New measurement of
θ
13via neutron capture on hydrogen at Daya Bay
F. P. An,1A. B. Balantekin,2H. R. Band,3 M. Bishai,4S. Blyth,5,6D. Cao,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.-H. Cheng,10J. Cheng,11Y. P. Cheng,8Z. K. Cheng,15J. J. Cherwinka,2M. C. Chu,9A. Chukanov,16J. P. Cummings,17
J. de Arcos,18Z. Y. Deng,8 X. F. Ding,8 Y. Y. Ding,8M. V. Diwan,4M. Dolgareva,16J. Dove,19D. A. Dwyer,20 W. R. Edwards,20R. Gill,4 M. Gonchar,16 G. H. Gong,12 H. Gong,12M. Grassi,8 W. Q. Gu,21M. Y. Guan,8 L. Guo,12
R. P. Guo,8 X. H. Guo,22Z. Guo,12R. W. Hackenburg,4 R. Han,13S. Hans,4 M. He,8 K. M. Heeger,3 Y. K. Heng,8 A. Higuera,23Y. K. Hor,24Y. B. Hsiung,5 B. Z. Hu,5 T. Hu,8 W. Hu,8E. C. Huang,19H. X. Huang,25 X. T. Huang,11 P. Huber,24W. Huo,26G. Hussain,12D. E. Jaffe,4 P. Jaffke,24K. L. Jen,10S. Jetter,8 X. P. Ji,27,12X. L. Ji,8 J. B. Jiao,11 R. A. Johnson,28J. Joshi,4L. Kang,29S. H. Kettell,4S. Kohn,30M. Kramer,20,30K. K. Kwan,9M. W. Kwok,9T. Kwok,31 T. J. Langford,3 K. Lau,23L. Lebanowski,12J. Lee,20J. H. C. Lee,31R. T. Lei,29R. Leitner,32J. K. C. Leung,31C. Li,11 D. J. Li,26F. Li,8G. S. Li,21Q. J. Li,8S. Li,29S. C. Li,31,24W. D. Li,8X. N. Li,8Y. F. Li,8Z. B. Li,15H. Liang,26C. J. Lin,20 G. L. Lin,10S. Lin,29 S. K. Lin,23Y.-C. Lin,5J. J. Ling,15J. M. Link,24L. Littenberg,4 B. R. Littlejohn,18D. W. Liu,23 J. J. Liu,31J. L. Liu,21J. C. Liu,8C. W. Loh,7C. Lu,33H. Q. Lu,8J. S. Lu,8K. B. Luk,30,20Z. Lv,34Q. M. Ma,8X. Y. Ma,8 X. B. Ma,13Y. Q. Ma,8Y. Malyshkin,35D. A. Martinez Caicedo,18K. T. McDonald,33R. D. McKeown,36,37I. Mitchell,23 M. Mooney,4Y. Nakajima,20J. Napolitano,38D. Naumov,16E. Naumova,16H. Y. Ngai,31Z. Ning,8J. P. Ochoa-Ricoux,35 A. Olshevskiy,16H.-R. Pan,5J. Park,24S. Patton,20V. Pec,32J. C. Peng,19L. Pinsky,23C. S. J. Pun,31F. Z. Qi,8M. Qi,7 X. Qian,4N. Raper,39J. Ren,25R. Rosero,4B. Roskovec,32X. C. Ruan,25H. Steiner,30,20G. X. Sun,8J. L. Sun,40W. Tang,4
D. Taychenachev,16T. Konstantin,16K. V. Tsang,20C. E. Tull,20N. Viaux,35B. Viren,4V. Vorobel,32C. H. Wang,6 M. Wang,11 N. Y. Wang,22R. G. Wang,8 W. Wang,37,15 W. W. Wang,7 X. Wang,41Y. F. Wang,8 Z. Wang,12Z. Wang,8
Z. M. Wang,8 H. Y. Wei,12 L. J. Wen,8 K. Whisnant,42C. G. White,18 L. Whitehead,23T. Wise,2 H. L. H. Wong,30,20 S. C. F. Wong,15E. Worcester,4C.-H. Wu,10Q. Wu,11D. M. Xia,43,8J. K. Xia,8Z. Z. Xing,8J. Y. Xu,9 J. L. Xu,8J. Xu,22
Y. Xu,15T. Xue,12J. Yan,34C. G. Yang,8 H. Yang,7 L. Yang,29 M. S. Yang,8 M. T. Yang,11M. Ye,8 Z. Ye,23M. Yeh,4 B. L. Young,42 G. Y. Yu,7 Z. Y. Yu,8 L. Zhan,8 C. Zhang,4 H. H. Zhang,15J. W. Zhang,8 Q. M. Zhang,34X. T. Zhang,8
Y. M. Zhang,12Y. X. Zhang,40Y. M. Zhang,15Z. J. Zhang,29Z. Y. Zhang,8 Z. P. Zhang,26J. Zhao,8 Q. W. Zhao,8 Y. F. Zhao,13Y. B. Zhao,8 W. L. Zhong,8 L. Zhou,8 N. Zhou,26H. L. Zhuang,8 and J. H. Zou8
(Daya Bay Collaboration) 1
Institute of Modern Physics, East China University of Science and Technology, Shanghai 2University of Wisconsin, Madison, Wisconsin 53706, USA
3
Department of Physics, Yale University, New Haven, Connecticut 06520, USA 4Brookhaven National Laboratory, Upton, New York 11973, USA
5
Department of Physics, National Taiwan University, Taipei 6National United University, Miao-Li
7
Nanjing University, Nanjing 8Institute of High Energy Physics, Beijing 9
Chinese University of Hong Kong, Hong Kong 10Institute of Physics, National Chiao-Tung University, Hsinchu
11
Shandong University, Jinan
12Department of Engineering Physics, Tsinghua University, Beijing 13
North China Electric Power University, Beijing 14Shenzhen University, Shenzhen 15
Sun Yat-Sen (Zhongshan) University, Guangzhou 16Joint Institute for Nuclear Research, Dubna, Moscow Region
17
Siena College, Loudonville, New York 12211, USA 18
Department of Physics, Illinois Institute of Technology, Chicago, Illinois 60616, USA 19
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA 20
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 21
Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai Laboratory for Particle Physics and Cosmology, Shanghai
22
Beijing Normal University, Beijing 23
Department of Physics, University of Houston, Houston, Texas 77204, USA 24
Center for Neutrino Physics, Virginia Tech, Blacksburg, Virginia 24061, USA 25
China Institute of Atomic Energy, Beijing 26
27School of Physics, Nankai University, Tianjin 28
Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA 29Dongguan University of Technology, Dongguan
30
Department of Physics, University of California, Berkeley, California 94720, USA 31Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong 32
Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 33Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544, USA
34
Xi’an Jiaotong University, Xi’an
35Instituto de Física, Pontificia Universidad Católica de Chile, Santiago, Chile 36
