Observation of Electron-Antineutrino Disappearance at Daya Bay
F. P. An,1J. Z. Bai,1A. B. Balantekin,2H. R. Band,2D. Beavis,3W. Beriguete,3M. Bishai,3S. Blyth,4K. Boddy,5 R. L. Brown,3B. Cai,5G. F. Cao,1J. Cao,1R. Carr,5W. T. Chan,3J. F. Chang,1Y. Chang,4C. Chasman,3H. S. Chen,1 H. Y. Chen,6S. J. Chen,7S. M. Chen,8X. C. Chen,9X. H. Chen,1X. S. Chen,1Y. Chen,10Y. X. Chen,11J. J. Cherwinka,2 M. C. Chu,9J. P. Cummings,12Z. Y. Deng,1Y. Y. Ding,1M. V. Diwan,3L. Dong,1E. Draeger,13X. F. Du,1D. A. Dwyer,5 W. R. Edwards,14S. R. Ely,15S. D. Fang,7J. Y. Fu,1Z. W. Fu,7L. Q. Ge,16V. Ghazikhanian,17R. L. Gill,3J. Goett,18
M. Gonchar,19G. H. Gong,8H. Gong,8Y. A. Gornushkin,19L. S. Greenler,2W. Q. Gu,20M. Y. Guan,1X. H. Guo,21 R. W. Hackenburg,3R. L. Hahn,3S. Hans,3M. He,1Q. He,22W. S. He,23K. M. Heeger,2Y. K. Heng,1P. Hinrichs,2 T. H. Ho,23Y. K. Hor,24Y. B. Hsiung,23B. Z. Hu,6T. Hu,1T. Hu,21H. X. Huang,25H. Z. Huang,17P. W. Huang,7 X. Huang,26X. T. Huang,27P. Huber,24Z. Isvan,3D. E. Jaffe,3S. Jetter,1X. L. Ji,1X. P. Ji,28H. J. Jiang,16W. Q. Jiang,1 J. B. Jiao,27R. A. Johnson,29L. Kang,30S. H. Kettell,3M. Kramer,14,31K. K. Kwan,9M. W. Kwok,9T. Kwok,32C. Y. Lai,23 W. C. Lai,16W. H. Lai,6K. Lau,26L. Lebanowski,26J. Lee,14M. K. P. Lee,32R. Leitner,33J. K. C. Leung,32K. Y. Leung,32 C. A. Lewis,2B. Li,1F. Li,1G. S. Li,20J. Li,1Q. J. Li,1S. F. Li,30W. D. Li,1X. B. Li,1X. N. Li,1X. Q. Li,28Y. Li,30 Z. B. Li,34H. Liang,35J. Liang,1C. J. Lin,14G. L. Lin,6S. K. Lin,26S. X. Lin,30Y. C. Lin,16,9,32,8J. J. Ling,3J. M. Link,24 L. Littenberg,3B. R. Littlejohn,2B. J. Liu,9,1,32C. Liu,1D. W. Liu,15H. Liu,32J. C. Liu,1J. L. Liu,20S. Liu,14X. Liu,1,*
Y. B. Liu,1C. Lu,22H. Q. Lu,1A. Luk,9K. B. Luk,14,31T. Luo,1X. L. Luo,1L. H. Ma,1Q. M. Ma,1X. B. Ma,11X. Y. Ma,1 Y. Q. Ma,1B. Mayes,26K. T. McDonald,22M. C. McFarlane,2R. D. McKeown,5,36Y. Meng,24D. Mohapatra,24 J. E. Morgan,24Y. Nakajima,14J. Napolitano,18D. Naumov,19I. Nemchenok,19C. Newsom,26H. Y. Ngai,32W. K. Ngai,15
Y. B. Nie,25Z. Ning,1J. P. Ochoa-Ricoux,14D. Oh,5A. Olshevski,19A. Pagac,2S. Patton,14C. Pearson,3V. Pec,33 J. C. Peng,15L. E. Piilonen,24L. Pinsky,26C. S. J. Pun,32F. Z. Qi,1M. Qi,7X. Qian,5N. Raper,18R. Rosero,3 B. Roskovec,33X. C. Ruan,25B. Seilhan,13B. B. Shao,8K. Shih,9H. Steiner,14,31P. Stoler,18G. X. Sun,1J. L. Sun,37
Y. H. Tam,9H. K. Tanaka,3X. Tang,1H. Themann,3Y. Torun,13S. Trentalange,17O. Tsai,17K. V. Tsang,14 R. H. M. Tsang,5C. Tull,14B. Viren,3S. Virostek,14V. Vorobel,33C. H. Wang,4L. S. Wang,1L. Y. Wang,1L. Z. Wang,11 M. Wang,27,1N. Y. Wang,21R. G. Wang,1T. Wang,1W. Wang,36,5X. Wang,8X. Wang,1Y. F. Wang,1Z. Wang,8,3Z. Wang,1 Z. M. Wang,1D. M. Webber,2Y. D. Wei,30L. J. Wen,1D. L. Wenman,2K. Whisnant,38C. G. White,13L. Whitehead,26
