y. Meng,22I. Mitchell,21J. Monari Kebwaro,35Y. Nakajima,17J. Napolitano,36D. Naumov,7E. Naumova,7H. Y. Ngai,28 Z. Ning,8J. P. Ochoa-Ricoux,37A. Olshevski,7J. Park,22S. Patton,17V. Pec,29J. C. Peng,18L. E. Piilonen,22L. Pinsky,21 C. S. J. Pun,28F. Z. Qi,8 M. Qi,38X. Qian,4 N. Raper,39B. Ren,26 J. Ren,23R. Rosero,4 B. Roskovec,29X. C. Ruan,23 B. B. Shao,12H. Steiner,27,17G. X. Sun,8J. L. Sun,40W. Tang,4D. Taychenachev,7H. Themann,4K. V. Tsang,17C. E. Tull,17 Y. C. Tung,5N. Viaux,37 B. Viren,4 V. Vorobel,29C. H. Wang,6 M. Wang,11 N. Y. Wang,20R. G. Wang,8 W. Wang,31 W. W. Wang,38X. Wang,41Y. F. Wang,8 Z. Wang,12Z. Wang,8Z. M. Wang,8 H. Y. Wei,12L. J. Wen,8 K. Whisnant,42 C. G. White,16L. Whitehead,21T. Wise,2H. L. H. Wong,27,17 S. C. F. Wong,9,31E. Worcester,4 Q. Wu,11D. M. Xia,8,43
J. K. Xia,8 X. Xia,11Z. Z. Xing,8 J. Y. Xu,9 J. L. Xu,8 J. Xu,20Y. Xu,24T. Xue,12J. Yan,35C. G. Yang,8 L. Yang,26 M. S. Yang,8M. T. Yang,11 M. Ye,8M. Yeh,4 Y. S. Yeh,10B. L. Young,42G. Y. Yu,38 Z. Y. Yu,8 S. L. Zang,38 L. Zhan,8 C. Zhang,4 H. H. Zhang,31J. W. Zhang,8Q. M. Zhang,35Y. M. Zhang,12Y. X. Zhang,40Y. M. Zhang,31
Z. J. Zhang,26Z. Y. Zhang,8 Z. P. Zhang,30J. Zhao,8Q. W. Zhao,8 Y. F. Zhao,13Y. B. Zhao,8 L. Zheng,30 W. L. Zhong,8 L. Zhou,8 N. Zhou,30 H. L. Zhuang,8 and J. H. Zou8
(Daya Bay Collaboration)
1Institute of Modern Physics, East China University of Science and Technology, Shanghai 2
University of Wisconsin, Madison, Wisconsin, USA
3Department of Physics, Yale University, New Haven, Connecticut, USA 4
Brookhaven National Laboratory, Upton, New York, USA 5Department of Physics, National Taiwan University, Taipei
6
National United University, Miao-Li
7Joint Institute for Nuclear Research, Dubna, Moscow Region 8
Institute of High Energy Physics, Beijing 9Chinese University of Hong Kong, Hong Kong 10
Institute of Physics, National Chiao-Tung University, Hsinchu 11Shandong University, Jinan
12
Department of Engineering Physics, Tsinghua University, Beijing 13North China Electric Power University, Beijing
14
Shenzhen University, Shenzhen 15Siena College, Loudonville, New York, USA 16
Department of Physics, Illinois Institute of Technology, Chicago, Illinois, USA 17Lawrence Berkeley National Laboratory, Berkeley, California, USA 18
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA 19Shanghai Jiao Tong University, Shanghai
20
Beijing Normal University, Beijing
21Department of Physics, University of Houston, Houston, Texas, USA 22
Center for Neutrino Physics, Virginia Tech, Blacksburg, Virginia, USA 23China Institute of Atomic Energy, Beijing
24School of Physics, Nankai University, Tianjin 25
Department of Physics, University of Cincinnati, Cincinnati, Ohio, USA 26Dongguan University of Technology, Dongguan
27
Department of Physics, University of California, Berkeley, California, USA 28Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong 29
Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 30University of Science and Technology of China, Hefei
31
Sun Yat-Sen (Zhongshan) University, Guangzhou
32Joseph Henry Laboratories, Princeton University, Princeton, New Jersey, USA 33
California Institute of Technology, Pasadena, California, USA 34College of William and Mary, Williamsburg, Virginia, USA
35
Xi’an Jiaotong University, Xi’an
36Department of Physics, College of Science and Technology, Temple University, Philadelphia, Pennsylvania, USA 37
Instituto de Física, Pontificia Universidad Católica de Chile, Santiago, Chile 38Nanjing University, Nanjing
39
Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York, USA 40China General Nuclear Power Group