California Institute of Technology, Pasadena, California 91125, USA 37College of William and Mary, Williamsburg, Virginia 23187, USA
38
Department of Physics, College of Science and Technology, Temple University, Philadelphia, Pennsylvania 19122, USA 39
Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
40
China General Nuclear Power Group
41College of Electronic Science and Engineering, National University of Defense Technology, Changsha 42
Iowa State University, Ames, Iowa 50011, USA 43Chongqing University, Chongqing (Received 14 March 2016; published 21 April 2016)
This article reports an improved independent measurement of neutrino mixing angleθ13at the Daya Bay Reactor Neutrino Experiment. Electron antineutrinos were identified by inverseβ-decays with the emitted neutron captured by hydrogen, yielding a data set with principally distinct uncertainties from that with neutrons captured by gadolinium. With the final two of eight antineutrino detectors installed, this study used 621 days of data including the previously reported 217-day data set with six detectors. The dominant statistical uncertainty was reduced by 49%. Intensive studies of the cosmogenic muon-induced9Li and fast neutron backgrounds and the neutron-capture energy selection efficiency, resulted in a reduction of the systematic uncertainty by 26%. The deficit in the detected number of antineutrinos at the far detectors relative to the expected number based on the near detectors yielded sin22θ13¼ 0.071 0.011 in the three-neutrino-oscillation framework. The combination of this result with the gadolinium-capture result is also reported.
DOI:10.1103/PhysRevD.93.072011
I. INTRODUCTION
Precise measurements of neutrino mixing parameters are crucial to searches for CP-symmetry violation among neutral leptons and tests of neutrino oscillation theory. In particular, the precision of neutrino mixing angleθ13is of key significance in constraining the leptonic CP phase δ[1–4]. Prior to 2012, many experimental efforts had been made to determineθ13[5–10]. The first measurement ofθ13with a significance greater than five standard deviations was reported by the Daya Bay Reactor Neutrino Experiment in 2012 [11]. The most recent determinations of θ13 from reactor and accelerator experiments[12–18]are consistent. The three reactor antineutrino experiments, Double Chooz [19], RENO [20], and Daya Bay [21], currently provide the most precise measurements of the mixing angle. They use gadolinium-doped liquid scintillator to identify electron antineutrinos through inverse β-decay (IBD) reactions (¯νeþ p → n þ eþ) with the neutron capturing on gadolinium (nGdnGd). A surrounding volume of undoped liquid scintillator improves the efficiency of detectingγ’s that escape from the doped volume, and has
been used (in conjunction with the doped volume) by each of the three reactor experiments to determine sin22θ13 independently through IBD reactions with the neutron captured by hydrogen (nH)[14,15,22,23]. The KamLAND experiment has used nH IBDs to measure the disappear-ance of reactor ¯νe [24] and the flux of geo-¯νe [25]. The Super-Kamiokande experiment has used nH IBDs to search for relic supernova ¯νe [26]. Future projects, including the medium-baseline reactor experiments JUNO[27]and RENO-50[28], and LENA[29], will also make use of nH IBDs. Techniques developed for this analysis may be useful for these future experiments.
The previous analysis of nH IBDs from Daya Bay[15]
is improved in this article with 3.6 times the number of detected IBDs and with reduced uncertainties of backgrounds and the neutron-capture energy selection effi-ciency. This statistically-independent measurement is also largely systematically independent from the nGd-IBD analy-sis, and improves the overall uncertainty of sin22θ13 from Daya Bay.
This article is organized as follows. SectionIIdescribes the Daya Bay experiment. The calculation of reactor anti-neutrino flux is described in Sec. III. Analysis of the data, including event reconstruction and IBD selection, is described in Sec.IV. SectionVdescribes the accidental background, and Sec.VIdescribes correlated backgrounds. The IBD selection efficiency is discussed in Sec.VII. The fit for sin22θ13and its combination with the nGd-IBD result are presented in Sec. VIII. Section IX briefly discusses the impact of the results and improvements expected in the future.
II. EXPERIMENT
Located in Guangdong province, China, the Daya Bay experiment measures electron antineutrinos emitted from three pairs of nuclear reactors, each reactor nominally producing 2.9 GW of thermal power. Inside the adjacent mountains, two near experimental halls (EH1 and EH2) are located roughly 360–470 m from their nearest reactor, and one far experimental hall (EH3) is located 1.52–1.93 km from all six reactors.