C. A. Whitten, Jr.,17,*J. Wilhelmi,18T. Wise,2H. C. Wong,32H. L. H. Wong,31J. Wong,9E. T. Worcester,3F. F. Wu,5 Q. Wu,27,13D. M. Xia,1S. T. Xiang,35Q. Xiao,2Z. Z. Xing,1G. Xu,26J. Xu,9J. Xu,21J. L. Xu,1W. Xu,17Y. Xu,28T. Xue,8 C. G. Yang,1L. Yang,30M. Ye,1M. Yeh,3Y. S. Yeh,6K. Yip,3B. L. Young,38Z. Y. Yu,1L. Zhan,1C. Zhang,3F. H. Zhang,1
J. W. Zhang,1Q. M. Zhang,1K. Zhang,3Q. X. Zhang,16S. H. Zhang,1Y. C. Zhang,35Y. H. Zhang,1Y. X. Zhang,37 Z. J. Zhang,30Z. P. Zhang,35Z. Y. Zhang,1J. Zhao,1Q. W. Zhao,1Y. B. Zhao,1L. Zheng,35W. L. Zhong,14L. Zhou,1
Z. Y. Zhou,25H. L. Zhuang,1and J. H. Zou1 1
Institute of High Energy Physics, Beijing
2University of Wisconsin, Madison, Wisconsin, USA 3Brookhaven National Laboratory, Upton, New York, USA
4National United University, Miao-Li
5California Institute of Technology, Pasadena, California, USA 6Institute of Physics, National Chiao-Tung University, Hsinchu
7Nanjing University, Nanjing
8Department of Engineering Physics, Tsinghua University, Beijing 9Chinese University of Hong Kong, Hong Kong
10Shenzhen Univeristy, Shen Zhen 11North China Electric Power University, Beijing
12Siena College, Loudonville, New York, USA
13Department of Physics, Illinois Institute of Technology, Chicago, Illinois, USA 14Lawrence Berkeley National Laboratory, Berkeley, California, USA
15Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA 16Chengdu University of Technology, Chengdu
17
University of California, Los Angeles, California, USA
18Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York, USA 19Joint Institute for Nuclear Research, Dubna, Moscow Region
20Shanghai Jiao Tong University, Shanghai 21Beijing Normal University, Beijing
23Department of Physics, National Taiwan University, Taipei 24Center for Neutrino Physics, Virginia Tech, Blacksburg, Virginia, USA
25China Institute of Atomic Energy, Beijing
26Department of Physics, University of Houston, Houston, Texas, USA 27Shandong University, Jinan
28School of Physics, Nankai University, Tianjin
29Department of Physics, University of Cincinnati, Cincinnati, Ohio, USA 30Dongguan Institute of Technology, Dongguan
31
Department of Physics, University of California, Berkeley, California, USA
32Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong 33Charles University, Faculty of Mathematics and Physics, Prague
34Sun Yat-Sen (Zhongshan) University, Guangzhou 35University of Science and Technology of China, Hefei 36College of William and Mary, Williamsburg, Virginia, USA
37China Guangdong Nuclear Power Group, Shenzhen 38Iowa State University, Ames, Iowa, USA
(Received 7 March 2012; published 23 April 2012)
The Daya Bay Reactor Neutrino Experiment has measured a nonzero value for the neutrino mixing angle 13with a significance of 5.2 standard deviations. Antineutrinos from six 2.9 GWthreactors were