41
College of Electronic Science and Engineering, National University of Defense Technology, Changsha 42Iowa State University, Ames, Iowa, USA
43
Chongqing University, Chongqing
(Received 13 May 2015; published 11 September 2015)
We report a new measurement of electron antineutrino disappearance using the fully constructed Daya Bay Reactor Neutrino Experiment. The final two of eight antineutrino detectors were installed in the summer of 2012. Including the 404 days of data collected from October 2012 to November 2013 resulted in a total exposure of6.9 × 105GWthton days, a 3.6 times increase over our previous results. Improvements in energy calibration limited variations between detectors to 0.2%. Removal of six241Am-13C radioactive calibration sources reduced the background by a factor of 2 for the detectors in the experimental hall furthest from the reactors. Direct prediction of the antineutrino signal in the far detectors based on the measurements in the near detectors explicitly minimized the dependence of the measurement on models of reactor antineutrino emission. The uncertainties in our estimates of sin22θ13andjΔm2eej were halved as a result of these improvements. An analysis of the relative antineutrino rates and energy spectra between detectors gave sin22θ13¼ 0.084 0.005 and jΔm2eej ¼ ð2.42 0.11Þ × 10−3 eV2 in the three-neutrino framework.
DOI:10.1103/PhysRevLett.115.111802 PACS numbers: 14.60.Pq, 13.15.+g, 28.50.Hw, 29.40.Mc
Neutrino flavor oscillation due to the mixing angleθ13 has been observed using reactor antineutrinos [1–3] and accelerator neutrinos [4,5]. The Daya Bay experiment previously reported the discovery of a nonzero value of sin22θ13 by observing the disappearance of reactor anti-neutrinos over kilometer distances [1,6,7], and the first measurement of the effective mass splittingjΔm2eej[8]via the distortion of the ¯νe energy spectrum [9]. Here, we present new results with significant improvements in energy calibration and background reduction. Installation of the final two detectors and a tripling of operation time provided a total exposure of6.9 × 105GWth ton days, 3.6
times more than reported in our previous publication [9]. With these improvements the precision of sin22θ13 was enhanced by a factor of 2 compared to the world’s previous best estimate. The precision of jΔm2eej was equally enhanced, and is now competitive with the precision of jΔm2
32j measured via the accelerator neutrino
disappear-ance[10,11].
The Daya Bay experiment started collecting data on 24 December 2011 with six antineutrino detectors (ADs) located in three underground experimental halls (EHs). Three ADs were positioned in two near halls at short distances from six nuclear reactor cores, two ADs in EH1 and one in EH2, and three ADs were positioned in the far hall, EH3. Data taking was paused on 28 July 2012 while two new ADs were installed, one in EH2 and the other in EH3. During the installation, a broad set of calibration sources were deployed into the two ADs of EH1 using automated calibration units[12] and a manual calibration system[13]. Operation of the full experiment with all eight ADs started on 19 October 2012. This Letter presents results based on 404 days of data acquired in the 8-AD period combined with all 217 days of data acquired in the 6-AD period. A blind analysis strategy was implemented by concealing the baselines and target masses of the two new ADs, as well as the operational data of all reactor cores for the new data period.