Each far (near) experimental hall contains 4 (2) antineu-trino detectors (ADs) submerged in a two-zone water Cherenkov detector[30]. An inner and outer zone together provide each AD with > 2.5 m of shielding against ambient radiation and spallation products of nearby cosmogenic muons. These inner and outer water shields (IWS and OWS) are independent cosmogenic muon detectors with 160 (121) and 224 (167) 20-cm photomultiplier tubes (PMTs), respectively, in the far (near) hall(s). Detecting muons enables estimates of muon-induced backgrounds; particularly,9Li=8He decay products and spallation neutrons. The ADs were identically designed and consist of three nested, coaxial cylindrical vessels: an inner and outer acrylic vessel (IAV and OAV) [31] and an outermost stainless steel vessel (SSV), as shown in Fig.1. For future reference, the z coordinate is defined by the central axis of the cylinders and the r coordinate is measured radially from the central axis. The IAV is about 3 m in both height and diameter, and holds 20 tons of gadolinium-doped (0.1% by mass) liquid scintillator (GdLS) [32]. The surrounding OAV is about 4 m in both height and diameter, and holds 22 tons of undoped liquid scintillator (LS) to improve the efficiency of detectingγ’s that escape from the GdLS. The surrounding SSV is about 5 m in both height and diameter, and holds 36 tons of mineral oil (MO) to shield against radiation from the PMTs and the SSV.
Each AD contains 192 20-cm PMTs arranged in 24 columns and 8 rings at a fixed radius (r ≈ 2.19 m) in the MO. Reflectors were installed above and below the OAV to improve light collection. Three automated calibration units (ACUs) are affixed atop each AD and house LEDs and various radioactive sources for calibrating the energy scale and position reconstruction of events in the ADs[33]. The ACUs deploy vertically at three radial positions: ACU-A at the center (r ¼ 0), ACU-B near the wall of the IAV
(r ¼ 1.35 m), and ACU-C near the wall of the OAV (r ¼ 1.77 m).
ADs were triggered, and recorded the time and charge information of each PMT channel, when the number of PMTs with pulses above threshold (NPMT) was ≥ 45 or when the integrated sum of PMT pulses from all 192 PMTs (Qsum) was ≳65 photoelectrons. Both trigger thresholds corresponded to approximately 0.4 MeV and accepted 100% of IBD positrons with > 0.7 MeV of deposited energy [34]. Water shields triggered independently under analogous conditions[30]. The trigger criteria were tested within each cycle of an 80-MHz clock, and if satisfied, the subsequent1 μs (and preceding 200 ns) of data from all channels were recorded. The physical interactions that caused a single trigger in a given detector are referred to as an“event.” The time of an event is defined as the time of the trigger.
More detailed descriptions of the detector hardware are given in Ref.[35].
The analysis presented in this article determines sin22θ13 by counting interactions of reactor antineutrinos in each AD in the one far and two near experimental halls. Antineutrinos were identified in both the GdLS and LS volumes via IBD reactions (¯νeþ p → n þ eþ) in which the positron carried away 99.4% of the kinetic energy of the final state on average. The positron deposited energy within Oð1Þ ns and then annihilated with an electron, usually producing two back-to-back 0.511-MeV γ’s (several percent of the positrons annihilated in flight such that the sum of γ energies was greater than 2 × 0.511 MeV).
FIG. 1. Schematic of an antineutrino detector. See the text for definitions.
The neutron thermalized and was captured primarily by Gd or H, releasing an approximately 8-MeV γ cascade or a single 2.22-MeVγ, respectively. The time from production to capture was typically tens to hundreds of microseconds. The temporal coincidence of the prompt positron and delayed neutron-capture clearly distinguishes antineutrinos from single-event backgrounds.
III. REACTOR ANTINEUTRINO FLUX The expected number of IBDs in an AD was calculated as the product of the number of IBDs per target protonΦ and the efficiency-weighted number of target protons Nε:
¯NIBD¼ ΦNε: ð1Þ
The latter is discussed in Sec.VIIand the former is defined for the dth AD as Φd≡ X6 r¼1 1 4πL2 dr Z Z ftdg σνðEÞPν Ldr E d2NrðE; tÞ dEdt dEdt; ð2Þ where Ldris the baseline distance between the dth AD and the rth reactor core, σνðEÞ is the IBD reaction cross section of an antineutrino with energy E, PνðLdr=EÞ is the neutrino survival probability, and d2NrðE; tÞ=dEdt is the number of antineutrinos emitted from the rth reactor at time t with energy E, which is integrated over the periods of data acquisition for the dth AD ftdg.
The baselines Ldr [36] were measured with negligible uncertainty [35]. The cross section σν was evaluated according to Ref. [37] using physical parameters from Ref. [38]. In the three-neutrino-oscillation framework, the survival probability of electron (anti)neutrinos is expressed as
Pν ¼ 1−cos4θ13sin22θ12sin2Δ21 −sin22θ
13cos2θ12sin2Δ31 −sin22θ
13sin2θ12sin2Δ32; ð3Þ whereΔij≡ 1.267Δm2ijL=E, E [MeV] is the energy of the neutrino at production, L [m] is the distance between the points of production and interaction of the neutrino, and Δm2
ij [eV2] is the difference between the squared masses of mass eigenstates νi and νj. The values of sin22θ12¼ 0.846 0.021, Δm2
21¼ ð7.53 0.18Þ × 10−5 eV2, and Δm2
32 ¼ ð2.44 0.06Þ × 10−3 eV2 (for the normal hier-archy) Δm232¼ ð2.52 0.07Þ × 10−3eV2 (for the inverted hierarchy)] were taken from Ref.[38]. These uncertainties were found to have negligible impact on the fit of sin22θ13 and its uncertainty. The reactor antineutrino emission rate was calculated as d2NðE;tÞ dEdt ¼ W thðtÞ P ifiðtÞei X i
fiðtÞSiðEÞcnei ðE;tÞþSsnfðE;tÞ; ð4Þ where the sum is over the four primary fissile isotopes: 235U,239Pu,238U,241Pu. The thermal power of the reactor WthðtÞ and fraction of fissions due to the ith isotope fiðtÞ were supplied by the nuclear power plant, the average thermal energies released per fission ei were from Ref.[39], the antineutrino yields per fission SiðEÞ from 238U, and from235U,239Pu, and241Pu, were from Ref.[40] and Ref.[41], respectively. The correction to the energy spectrum due to nonequilibrium effects of long-lived fission fragments cne
i ðE; tÞ followed Ref. [40]. The con-tribution from spent nuclear fuel SsnfðE; tÞ was estimated following Refs. [42,43]. Combining the uncertainties of these components gave a 0.9% reactor-uncorrelated uncertainty of predicted IBD rate associated with a single reactor [44]. Additional information is given in Refs.[44,45]. These quantities were estimated on a daily basis, weighted by the fractional data acquisition time of each day for each experimental hall, and then summed for each week. The accumulated predicted spectra dNrðEÞ=dE are provided[36].