detected in six antineutrino detectors deployed in two near (flux-weighted baseline 470 m and 576 m) and one far (1648 m) underground experimental halls. With a 43 000 ton–GWth–day live-time exposure
in 55 days, 10 416 (80 376) electron-antineutrino candidates were detected at the far hall (near halls). The ratio of the observed to expected number of antineutrinos at the far hall is R ¼ 0:940 0:011ðstat:Þ 0:004ðsyst:Þ. A rate-only analysis finds sin2213¼ 0:092 0:016ðstat:Þ 0:005ðsyst:Þ in
a three-neutrino framework.
DOI:10.1103/PhysRevLett.108.171803 PACS numbers: 14.60.Pq
It is well established that the flavor of a neutrino oscil-lates with time. Neutrino oscillations can be described by the three mixing angles (12, 23, and 13) and a phase of the Pontecorvo-Maki-Nakagawa-Sakata matrix, and two mass-squared differences (m2
32and m221) [1,2]. Of these mixing angles, 13 is the least known. The CHOOZ neu-trino oscillation experiment obtained a 90%-confidence-level upper limit of 0.17 for sin22
13[3]. Recently, results from T2K (Tokai to Kamioka, Japan) [4], MINOS (Main Injector Neutrino Oscillation Search) [5], and Double Chooz [6] experiments have indicated that 13 could be nonzero. In this Letter, we present the observation of a nonzero value for 13.
For reactor-based experiments, an unambiguous deter-mination of 13can be extracted via the survival probabil-ity of the electron-antineutrino e at short distances from the reactors,
Psur 1 sin2213sin2ð1:267m231L=EÞ; (1) where m231¼ m232 m221, E is the e energy in MeV and L is the distance in meters between the esource and the detector (baseline).
The near-far arrangement of antineutrino detectors (ADs), as illustrated in Fig. 1, allows for a relative mea-surement by comparing the observed e rates at various baselines. With functionally identical ADs, the relative rate is independent of correlated uncertainties and uncorrelated reactor uncertainties are minimized.
A detailed description of the Daya Bay experiment can be found in Refs. [7,8]. Here, only the apparatus relevant to this analysis will be highlighted. The six pressurized water reactors are grouped into three pairs with each pair referred to as a nuclear power plant (NPP). The maximum thermal power of each reactor is 2.9 GW. Three underground experimental halls (EHs) are connected with horizontal tunnels. Two ADs are located in EH1 and one in EH2 (the near halls). Three ADs are positioned near the oscil-lation maximum in the far hall, EH3. The vertical over-burden in equivalent meters of water (m.w.e.), the
FIG. 1 (color online). Layout of the Daya Bay experiment. The dots represent reactors, labeled as D1, D2, L1, L2, L3, and L4. Six ADs, AD1–AD6, are installed in three EHs.
simulated muon rate and average muon energy, and aver-age distance to the reactor pairs are listed in TableI.