Each of the three Daya Bay experimental halls hosts functionally identical ADs inside a muon detector system. The latter consists of a two-zone pure water Cherenkov detector, referred to as the inner and outer water shields, covered on top by an array of resistive plate chambers. Each AD consists of three nested cylindrical vessels. The inner vessel is filled with 0.1% gadolinium-doped liquid scin-tillator (Gd-LS), which constitutes the primary antineutrino target. The vessel surrounding the target is filled with undoped LS, increasing the efficiency of detecting gamma rays produced in the target. The outermost vessel is filled with mineral oil. A total of 192 20-cm photomultiplier tubes (PMTs) are radially positioned in the mineral-oil region of each AD. Further details on the experimental setup are contained in Refs.[14–17]. Reactor antineutrinos are detected via the inverse β-decay (IBD) reaction, ¯νeþ p → eþþ n. The gamma rays (totalling ∼8 MeV)
generated from the neutron capture on Gd with a mean capture time of ∼30 μs form a delayed signal and enable powerful background suppression. The light from the eþ gives an estimate of the incident ¯νe energy, E¯νe≈ Epþ
¯Enþ 0.78 MeV, where Epis the prompt energy including
the positron kinetic and annihilation energy, and ¯Enis the
average neutron recoil energy (∼10 keV).
Differences in energy responses between detectors directly impacted the estimation of jΔm2eej. PMT gains were calibrated continuously using uncorrelated single electrons emitted by the photocathode. The signals of 0.3% of the PMTs were discarded due to abnormal hit rates or charge distributions. The detector energy scale was calibrated using Am-C neutron sources[18]deployed at the detector center, with the ∼8 MeV peaks from neutrons captured on Gd aligned across all eight detectors. The time variation and the position dependence of the energy scale was corrected using the 2.506 MeV gamma-ray peak from
60Co calibration sources. The reconstructed energies of
various calibration reference points in different ADs are compared in Fig. 1. The spatial distribution of each calibration reference varies, incorporating deviations in spatial response between detectors. Figure 1 presents measurements of68Ge,60Co, and Am-C calibration sources when placed at the center of each detector. Neutrons from IBD and muon spallation that were captured on gadolin-ium, were distributed nearly uniformly throughout the Gd-LS region. Those neutrons that were captured on 1H, intrinsicα particles from polonium and radon decays, and gammas from40K and208Tl decays, were distributed inside and outside of the target volume. All of these events were selected within the Gd-LS region based on their recon-structed vertices. The uncorrelated relative uncertainty of the energy scale is thus determined to be 0.2%. This reduction of 43% compared to the previous publication [9] was enabled by improvements in the correction of position and time dependence, and enhanced the precision of jΔm2 j by 9%. The reduction was confirmed by an
alternative method which used the n-Gd capture of muon-induced spallation neutrons to calibrate the scale, time dependence, and spatial dependence of the detector energy response.
Nonlinearity in the energy response of an AD originated from two dominant sources: particle-dependent nonlinear light yield of the scintillator and charge-dependent non-linearity in the PMT readout electronics. Each effect was at the level of 10%. We constructed a semiempirical model that predicted the reconstructed energy for a particle assuming a specific energy deposited in the scintillator. The model contained four parameters: Birks’ constant, the relative contribution to the total light yield from Cherenkov radiation, and the amplitude and scale of an exponential correction describing the nonlinear electronics response. This exponential form of the electronics response was motivated by MC and confirmed with an independent FADC measurement.
The nominal parameter values were obtained from an unconstrained χ2 fit to various AD calibration data sets, comprising twelve gamma lines from both deployed and naturally occurring sources as well as the continuous β-decay spectrum of 12B produced by muon spallation
inside the Gd-LS volumes. The nominal positron response derived from the best fit parameters is shown in Fig.2. The depicted uncertainty band represents other response func-tions consistent with the fitted calibration data within a
Reconstructed Energy [MeV]
0.5 1 1.5 2 2.5 3 7.5 8 1 1.5 2 2.5 3 7.5 8 8.5 0 -1 -2 1 2 0 -1 -2 1 2 0 -1 -2 1 2 0 -1 -2 1 2 AD 1 AD 2 AD 3 AD 8 AD 4 AD 5 AD 6 AD 7
Gamma from natural radioactivity Alpha from natural radioactivity Gamma from calibration source Neutron from muon spallation
Neutron from IBD Neutron from Am-C source
FIG. 1 (color online). Comparison of the reconstructed energy between antineutrino detectors for a variety of calibration references. EAD is the reconstructed energy determined using each AD, andhEi is the eight-detector average. Error bars are statistical only, and systematic variations between detectors for all calibration references were < 0.2%. The ∼8 MeV n-Gd capture gamma peaks from Am-C sources were used to define the energy scale of each detector, and hence show zero deviation.