IV. DATA ANALYSIS
The data used in this analysis were recorded beginning on December 24, 2011, with two ADs in EH1, one in EH2, and three in EH3. Recording was paused on July 28, 2012, to install the final two ADs in EH2 and EH3. On October 19, 2012, recording resumed with the full-design configu-ration of eight ADs. The first measurement with nH IBDs at Daya Bay[15] used the 217 days of data recorded in the six-AD configuration while this study uses an additional 404 days of data recorded in the full eight-AD configura-tion until November 27, 2013. Data acquisiconfigura-tion maintained an operational efficiency of > 97% with occasional pauses for maintenance. Excluding weekly calibrations, special calibrations, and problematic data, the data acquisition (DAQ) time TDAQof each AD is listed in TableII. With the nH selection criteria described in the following sections, about 780000 IBDs were observed.
A. Calibration and reconstruction
The gain [analog-to-digital converter channel/photoelec-tron] of each PMT channel was calibrated in situ by fitting the single photoelectron peak in the PMT dark noise spectrum. The peak was fit with a Poisson-Gaussian convolution [35]. This gain calibration was validated by an independent method using low-intensity LED pulses. The energy scale [MeV/photoelectron] of each AD was calibrated in situ with muon-induced spallation neutrons that captured on Gd throughout the GdLS volume. The two
isotopes157Gd and155Gd, which releaseγ-cascades of 7.94 and 8.54 MeV, respectively, were fit with two Crystal Ball functions[46]as described in Ref.[34]. This energy scale calibration was validated by an independent method using weekly deployments of the160Coγ source of ACU A at the center of each AD.
The energy scale of an AD increased by 10%–15% from the center of the detector to the wall of the OAV, and changed by 2%–6% between the bottom and the top of the OAV, depending on the radial position. Corrections of energy scale as a function of position were applied with two-dimensional maps (zvs:r) derived from spallation neutron-captures on Gd in each AD. The maps were extrapolated to the LS volume using spallation neutron-captures on H throughout the GdLS and LS volumes. The energy after correction is referred to as the“reconstructed” energy Erec. Using nH γ’s, the standard deviation of Erec across an AD was observed to be less than 1.0% for all ADs. The energy resolution was measured to be roughly 9%= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiErec ½MeV
p
at the center of an AD. It improved by around 20% (relative) from the center to the wall of the OAV.
A single position associated with each event in an AD was“reconstructed” using charge-pattern templates derived from Monte Carlo simulation [34]. From a simulation of positrons, the average distribution of charge from the 192 PMT channels, or the charge-pattern, was determined for each of 9600 voxels within the OAV, corresponding to 20, 20, and 24 divisions in r2, z, and ϕ (where symmetry of ϕ was assumed to decrease statistical uncertainty). For each event, aχ2was calculated for each voxel using the expected (from the templates) and observed charges from each PMT
channel. The voxel with the smallestχ2was selected and, with its nearest-neighbor voxels, interpolated to obtain the reconstructed position. The reconstructed positions of prompt events (see Sec. IV B) are shown in Figs. 2(e)
and 2(f), where a residual voxel grid is apparent. The resolution for a 2.2-MeV γ was about 12 cm in the r-ϕ plane and 13 cm along the z axis, in the LS volume. The position resolution improved by more than 40% from the center of a detector to the wall of an OAV, and varied within a few percent vertically. Using the160Coγ sources of the ACUs, the bias of the reconstruction was found to be about four times smaller than the resolution, near the wall of an OAV.
B. IBD candidate selection
IBD candidates were selected from pairs of successive events in an AD, excluding those within predefined time ranges of detected muons to suppress muon-induced back-grounds. The IBD selection criteria for the nGd-[12]and nH-IBD analyses are listed in Table I. First, AD events caused by spontaneous light emission from PMTs (PMT flashes) were removed as described in Section IV B 1. Then, for the nH-IBD analysis, AD events were required to have Erec> 1.5 MeV to exclude low-energy backgrounds (see Section IV B 2). The AD events remaining after muon-event vetoes (see Section IV B 3) were grouped within a time window to identify double coincidences (see Section IV B 4). The resulting prompt and delayed events were required to have Erec < 12 MeV and Erec within three standard deviations of the fitted nH γ energy in each AD, respectively. Finally, the distance between the reconstructed positions of the prompt and delayed events
D el aye d E n er gy [M eV ] 2 3 4 5 6 7 8 9 10 1 10 2 10 1 10 2 10 (a) 1 10 2 10 3 10 4 10
Prompt Energy [MeV]
2 3 4 5 6 7 8 9 10 D el aye d E n er gy [M eV ] 2 3 4 5 6 7 8 9 10 1 10 2 10 3 10 4 10 (b) 0 100 200 300 400 500 600 700 D el aye d E n er gy [M eV ] 2 3 4 5 6 7 8 9 10 0 100 200 300 400 500 600 700 (c) 0 1000 2000 3000 4000 5000
Prompt Energy [MeV]
2 3 4 5 6 7 8 9 10 D el aye d E n er gy [M eV ] 2 3 4 5 6 7 8 9 10 0 1000 2000 3000 4000 5000 (d) 3 10 × Z [mm] -2000 -1000 0 1000 2000 0 10 20 30 40 0 10 20 30 40 (e) -2 -1 0 1 2 z [m] ] 2 [m 2 R 0 1000 2000 3000 4000 3 10 × Z [mm] -2000 -1000 0 1000 2000 0 50 100 150 200 250 0 50 100 150 200 250 (f) 0 1 2 3 4 -2 -1 0 1 2 2 r [m2] z [m]
FIG. 2. (a) Distribution of prompt vs. delayed reconstructed energy for all double coincidences with a maximum 50-cm separation in all near-hall ADs, (b) total (621-day) accidental background sample (ABS) for all ADs in the near halls, (c) and (d) are the distributions of prompt vs. delayed reconstructed energy after subtracting the total ABS for the far and near halls, respectively, (e) and (f) are the reconstructed positions of all prompt events after subtracting the total ABS for the far and near halls, respectively. The sparser distribution of events at the bottoms of the ADs is due to the presence of acrylic supports below the IAV.
was required to be within 50 cm to suppress uncorrelated double coincidences (accidentals), which dominated the set of double coincidences (see SectionIV B 5). The resulting number of nH-IBD candidates (NDC) is listed in TableII for each AD. Details of the selection criteria are described below.