As shown in Fig. 2, the ADs in each EH are shielded with >2:5 m of high-purity water against ambient radia-tion in all direcradia-tions. Each water pool is segmented into inner and outer water shields (IWS and OWS) and instru-mented with photomultiplier tubes (PMTs) to function as Cherenkov-radiation detectors whose data were used by offline software to remove spallation neutrons and other cosmogenic backgrounds. The detection efficiency for long-track muons is >99:7% [7]. The water pool is covered with an array of resistive plate chambers (RPC).
The e is detected via the inverse -decay (IBD) reac-tion, eþ p ! eþþ n, in a gadolinium-doped liquid scin-tillator (Gd-LS) [9,10]. The coincidence of the prompt scintillation from the eþ and the delayed neutron capture on Gd provides a distinctive esignature.
Each AD consists of a cylindrical, 5 m diameter stainless steel vessel (SSV) that houses two nested, UV-transparent acrylic cylindrical vessels. A 3.1 m diameter inner acrylic vessel (IAV) holds 20 t of Gd-LS (target). It is surrounded by a region with 20 t of liquid scintillator (LS) inside a 4 m diameter outer acrylic vessel (OAV). Between the SSV and OAV, 37 t of mineral oil (MO) shields the LS and Gd-LS from radioactivity. IBD interactions are detected by 192 Hamamatsu R5912 PMTs. A black radial shield and spec-ular reflectors are installed on the vertical detector walls and above and below the LS volume, respectively. Gd-LS and LS are prepared and filled into ADs systematically to ensure all ADs are functionally identical [7]. Three auto-mated calibration units (ACUs) mounted on the SSV lid allow for remote deployment of a light-emitting diode, a 68Ge source, and a combined source of241Am 13C and 60Co into the Gd-LS and LS liquid volumes along three vertical axes.
The results are based on data taken from 24 December 2011 to 17 February 2012. A blind analysis strategy was adopted, with the baselines, the thermal-power histories of the cores, and the target masses of the ADs hidden until the analyses were frozen. Triggers were formed from the number of PMTs with signals above a0:25 photoelectron (pe) threshold (NHIT) or the charge sum of the over-threshold PMTs (ESUM). The AD triggers were NHIT > 45 or ESUM * 65 pe. The trigger rate per AD was <280 Hz with a negligible trigger inefficiency for IBD candidates. The data consist of charge and timing
information for each PMT, and were accumulated independently for each detector. To remove systematic effects due to reactor flux fluctuations, only data sets with all detectors in operation were used.
The energy of each trigger in an AD was reconstructed based on the total photoelectrons collected by the PMTs. The energy calibration constant, 163 pe=MeV for all ADs and stable throughout the data collection period, was determined by setting the energy peak of the 60Co source deployed at each AD center to 2.506 MeV. Vertex reconstruction was based on center-of-charge, defined as the charge-weighted-mean of the coordinates of all PMTs. The mapping from center-of-charge to vertex was done by analytic corrections determined using data collected with 60Co sources deployed at various points within the AD. A vertex-dependent correction to energy (< 10%) and a con-stant factor (0.988) were applied equally to all ADs to correct for geometrical effects and energy nonlinearity between the 60Co and the neutron capture on Gd (nGd), determined by the60Co and Am-C sources at the detector center. An independent energy calibration that utilized the peak of the nGd from spallation neutron to set the energy scale and templates derived from Monte Carlo simulations (MC) for vertex reconstruction, gave consistent perform-ance [7]. The energy resolution was (7:5=pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEðMeVÞþ 0:9Þ% for all 6 ADs.
IWS and OWS triggers with NHIT > 12 were classified as ‘‘WS muon candidates’’ or WS. Events in an AD within 2 s of a WS with energy >20 MeV and >2:5 GeV were classified as muons (AD) and showering muons (sh), respectively, for vetoing purposes. An instrumental background due to spontaneous light emission from a PMT, denoted as a flasher, was rejected efficiently [7].