68.3% C.L. This χ2-based approach to obtain the energy response resulted in < 1% uncertainties of the absolute energy scale above 2 MeV. The uncertainties of the positron response were validated using the 53-MeV cutoff in the Michel electron spectrum from muon decay at rest and the continuousβ þ γ spectra from natural bismuth and thallium decays. These improvements added confidence in the characterization of the absolute energy response of the detectors, although they resulted in negligible changes to the measured mixing parameters.
IBD candidates were selected using the same criteria discussed in Ref. [1]. Noise introduced by PMT light emission in the voltage divider, called flashing, was efficiently removed using the techniques of Ref. [6]. We required 0.7 MeV < Ep< 12.0 MeV, 6.0 MeV < Ed<
12.0 MeV, and 1 μs< Δt < 200 μs , where Ed is the
delayed energy and Δt ¼ td− tp was the time difference between the prompt and delayed signals. In order to suppress cosmogenic products, candidates were rejected if their delayed signal occurred (i) within a (−2 μs, 600 μs) time window with respect to an inner water shield or outer water shield trigger with a PMT multiplicity > 12, (ii) within a (−2 μs, 1000 μs) time window with respect to triggers in the same AD with reconstructed energy > 20 MeV, or (iii) within a (−2 μs, 1 s) time window with respect to triggers in the same AD with reconstructed energy > 2.5 GeV. To select only definite signal pairs, we required the signal to have a multiplicity of 2: no other > 0.7 MeV signal occurred within a (tp− 200 μs; tdþ
200 μs) time window.
Estimates for the five major sources of background for the new data sample are improved with respect to Ref.[9]. The background produced by the three Am-C neutron sources inside the automated calibration units contributed significantly to the total systematic uncertainty of the correlated backgrounds in the 6-AD period. Because of this, two of the three Am-C sources in each AD in EH3 were removed during the 2012 summer installation period. As a result, the average correlated Am-C background rate in the far hall decreased by a factor of 4 in the 8-AD period. As in previous publications[1,9], this rate was determined by monitoring the single-neutron production rate from the Am-C sources. Removal of these Am-C sources had negligible consequences for our calibration.
Energetic, or fast, neutrons of cosmogenic origin pro-duced a correlated background for this study. Relaxing the prompt-energy selection to (0.7–100) MeV revealed the fast-neutron background spectrum above 12 MeV. Previously we deduced the rate and spectrum of this background using a linear extrapolation into the IBD prompt signal region. Here we used a background-enhanced data set to improve the estimate. We found 6043 fast-neutron candidates with prompt energy from 0.7 to 100 MeV in the 200 μs following cosmogenic signals only detected by the outer water shield or resistive plate chambers. The energy spectrum of these veto-tagged signals was consistent with the spectrum of IBD-like candidate signals above 12 MeV, and was used to estimate the rate and energy spectrum for the fast-neutron back-ground from 0.7 to 12 MeV. The systematic uncertainty was estimated from the difference between this new analysis and the extrapolation method previously employed, and was determined to be half of the estimate reported in Ref.[6].
The methods used in Refs. [1,6] to estimate the back-grounds from the uncorrelated prompt-delayed pairs (i.e., accidentals), the correlatedβ − n decays from cosmogenic
9Li and8He, and the13Cðα; nÞ16O reaction, were extended
to the current6 þ 8 AD data sample. The decrease in the single-neutron rate from the Am-C sources reduced the average rate of accidentals in the far hall by a factor of 2.7. As a result, the total backgrounds amount to about 3% (2%) of the IBD candidate sample in the far (near) hall(s). The systematic uncertainties in the13Cðα; nÞ16O cross section and in the transportation of theα particles were reassessed through a comparison of experimental results and simu-lation packages, respectively [19]. The estimation of
9Li=8He now dominated the background uncertainty in
both the near and far halls. The estimated signal and background rates, as well as the efficiencies of the muon veto,ϵμ, and multiplicity selection, ϵm, are summarized in TableI.