1. PMT flashes
PMT flashes are spontaneous emissions of light from the voltage divider of a PMT. AD events caused by a flash from any one of the 192 20-cm PMTs were removed by requiring Ellipse≡pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiQuadrant2þ ðqmax=0.45Þ2< 1, where qmax is the largest fraction of an AD event’s total charge in a single PMT and Quadrant is defined as Q3=ðQ2þ Q4Þ in which Qi is the total charge in AD azimuthal quadrant i and quadrant 1 is approximately centered on the PMT with qmax. The efficiency of this criterion to select IBDs in the combined GdLS plus LS volume was estimated with Monte Carlo simulation [45] to be > 99.99%. Flashes from six 5-cm calibration PMTs [35] near the top and bottom reflectors were simply removed by requiring the charge output from each 5-cm PMT to be < 100 photoelectrons.
2. Low-energy criterion
AD events were required to have Erec > 1.5 MeV to exclude events caused by correlated β-α decays from the 214Bi-214Po-210Pb and 212Bi-212Po-208Pb decay chains, which originate from naturally-occurring238U and232Th, respectively. Due to the greater quenching associated with α’s, the 8.78-MeV α from the latter chain resulted in an apparent energy of Erec¼ 1.26 MeV and the 7.68-MeV α from the former chain resulted in Erec¼ 1.00 MeV. Excluding these decays reduced the uncertainty of the total rate of accidentals by an order of magnitude. This criterion rejected about 10% of IBD prompt events.
3. Muon-event vetoes
To suppress backgrounds from muon-induced spallation neutrons (Sec. VI B) and long-lived spallation products such as9Li and8He (Sec.VI A), an AD event was excluded from the analysis if it occurred within predefined veto time windows after cosmogenic muon events identified by the water shields or ADs. Muon events from the ADs, IWS, and OWS that occurred within the 2-μs detector latency were grouped together for the accounting of all events associated with cosmogenic muons. The muon event with the earliest time in the group defined the start of the muon-veto time window.
A muon event in a water shield, referred to as aμWS, was defined by requiring NPMT> 12 (15) in the IWS (OWS). The muon-detection efficiency of these selections was essentially 100%, as determined relative to the ADs
[30]. The higher threshold of the OWS in the nH-IBD analysis (see Table I) removed correlated triggers that sometimes occurred Oð100Þ μs after an OWS event, due to electronics noise. These triggers were handled in the nGd-IBD analysis by slightly modifying the multiple-coincidence criteria (see Sec.IV B 4) to have no overlap with a muon-veto time window.
An AD event that was grouped with a μWS and with 20 MeV < Erec < 2.5 GeV was defined as an AD muon event μAD. If instead, Erec> 2.5 GeV, the event was defined as a showering AD muon eventμsh. The total rate of muon events measured by each AD (Rμ) is listed in TableII.
An AD event was excluded if it occurred within a veto time window of400 μs, 800 μs, or 1 s after a μWS, μAD, or μsh, respectively. The fraction of DAQ time remaining for IBD analysis after implementing these offline muon-vetoes is reported as εμ in Table II, with typical values of 79%, 83% and 98% in EH1, EH2, and EH3, respectively.
4. Coincidence time
Correlated AD events were selected using a coinci-dence time window of ½1; 400 μs, which is about two times longer than the mean capture time of an IBD neutron on hydrogen in LS and about 14 times longer than that in GdLS. Given the data recording window of 1 μs, coincidence windows were initiated 1 μs after an event to ensure distinction of prompt and delayed events. Lone events are denoted as“singles” and were used to construct accidental background samples (see Sec. V). Only pairs of events, denoted as double coincidences (DCs), were used to select IBD candidates. If more than two events occurred within ½1; 400 μs, they were excluded from further analysis. In addition, if the first, or prompt, event of a DC occurred within½1; 400 μs of a preceding event or muon-veto time window, the DC was excluded (this requirement was also applied to singles).
TABLE I. IBD selection criteria for the nH and nGd [12] analyses. See text for details.
nH nGd
AD trigger NPMT≥ 45ORQsum≳ 65 p.e.
20-cm PMT flash Ellipse < 1
5-cm PMT flash Q < 100 p.e.