IBD events were selected with the following criteria: 0:7 < Ep< 12:0 MeV, 6:0 < Ed< 12:0 MeV, 1 < t < 200 s, the prompt-delayed pair was vetoed by preceding
TABLE I. Vertical overburden (m.w.e.), muon rate RðHz=m2Þ, and average muon energy E ðGeVÞ of the three
EHs, and the distances (m) to the reactor pairs.
Overburden R E D1,2 L1,2 L3,4
EH1 250 1.27 57 364 857 1307
EH2 265 0.95 58 1348 480 528
EH3 860 0.056 137 1912 1540 1548 FIG. 2 (color online). Schematic diagram of the Daya Bay
muons if td tWS< 600 s, td tAD< 1000 s, or
td tsh< 1 s, and a multiplicity cut that requires no additional >0:7 MeV trigger in the time range (tp 200 s, tdþ 200 s), where Ep (Ed) is the prompt (de-layed) energy and t ¼ td tp is the time difference between the prompt and delayed signals. Statistically con-sistent performance was achieved by an independent analy-sis that used different energy reconstruction, muon veto, and multiplicity cuts.
The inefficiency of the muon veto for selecting IBD eventsð1 Þ was calculated by integrating the vetoed time of each muon with temporal overlaps taken into account. Inefficiency due to the multiplicity selection ð1 mÞ was calculated by considering the probability that a random signal occurred near an IBD in time. The average values of mare given for each AD in TableII. We considered the following kinds of background: ac-cidental correlation of two unrelated signals, -n decay of 9Li–8He produced by muons in the ADs, fast-neutron backgrounds produced by muons outside the ADs, 13Cð; nÞ16O interactions, and correlated events due to the retracted Am-C neutron source in the ACUs. The estimated background rates per AD are summarized in TableII.
The accidental background was determined by measur-ing the rate of both prompt- and delayed-type signals, and then estimating the probability that two signals randomly satisfied the t required for IBD selection. Additional estimates using prompt and delayed candidates separated by more than 1 ms or 2 m provided consistent results. The uncertainty in the measured accidental rate was dominated by the statistical uncertainty in the rate of delayed candidates.
The rate of correlated background from the -n cascade of9Li–8He decays was evaluated from the distribution of the time since the last muon using the known decay times for these isotopes [11]. The9Li–8He background rate as a function of the muon energy deposited in the AD was
estimated by preparing samples with and without detected neutrons 10 s to 200 s after the muon. A 50% system-atic uncertainty was assigned to account for the extrapola-tion to zero deposited muon energy.
An energetic neutron entering an AD can form a fast-neutron background by recoiling off a proton before being captured on Gd. By relaxing the Ep< 12 MeV criterion in the IBD selection, a flat distribution in Epwas observed up to 100 MeV. Extrapolation into the IBD energy region gave an estimate for the residual fast-neutron background. A similar flat Epdistribution was found in the muon-tagged fast-neutron sample produced by inverting the muon veto cut. Consistent results were obtained by scaling the muon-tagged fast-neutron rate with muon inefficiency, and by MC.
The 13Cð; nÞ16O background was determined using MC after estimating the amount of 238U, 232Th, 227Ac, and210Po in the Gd-LS from their cascade decays, or by fitting their -particle energy peaks in the data.
A neutron emitted from the 0.5 Hz Am-C neutron source in an ACU could generate a -ray via inelastic scattering in the SSV before subsequently being captured on Fe–Cr–Mn–Ni. An IBD was mimicked if both rays from the scattering and capture processes entered the scin-tillating region. This correlated background was estimated using MC. The normalization was constrained by the mea-sured rate of single delayed-type candidates from this source.
TableIIIis a summary of the absolute efficiencies and the systematic uncertainties. The uncertainties of the ab-solute efficiencies are correlated among the ADs. No rela-tive efficiency, except m, was corrected. All differences between the functionally identical ADs were taken as uncorrelated uncertainties.