A detailed treatment of the absolute and relative efficiencies using the first six ADs was reported in Refs.[6,14]. The uncertainties of the absolute efficiencies
0 2 4 6 8 10
0.9 0.94 1 1.04
Reconstructed Energy / True Energy
True Positron Energy [MeV] 0.92 0.96 0.98 1.02 Nominal response + 68.3% C.L. Cross-validation
FIG. 2 (color online). Estimated energy response of the detectors to positrons, including both kinetic and annihilation gamma energy (red solid curve). The prominent nonlinearity below 4 MeV was attributed to scintillator light yield (from ionization quenching and Cherenkov light production) and the charge response of the electronics. Gamma rays from both deployed and intrinsic sources as well as spallation12Bβ decay determined the model, and provided an envelope of curves consistent with the data within a 68.3% C.L. (grey band). An independent estimate using the beta+gamma energy spectra from 212Bi, 214Bi, 208Tl, as well as the 53-MeV edge in the Michel electron spectrum gave a similar result (blue dashed line), albeit with larger systematic uncertainties.
are correlated among the ADs and thus play a negligible role in the relative measurement of ¯νe disappearance. The performance of the two new ADs was found to be consistent with the other detectors. Estimates of two prominent uncorrelated uncertainties, the delayed-energy selection efficiency and the fraction of neutrons captured on Gd, were confirmed for all eight ADs using improved energy reconstruction and increased statistics.
Oscillation was measured using the L=E-dependent disappearance of ¯νe, as given by the survival probability
P ¼ 1 − cos4θ13sin22θ12sin21.267Δm 2 21L E − sin22θ 13sin21.267Δm 2 eeL E : ð1Þ
Here E is the energy in MeV of the ¯νe, L is the distance in
meters from its production point, θ12 is the solar mixing angle, andΔm221¼ m22− m21is the mass-squared difference of the first two neutrino mass eigenstates in eV2.
Recent precise measurements of the IBD positron energy spectrum disagree with models of reactor ¯νe emission [3,20–22]. The characteristics of the signals in this energy range are consistent with reactor antineutrino emission, and disfavor background or detector response as possible origins for the discrepancy. Reference [20] presents the evidence in detail and provide the necessary data to allow detailed comparison of our measurement with existing and future models. Given these discrepancies between
measurements and models, here we present a technique for predicting the signal in the far hall based on measure-ments obtained in the near halls, with minimal dependence on models of the reactor antineutrinos. In our previous measurements [9], model dependence was limited by allowing variation of the predicted ¯νe flux within model uncertainties, while the technique here provides an explicit demonstration of the negligible model dependence. A χ2 was defined as χ2¼X i;j ðNf j− wjNnjÞðV−1ÞijðN f i − wiNniÞ; ð2Þ
where Ni is the observed number of events after
back-ground subtraction in the ith bin of reconstructed positron energy Erec. The superscript fðnÞ denotes a far (near)
detector. The symbol V represents a covariance matrix that includes known systematic and statistical uncertainties. The quantity wi is a weight that accounts for the differences
between near and far measurements. For the case of a single reactor, the weight wi can be simply calculated from the
ratios of detector mass, distance to the reactor, efficiency, and antineutrino oscillation probability, as given by the relation: wSR i ¼ Nfi Nn i ¼ Tf Tn ϵf ϵn Ln Lf 2 Pfi Pn i ϕ ϕ : ð3Þ
Here T is the number of target protons, ϵ is the efficiency, and L is the distance to the reactor for a given detector. P is
TABLE I. Summary of signal and backgrounds. Rates are corrected for the muon veto and multiplicity selection efficienciesεμ·εm. The measured ratio of the IBD rates in AD1 and AD2 (AD3 and AD8 in the 8-AD period) was0.981 0.004 (1.019 0.004) while the expected ratio was 0.982 (1.012).