Low energy > 1.5 MeV > 0.7 MeV
Detector latency < 2 μs
WS muon (μWS) [IWS/OWS] NPMT> 12=15 NPMT> 12=12
AD muon (μAD) > 20 MeV
Showering AD muon (μsh) > 2.5 GeV
WS muon veto ð0; 400Þ μs ð−2; 600Þ μs
AD muon veto ð0; 800Þ μs ð−2; 1000Þ μs
Showering AD muon veto (0 μs, 1 s) (−2 μs, 1 s) Coincidence time (tc) ½1; 400 μs ½1; 200 μs
Prompt energy (Ep) < 12 MeV
Delayed energy (Ed) peak3σ [6, 12] MeV
The fraction of DAQ time remaining for IBD analysis after implementing these multiple-coincidence criteria was about 98.4% for each AD, and is reported as εm in Table II. This multiplicity selection efficiency was derived as described in Ref.[47], and calculated using the duration of the coincidence time window Tc¼ 399 μs and the rate of uncorrelated single events Rs (which are uncorrelated events that satisfy the criteria of Sections IV B 1–IV B 3; not singles, which exclude events involved in coincidences):
εm ¼ e−RsTc e−ðRsþRμÞTcþ Rμ Rsþ Rμ ½1 − e−ðRsþRμÞTc þ Rs Rsþ Rμ e−RμTc½1 − e−ðRsþRμÞTc − Rs 2Rsþ Rμ e−RμTc½1 − e−ð2RsþRμÞTc : ð5Þ 5. Coincidence distance
The set of DCs was largely comprised of accidental coincidences (whose positions are uncorrelated throughout the detector); therefore, the spatial separation of the reconstructed positions of the prompt and delayed events dc was required to be within 50 cm. This rejected 98% of the accidental coincidences at a loss of 25% of the IBDs. Figure2(a)shows the distribution of prompt energy vs. delayed energy for all DCs in all near-hall ADs after applying the coincidence-distance criterion. Bands for both the 2.22-MeV nH and 8-MeV nGd delayed events are apparent, with a large background of low-energy DCs around the nH band. The clusters around 1.5 and 2.7 MeV are due toγ’s from40K and208Tl decays, respectively. The bands between these clusters are dominated by the decay
products of238U. The measured nH γ energy was around 2.33 MeV, which is offset from the true value of 2.22 MeV because of nonlinear detector response and the calibration of the energy scale with nGd events. The nH delayed events were fit as described in Sec. VII C, providing a mean and a standard deviation σ for each AD. Delayed events were required to have Erec within3σ (≈0.42 MeV) of the mean for each AD, which excludesγ’s from 40K. The accidental background from the remaining decays was effectively removed by the subtraction described in Sec.V. Backgrounds from correlated events are described in Sec.VI. Efficiencies and uncertainties of the IBD selection criteria are described in Sec.VII.
V. ACCIDENTAL BACKGROUND
Accidental backgrounds were caused by two uncorre-lated AD events that satisfied the IBD selection criteria, and were almost entirely due to natural radioactivity in the materials around and within the detectors. The energy spectra of this background are visible below 3 MeV in Fig.2(a). Because the delayed event of an nH IBD is from a 2.22-MeV γ, which overlaps with this background spec-trum, the accidental background rate relative to the IBD rate was typically > 50 times that of the nGd-IBD analysis for the ADs in EH3 after applying all IBD selection criteria. The background was estimated for each AD within each run (about 2–3 days) by constructing accidental back-ground samples (ABSs) from the singles in a run. An ABS was constructed by sequentially pairing singles from the first half of the run with singles from the second half of the run. The resulting ABS consisted of NABS-tot accidentals, and after applying the remaining IBD selection criteria (distance and energy), the ABS consisted of NABS-cut TABLE II. Data summary for each AD. All per-day rates are corrected with εμεm. TDAQ is the DAQ time, εμ is the muon-veto efficiency,εmis the multiplicity selection efficiency, Rμis the muon rate, Rsis the rate of uncorrelated single events, NDCis the number of double-coincidence (DC) events satisfying all IBD selection criteria, NAccis the number of accidental DCs, NCoris the number of correlated DCs, RAcc, RLi9, RFastN, RAmC, and RIBD are the rates of accidental, fast neutron,9Li=8He, Am-C, and IBD (with all the backgrounds subtracted) DCs, and nH/nGd is the ratio of the efficiency- and target proton-corrected RIBDfor the nH- and nGd-IBD analyses. The differences in RIBDamong ADs in the same near hall are due primarily to differences in baselines to the reactors, and secondarily to differences in target mass.
EH1-AD1 EH1-AD2 EH2-AD1 EH2-AD2 EH3-AD1 EH3-AD2 EH3-AD3 EH3-AD4
TDAQ[d] 565.436 565.436 568.019 378.407 562.414 562.414 562.414 372.685 εμ 0.7949 0.7920 0.8334 0.8333 0.9814 0.9814 0.9812 0.9814 εm 0.9844 0.9845 0.9846 0.9846 0.9844 0.9841 0.9839 0.9845 Rμ [Hz] 200.32 200.32 150.08 149.80 15.748 15.748 15.748 15.757 Rs [Hz] 20.111 19.979 19.699 19.702 19.651 20.020 20.182 19.649 NDC 217613 219721 208606 136718 56880 56106 59230 38037 NAcc 26240 49 25721 49 25422 43 16365 29 29920 19 30065 20 32179 21 20427 15 NCor 191373 473 194000 475 183184 465 120353 449 26960 246 26041 244 27051 251 17610 196 RAcc [d−1] 59.31 0.11 58.34 0.11 54.54 0.09 52.71 0.09 55.07 0.04 55.35 0.04 59.27 0.04 56.73 0.04 RLi9[d−1] 2.36 1.02 1.73 0.75 0.19 0.09 RFastN [d−1] 2.11 0.18 1.81 0.17 0.16 0.03 RAmC [d−1] 0.07 0.04 0.07 0.04 0.07 0.03 0.07 0.03 0.03 0.02 0.03 0.02 0.03 0.02 0.02 0.01 RIBD[d−1] 428.01 1.48 435.49 1.49 389.41 1.25 384.03 1.42 49.24 0.45 47.56 0.45 49.44 0.46 48.54 0.55 nH/nGd 0.993 0.007 0.993 0.007 0.995 0.007 0.995 0.008 1.015 0.012 0.981 0.012 1.019 0.012 0.987 0.014 13
accidentals. To obtain the true value for εABS≡ NABS-cut=NABS-tot, the calculation of εABS was repeated for several hundred different pairing sequences of the singles, and the Gaussian mean of the resulting distribution was taken asεABS. Figure2(a)shows the energy distribu-tion of all DCs (621 days) of all near-hall ADs without applying the delayed-energy criterion, and Fig.2(b)shows the energy distribution of the total ABS (621 days) of all near-hall ADs after applying the coincidence-distance criterion. Each ABS was scaled to a calculated number of accidentals (NAcc) and subtracted from its corresponding number of DCs (NDC) to obtain the energy distribution of correlated DCs (NCor), which are dominantly due to IBDs:
NCor ¼ NDC− NAcc;
NAcc≡ RAcc· TDAQ·εμ·εABS; ð6Þ where TDAQ is the DAQ time, εμ is the muon-veto efficiency, and RAccis the rate of coincidence of uncorre-lated single events, which is expressed as [47]
RAcc¼ R2s· Tc·εm
≈Rs· e−RsTc· RsTce−RsTc; ð7Þ where Rs is the rate of uncorrelated single events andεm is the multiplicity selection efficiency, both defined in Eq. (5). The approximation of Eq.(5)used in the second line (εm≈ e−RsTc· e−RsTc) results from the conditionðR
sþ RμÞTc≪ 1 and is valid to within 0.1% for Tc ¼ 399 μs, Rs¼ 20 Hz, and the Rμin TableII. This approximation is not used in this analysis, but is shown here to illustrate the basic components of the calculation: e−RsTc is the
proba-bility of no prior event within Tc and RsTce−RsTc is the probability of a subsequent event within Tc. NDC, NAcc, and NCor are listed for each AD in TableII.