The spill-in enhancement resulted when neutrons from IBD outside the target drift into the target, and was eval-uated using MC. The spillout deficit ( 2:2%) was in-cluded in the absolute Gd capture ratio. The Gd capture
TABLE II. Signal and background summary. The background and IBD rates were corrected for the m efficiency. The
no-oscillation predictions based on reactor flux analyses and detector simulation have been corrected with the best-fit normalization parameter in determining sin22
13.
AD1 AD2 AD3 AD4 AD5 AD6
IBD candidates 28 935 28 975 22 466 3528 3436 3452
No-oscillation prediction for IBD 28 647 29 096 22 335 3566.5 3573.0 3535.9
Data acquisition live time (days) 49.5530 49.4971 48.9473
Muon veto time (days) 8.7418 8.9109 7.0389 0.8785 0.8800 0.8952
m 0.8019 0.7989 0.8363 0.9547 0.9543 0.9538
Accidental signals (per day) 9:82 0:06 9:88 0:06 7:67 0:05 3:29 0:03 3:33 0:03 3:12 0:03 Fast-neutron (per day) 0:84 0:28 0:84 0:28 0:74 0:44 0:04 0:04 0:04 0:04 0:04 0:04
9Li–8He (per AD per day) 3:1 1:6 1:8 1:1 0:16 0:11
Am-C correlated (per AD per day) 0:2 0:2
13Cð; nÞ16O background (per day) 0:04 0:02 0:04 0:02 0:035 0:02 0:03 0:02 0:03 0:02 0:03 0:02
ratio was studied using Am-C neutron data and MC at the detector center and the spallation neutron data and was determined using IBD MC. Efficiencies associated with the delayed-energy, the prompt-energy, and the capture-time cuts were evaluated with MC. Discussion of the uncertain-ties in the number of target protons, live time, and the efficiency of the flasher cut can be found in Ref. [7].
Uncorrelated relative uncertainties have been addressed in detail by performing a side-by-side comparison of two ADs [7]. The IBD nGd energy peaks for all six ADs were reconstructed to 8:05 0:04 MeV. The relative energy scale between ADs was established by comparing the nGd peaks of the IBD- and spallation-neutrons, and particles in the Gd-LS. Both energy-reconstruction ap-proaches yielded a 0.5% uncorrelated energy-scale uncer-tainty for all six ADs. The relative unceruncer-tainty in efficiency due to the Ed cut was determined to be 0.12% using data. By measuring the difference in the neutron capture time of each AD, from which the Gd-concentration can be calcu-lated, the relative uncertainty in the fraction of neutrons captured on Gd (the Gd capture ratio) was found to be <0:1%. All other relative uncertainties were Oð0:01%Þ and the combined uncertainty was 0.2%. Independent analyses obtained similar results on the background and relative uncertainties.
This analysis was independent of reactor flux models. The eyield per fission [12] was not fixed when determin-ing sin2213. Whether we used the conventional Institut Laue-Langevin fluxes [13–16] (2.7% uncertainty) or the recently calculated fluxes [17,18] (3.1% uncertainty) had little impact on the results. The thermal energy released per fission is given in Ref. [19]. Nonequilibrium corrections for long-lived isotopes were applied following Ref. [17].
Contributions from spent fuel [20,21] ( 0:3%) were in-cluded as an uncertainty.
Thermal-power data provided by the power plant carry an uncertainty of 0.5% per core [22–24] that we conserva-tively treat as uncorrelated. The fission fractions were also provided for each fuel cycle as a function of burn-up, with a 5% uncertainty from validation of the simulation [25,26]. A DRAGON[27] model was constructed to study the correlation among the fission rates of isotopes. The uncertainties of the fission fraction simulation resulted in a 0.6% uncorrelated uncertainty of the eyield per core. The baselines have been surveyed with a Global Positioning System and modern theodolites to a precision of 28 mm. The uncertainties in the baseline and the spatial distribu-tion of the fission fracdistribu-tions in the core had a negligible effect to the results. Figure 3 presents the background-subtracted and efficiency-corrected IBD rates in the three EHs. Relative reactor flux predictions are shown for comparison.