EH1 EH2 EH3
AD1 AD2 AD3 AD8 AD4 AD5 AD6 AD7
IBD candidates 304 459 309 354 287 098 190 046 40 956 41 203 40 677 27 419
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 0.01 Fast 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 0.14
Am-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 0.09 Am-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 13Cðα; nÞ16O (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 0.03 IBD 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
the oscillation probability for the ith reconstructed energy bin andϕ the reactor antineutrino flux (which cancels from wi). With Pi calculated in reconstructed positron energy,
the detector response introduces small (< 0.2% above 2 MeV) calculable deviations from Eq.(1).
For multiple reactor cores, the weight wiwas modified:
wi¼ Nfi Nn i ¼ Tf Tn ϵf ϵn X j PðEtrue j jEreci Þrj: ð4Þ
The probability distributionPðEtrue
j jEreci Þ accounts for the
energy transfer from the ¯νe to the eþ and imperfections in the detector energy response (loss in nonactive elements, nonlinearity, and resolution). The extrapolation factor rj
was calculated as rj¼ Pcores k PðEtruej ; L f kÞϕjk=ðLfkÞ2 Pcores k PðEtruej ; LnkÞϕjk=ðLnkÞ2 ; ð5Þ
where P is given by Eq.(1), LfðnÞk is the distance between a far (near) detector and core k, and ϕjk is the predicted
antineutrino flux from core k for the jth true energy bin. In the single-reactor core case, the antineutrino fluxϕ cancels in the expression for rj and Eq. (4) reduces to Eq. (3).
Although the cancellation is not exact for multiple cores, the impact of the uncertainty in reactor antineutrino flux was found to be ≤ 0.1%.
The covariance matrix element Vij was the sum of a
statistical term, calculated analytically, and a systematic term determined by Monte Carlo calculation using
Vij¼ 1 N XN ðSf i − wiSniÞðS f j− wjSnjÞ: ð6Þ
Here, N is the number of simulated experiments generated with energy spectra S, including systematic variations of detector response, ¯νe flux, and background. The choice of reactor antineutrino model [22–28] in calculating the covariance had negligible (< 0.2%) impact on the deter-mination of the oscillation parameters.
Without loss of sensitivity, we summed the IBD signal candidates of the ADs within the same hall, accounting for small differences of target mass, detection efficiency, background, and baseline. We considered the 6-AD and 8-AD periods separately in order to properly handle correlations in reactor antineutrino flux, detector exposure, and background. This means that i and j in the above equations ran over the 37 reconstructed energy bins for the two near versus far combinations and for the two periods considered (37 × 2 × 2 ¼ 148). More details of this method are described in Ref.[29].
Using this method, we found sin22θ13¼ 0.084 0.005 andjΔm2eej ¼ ð2.42 0.11Þ × 10−3 eV2, with χ2=NDF ¼ 134.6=146 (see the Supplemental Material[30]). While we
use sin22θ12¼ 0.857 0.024 and Δm221¼ ð7.50 0.20Þ × 10−5 eV2 from Ref. [31], our result was largely
independent of these values. Consistent results were obtained when our previous methods [1,9] were applied to this larger data set. Under the normal (inverted) hierarchy assumption, jΔm2eej yields Δm232¼ ð2.37 0.11Þ × 10−3 eV2 (Δm2
32¼ −ð2.47 0.11Þ × 10−3 eV2).
This result was consistent with and of comparable precision to measurements obtained from accelerator νμ and ¯νμ disappearance [10,11]. Using only the relative rates between the detectors andΔm232 from Ref.[10]we found sin22θ13¼ 0.085 0.006, with χ2=NDF ¼ 1.37=3.