Figure2(d)shows the energy distribution of NCorfor all near-hall ADs [Fig.2(c)shows NCor for the far-hall ADs], where the nH γ peak is cleanly isolated from the accidental-dominated DCs shown in Fig.2(a). The effectiveness of the subtraction is also illustrated in Fig. 3, which shows the energy spectrum of the delayed events after subtracting the accidental background for all near-hall ADs and all far-hall ADs. Both the nH and nGd peaks are very similar between the two groups of ADs. Figures2(e)and2(f)show the reconstructed positions of NCor prompt events after subtracting the accidental background for all ADs in the far and near halls, respectively. The positions are generally uniform throughout the GdLS and LS volumes. The smaller concentration of events in the GdLS volume (r2< 2.40 m2 andjzj < 1.50 m) is due to the greater fraction of neutron-captures on Gd.
The uncertainty of NCor is composed of the statistical uncertainties of NDC and NABS-cut, and the systematic uncertainty of RAcc, which is determined by the uncertainty of Rs. The uncertainty from εm was negligible: using
Eq. (5)and Rs¼ 40 Hz, Rμ¼ 200 Hz, and Tc¼ 399 μs (which are conditions similar to those in EH1), dεm ¼ 3 × 10−6dRμ–6 × 10−3dRs. By taking the average over a run, the induced systematic uncertainty from variations in Rs or Rμ was negligible.
Rswas estimated as the average of an upper and lower limit. The upper limit was derived from the total number of AD events after applying muon-event vetoes. These events were dominantly singles but included DCs and multiple coincidences. The lower limit was derived from the number of singles plus DCs that did not satisfy the coincidence-distance criterion. These DCs were dominantly accidentals. Time-averaged values of Rsare listed in TableIIfor each AD. The difference between the two limits was assigned as the systematic uncertainty of Rs and propagated to RAcc, resulting in 0.18%, 0.16% and 0.05% uncertainties of the accidental rate in EH1, EH2, and EH3, respectively. The
Delayed Energy [MeV]
2 3 4 5 6 7 8 9 10 Entries/0.01 MeV 0 500 1000 1500 2000 2500 Near halls Far hall
FIG. 3. Reconstructed delayed-energy distribution after subtracting the accidental background for all four ADs in EH3 (black) and all four ADs in EH1 and EH2 (red), where the far-hall spectrum has been normalized to the area of the near-halls spectrum. (621 days of data.)
Date (Year/Month/Day) 12/01/01 12/07/01 12/12/31 13/07/02 13/12/31 Single-event rate [Hz] 19 20 21 22 23 24 25 26 EH1-AD1 EH1-AD2 EH2-AD1 EH2-AD2 EH3-AD1 EH3-AD2 EH3-AD3 EH3-AD4
FIG. 4. Rate of uncorrelated single events vs. time for each AD. Rates stabilized several months after water shields were filled (EH3 was filled less than a month before data-recording began).
larger uncertainties for the near halls are due to the higher rates of IBD reactions from reactor antineutrinos, which enlarged the upper limits. Figure4shows Rsas a function of time for each AD, where a downward trend began after the water shields were filled. During the first few weeks, Rs decreased by < 0.05 Hz per day for near-hall ADs and by < 0.08 Hz per day for far-hall ADs. The near-hall water shields were filled earlier and so, the AD rates stabilized earlier. Considering that Rswas calculated every 2-3 days, the uncertainty introduced to RAcc by these trends was estimated to be < 2 × 10−5, which is more than an order of magnitude smaller than the uncertainty in EH3. There were also instantaneous increases of Rs, which were caused by muon-generated spallation products such as 9Li and 8He (Sec. VI A), and spallation neutrons (Sec. VI B). From a study of Rsvs. time after muon-event vetoes, the impact of these products was estimated to be negligible.
Two methods were used to validate the subtraction of the accidental background. The first method used the distribution of distance between the prompt and delayed events, which was dominated by accidental coincidences
at large separations. After subtracting the accidental back-ground, the resulting number of correlated DCs with large separations is expected to be zero. Figure 5 shows the distribution of distance between the prompt and delayed events for DCs, accidentals, and correlated DCs. The two upper panels of Fig. 5 contain calculations of the relative difference between the measured number of double coinci-dences (NDC) and the predicted number of accidentals (NAcc), beyond 200 cm. These differences are consistent with zero with respect to their statistical uncertainties. A constant fit in the bottom panel also shows that the distribution of selected nH IBD candidates (NCor) beyond 200 cm is consistent with an expected fraction of about 0.05%, which was determined from Monte Carlo simulation. This fraction corresponds to an expected fitted constant of about0 ð3Þ entries=2 cm for the far (near) hall(s).