The erate in the far hall was predicted with a weighted combination of the two near-hall measurements assuming no oscillation. The weights were determined by the thermal power of each reactor and its baseline to each AD. We observed a deficit in the far hall, expressed as a ratio of observed to expected events,
R ¼ 0:940 0:011ðstat:Þ 0:004ðsyst:Þ:
In addition, the residual reactor-related uncertainties were found to be 5% of the uncorrelated uncertainty of a single core.
TABLE III. Summary of absolute efficiencies, and correlated and uncorrelated systematic uncertainties.
Detector
Efficiency Correlated Uncorrelated
Target Protons 0.47% 0.03% Flasher cut 99.98% 0.01% 0.01% Delayed-energy cut 90.9% 0.6% 0.12% Prompt-energy cut 99.88% 0.10% 0.01% Multiplicity cut 0.02% <0:01% Capture-time cut 98.6% 0.12% 0.01% Gd capture ratio 83.8% 0.8% <0:1% Spill in 105.0% 1.5% 0.02% Live time 100.0% 0.002% <0:01% Combined 78.8% 1.9% 0.2% Reactor Correlated Uncorrelated
Energy per fission 0.2% Power 0.5%
IBD reaction per fission 3% Fission fraction 0.6%
Spent fuel 0.3%
Combined 3% Combined 0.8%
Sep28 Oct28 Nov27 Dec27 Jan26
IBD rate (/day)
400 600 800 EH1 D2 off D2 on
IBD rate (/day) 400
500 600 700 EH2 L3 on L2 off L2 on L1 off L1 on Run time
Sep 28 Oct 28 Nov 27 Dec 27 Jan 26
IBD rate (/day)
40 60
80 EH3
Predicted Measured
FIG. 3 (color online). Daily average measured IBD rates per AD in the three experimental halls as a function of time. Data between the two vertical dashed lines were used in this analysis. The solid curves represent no-oscillation predictions based on reactor flux analyses and detector simulation for comparison. The predictions have been corrected with the best-fit normaliza-tion parameter in determining sin22
The value of sin22
13 was determined with a 2 con-structed with pull terms accounting for the correlation of the systematic errors [28],
2 ¼ X 6 d¼1 ½Md Tdð1 þ " þ P r !d rrþ "dÞ þ d2 Mdþ Bd þX r 2 r 2 r þX6 d¼1 "2 d 2 d þ 2d 2 B ; (2)
where Mdare the measured IBD events of the dth AD with backgrounds subtracted, Bd is the corresponding back-ground, Td is the prediction from neutrino flux, MC, and neutrino oscillations [29], !d
r is the fraction of IBD con-tribution of the rth reactor to the dth AD determined by baselines and reactor fluxes. The uncertainties are listed in Table III. The uncorrelated reactor uncertainty is r (0.8%), d (0.2%) is the uncorrelated detection uncer-tainty, and B is the background uncertainty listed in Table II. The corresponding pull parameters are (r,"d, d). The detector- and reactor-related correlated uncertainties were not included in the analysis; the abso-lute normalization " was determined from the fit to the data. The best-fit value is
sin2213¼ 0:092 0:016ðstat:Þ 0:005ðsyst:Þ; with a 2=NDF of 4:26=4 (where NDF is the number of degrees of freedom). All best estimates of pull parameters are within its 1 standard deviation based on the
correspond-ing systematic uncertainties. The no-oscillation hypothesis is excluded at 5.2 standard deviations.
The accidental backgrounds were uncorrelated while the Am-C and (,n) backgrounds were correlated among ADs. The fast-neutron and9Li–8He backgrounds were site-wide correlated. In the worst case where they were correlated in the same hall and uncorrelated among different halls, we found the best-fit value unchanged while the systematic uncertainty increased by 0.001.