The reconstructed positron energy spectrum observed in the far site is compared in Fig.3with the expectation based on the near-site measurements. The 68.3%, 95.5%, and 99.7% C.L. allowed regions in thejΔm2eej − sin22θ13plane are shown in Fig. 4. The spectral shape from all exper-imental halls is compared in Fig. 5 to the electron antineutrino survival probability assuming our best esti-mates of the oscillation parameters. The total uncertainties of both sin22θ13 and jΔm2eej are dominated by statistics. The most significant systematic uncertainties for sin22θ13 are due to the relative detector efficiency, reactor power, relative energy scale, and 9Li=8He background. The
Events/day (bkg. subtracted) 2 4 6 8 10 12 14 16 18
Far site data
Weighted near site data (best fit) Weighted near site data (no oscillation)
Reconstructed Positron Energy (MeV)
1 2 3 4 5 6 7 8 Far / Near(weighted) 0.85 0.9 0.95 1 1.05 1.1
FIG. 3 (color online). Upper: Background-subtracted recon-structed positron energy spectrum observed in the far site (black points), as well as the expectation derived from the near sites excluding (blue line) or including (red line) our best estimate of oscillation. The spectra were efficiency corrected and normalized to one day of live time. Lower: Ratio of the spectra to the no-oscillation case. The error bars show the statistical uncertainty of the far site data. The shaded area includes the systematic and statistical uncertainties from the near-site measurements.
systematic uncertainty in jΔm2eej is dominated by uncer-tainty in the relative energy scale.
In summary, enhanced measurements of sin22θ13 and jΔm2
eej have been obtained by studying the
energy-dependent disappearance of the electron antineutrino inter-actions recorded in a 6.9 × 105 GWth ton days exposure.
Improvements in calibration, background estimation, as
well as increased statistics allow this study to provide the most precise estimates to date of the neutrino mass and mixing parametersjΔm2eej and sin22θ13.
Daya Bay is supported in part by the Ministry of Science and Technology of China, the U.S. Department of Energy, the Chinese Academy of Sciences, the CAS Center for Excellence in Particle Physics, the National Natural Science Foundation of China, the Guangdong provincial government, the Shenzhen municipal government, the China General Nuclear Power Group, Key Laboratory of Particle and Radiation Imaging (Tsinghua University), the Ministry of Education, Key Laboratory of Particle Physics and Particle Irradiation (Shandong University), the Ministry of Education, Shanghai Laboratory for Particle Physics and Cosmology, the Research Grants Council of the Hong Kong Special Administrative Region of China, the University Development Fund of The University of Hong Kong, the MOE program for Research of Excellence at National Taiwan University, National Chiao-Tung University, and NSC fund support from Taiwan, the U.S. National Science Foundation, the Alfred P. Sloan Foundation, the Ministry of Education, Youth, and Sports of the Czech Republic, the Joint Institute of Nuclear Research in Dubna, Russia, the NSFC-RFBR joint research program, the National Commission of Scientific and Technological Research of Chile, and the Tsinghua University Initiative Scientific Research Program. We acknowledge Yellow River Engineering Consulting Co., Ltd., and China Railway 15th Bureau Group Co., Ltd., for building the underground 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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Daya Bay: 621 days
99.7% C.L. 95.5% C.L. 68.3% C.L. Best fit 2 χΔ 5 10 15 2 χ Δ 5 10 15 MINOS T2K
FIG. 4 (color online). Regions in thejΔm2eej − sin22θ13 plane allowed at the 68.3%, 95.5%, and 99.7% confidence levels by the near-far comparison of ¯νe rate and energy spectra. The best estimates were sin22θ13¼ 0.084 0.005 and jΔm2eej ¼ ð2.42 0.11Þ × 10−3eV2 (black point). The adjoining panels show the dependence ofΔχ2 on sin22θ13 (top) and jΔm2eej (right). The jΔm2
eej allowed region (shaded band, 68.3% C.L.) was consistent with measurements ofjΔm232j using muon disappearance by the MINOS [10] and T2K [11] experiments, converted to jΔm2eej assuming the normal (solid) and inverted (dashed) mass hierarchy. [km/MeV] 〉 ν E 〈 / eff L 0 0.2 0.4 0.6 0.8 )e ν → e ν P( 0.9 0.95 1 EH1 EH2 EH3 Best fit
FIG. 5 (color online). Electron antineutrino survival probability versus effective propagation distance Leffdivided by the average antineutrino energyhEνi. The data points represent the ratios of the observed antineutrino spectra to the expectation assuming no oscillation. The solid line represents the expectation using the best estimates of sin22θ13 and jΔm2eej. The error bars are statistical only. hEνi was calculated for each bin using the estimated detector response, and Leff was obtained by equating the actual flux to an effective antineutrino flux using a single baseline.
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