Figure4shows the measured numbers of events in each detector, relative to those expected assuming no oscilla-tion. The 6.0% rate deficit is obvious for EH3 in compari-son with the other EHs, providing clear evidence of a nonzero 13. The oscillation survival probability at the best-fit values is given by the smooth curve. The 2versus sin22
13 is shown in the inset.
The observed espectrum in the far hall is compared to a prediction based on the near-hall measurements in Fig.5. The disagreement of the spectra provides further evidence of neutrino oscillation. The ratio of the spectra is consistent with the best-fit oscillation solution of sin2213¼ 0:092 obtained from the rate-only analysis [31].
In summary, with a 43 000 ton–GWth–day live-time ex-posure, 10 416 reactor antineutrinos were observed at the far hall. Comparing with the prediction based on the near-hall measurements, a deficit of 6.0% was
Weighted Baseline [km] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 expected / N detected N 0.9 0.95 1 1.05 1.1 1.15 EH1 EH2 EH3 13 θ 2 2 sin 0 0.05 0.1 0.15 2χ 0 5 10 15 20 25 30 35 σ 1 σ 3 σ 5
FIG. 4 (color online). Ratio of measured versus expected sig-nal in each detector, assuming no oscillation. The error bar is the uncorrelated uncertainty of each AD, including statistical, detector-related, and background-related uncertainties. The ex-pected signal is corrected with the best-fit normalization parame-ter. Reactor and survey data were used to compute the flux-weighted average baselines. The oscillation survival probability at the best-fit value is given by the smooth curve. The AD4 and AD6 data points are displaced by 30 and þ30 m for visual clarity. The 2versus sin22
13is shown in the inset.
Entries / 0.25MeV 0 200 400 600 800 Far hall
Near halls (weighted)
Prompt energy (MeV)
0 5 10
Far / Near (weighted) 0.8 1 1.2
No oscillation Best Fit
FIG. 5 (color online). Top: Measured prompt-energy spectrum of the far hall (sum of three ADs) compared with the no-oscillation prediction from the measurements of the two near halls. Spectra were background subtracted. Uncertainties are statistical only. Bottom: The ratio of measured and predicted no-oscillation spectra. The solid curve is the best-fit solution with sin22
13¼ 0:092 obtained from the rate-only analysis. The
found. A rate-only analysis yielded sin22
13¼ 0:092 0:016ðstat:Þ 0:005ðsyst:Þ. The neutrino mixing angle 13 is nonzero with a significance of 5.2 standard deviations.
The Daya Bay experiment is supported in part by the Ministry of Science and Technology of China, the United States Department of Energy, the Chinese Academy of Sciences, the National Natural Science Foundation of China, the Guangdong provincial government, the Shenzhen municipal government, the China Guangdong Nuclear Power Group, Shanghai Laboratory for Particle Physics and Cosmology, the Research Grants Council of the Hong Kong Special Administrative Region of China, 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 Czech Science Foundation, and the Joint Institute of Nuclear Research in Dubna, Russia. We thank Yellow River Engineering Consulting Co., Ltd. and China railway 15th Bureau Group Co., Ltd. for build-ing the underground laboratory. We are grateful for the ongoing cooperation from the China Guangdong Nuclear Power Group and China Light & Power Company.
*Deceased.
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[29] The survival probability used in the 2 was P sur ¼
1 sin22
13sin2ð1:267m231L=EÞ cos413sin2212
sin2ð1:267m2
21L=EÞ where, m231¼ 2:32 103eV2,
sin22
12¼ 0:861þ0:0260:022, and m221¼ 7:59þ0:200:21105eV2.
The uncertainty in m2
31[30] has not been included in the
fit. The fit sin22
13will change byþ0:0007 and 0:0004
when m2
31changes by 1 standard deviation.
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[31] Without correcting for the nonlinearity of the detector response, we have performed a preliminary shape analysis that yielded a consistent result for sin22