The subtraction of the accidental background was also validated by the distribution of time between prompt and delayed events. Figure 6 shows the distribution of time between prompt and delayed events for DCs, accidentals, and correlated DCs. The two upper panels of Fig.6contain calculations of the relative difference between the measured Distance [mm] 1000 2000 3000 4000 Entries/2 cm 0 20000 40000 60000
80000 Before subtraction: Far hall
Double-coincidences (DCs) Accidentals predicted N predicted -N measured N 0.05%(stat.) ± = -0.01% Distance [mm] 1000 2000 3000 4000 Entries/2 cm 0 20000 40000 60000 80000
Before subtraction: Near halls Double-coincidences (DCs) Accidentals predicted N predicted -N measured N 0.06%(stat.) ± = -0.12% Distance [mm] 0 1000 2000 3000 4000 5000 Entries/2 cm 0 10000 20000 30000 40000 After subtraction:
correlated DCs (primarily IBDs) Far hall
Near halls
Far hall constant fit:
/ndf = 146.9/149) 2 χ 13.3 ( ± 0.7
Near halls constant fit: /ndf = 140.5/149) 2 χ 12.1 ( ± -16.6 Distance [cm] 0 100 200 300 400 500
FIG. 5. Distributions of the distance between the prompt and delayed events of all measured double coincidences and of the predicted accidental backgrounds (black points) in the far hall (top panel) and near halls (middle panel). The bottom panel shows the distance distributions after subtracting the accidental backgrounds for the near halls (blue) and the far hall (red). See the text for details.
s µ / 10 3 10 × Entries 440 460 480 500 10
Before subtraction: Near halls Double-coincidences (DCs) Accidentals predicted N predicted - N measured N 0.02%(stat.) ± = 0.02% s µ / 10 3 10 × Entries 635 640 645
Before subtraction: Far hall Double-coincidences (DCs) Accidentals predicted N predicted - N measured N 0.02%(stat.) ± = 0.04% s] µ Capture Time [ 0 200 400 600 800 1000 1200 1400 s µ / 10 3 10 × Entries 0 20 40 60 After subtraction:
correlated DCs (primarily IBDs) Far hall
Near halls
Far hall constant fit: 126 ± 248 /ndf = 33.3/49) 2 χ (
Near halls constant fit: 149 ± 83 /ndf = 30.3/49) 2 χ (
FIG. 6. Distributions of the time between the prompt and delayed events of all measured double coincidences and of the predicted accidental backgrounds (black points) in the far hall (top panel) and near halls (middle panel). The bottom panel shows the time distributions after subtracting the accidental backgrounds for the near halls (blue) and the far hall (red). See the text for details.
number of double coincidences (NDC) and the predicted number of accidentals (NAcc), beyond 1000 μs. These differences are consistent with zero with respect to their statistical uncertainties. A constant fit in the bottom panel also shows that the distribution of selected nH IBD candidates (NCor) beyond 1000 μs is consistent with an expected fraction of 0.7%, which was determined from Monte Carlo simulation. This fraction corresponds to an expected fitted constant of about16 ð110Þ entries=10 μs for the far (near) hall(s).
VI. CORRELATED BACKGROUNDS
After the accidental background was subtracted to obtain NCor, correlated backgrounds were subtracted to obtain the number of measured nH IBDs (NIBD). In EH3 (EH1), NIBD=NCor ¼ 99.2% (99.0%). Correlated backgrounds consist of prompt and delayed events that originate from a single source and satisfy the IBD selection criteria. These backgrounds are primarily from cosmogenic muon-induced 9Li=8He isotopes and spallation neutrons, and neutrons from 241Am-13C calibration sources interacting with the SSV and its appendages. The 13Cðα; nÞ16O background is less significant for the nH-IBD analysis than for the nGd-IBD analysis and is briefly discussed.
A. 9Li=8He background
Cosmogenic muons and their spallation products interact with the 12C in organic liquid scintillators, producing neutrons and isotopes via hadronic or electromagnetic processes. Among the muon-induced isotopes, 9Li and 8He β−-decay to neutron-unstable excited states, immedi-ately followed by the ejection of a neutron. These β−-neutron decays mimic the prompt and delayed events of IBD reactions. The lifetimes of9Li and8He (257.2 and 171.7 ms, respectively) are longer than the muon-veto windows for a μWS or μAD (see Sec. IV B), leading to a contamination of the IBD candidate sample. The temporal relation between9Li=8He decays and prior detected muons was used to estimate the collective yield of the9Li and8He background NLi=Hein each hall. The distribution of the time between the prompt event of a DC and its preceding muon was described by a formula following Ref. [48]:
NðtÞ ¼ NLi=He½r · λLi· e−λLitþ ð1 − rÞ · λHe· e−λHet
þ NBB·λBB· e−λBBtþ NDCμ· Rμ· e−Rμt; ð8Þ where λisotope≡ Rμþ 1=τisotope and τisotope is the lifetime of the specific isotope (9Li or 8He), Rμ is the muon rate (which depends on the muon selection criteria), r is the fraction of 9Li decays among the 9Li and 8He decays, λBB≡ Rμþ 2=τB, and NBB and NDCμ are the numbers of 12B-12B coincidences and all other double coincidences
(excluding those from cosmogenically-produced isotopes), respectively.
The beta-decaying isotope12B was produced with a yield about one order of magnitude greater than the combined yield of 9Li and 8He. With its lifetime of τB≈ 29 ms, double coincidences of12B-12B originating from a single muon contributed mainly within the first ≈50 ms of the time since the preceding muon distribution. The fitted value of NLi=He changed by up to 10% when including and excluding the12B term.
The fraction of 9Li r could not be reliably determined because of the similar lifetimes of 9Li and 8He. Measurements of 9Li and 8He yields from Ref. [49]
indicate that r should be between roughly 85% and 100% at Daya Bay. Varying r in this range resulted in a 4% variation in the fitted value of NLi=Hein all halls.
To obtain a better estimate of NLi=He, NDCμwas reduced by suppressing accidentals among the double coincidences. This was done by augmenting the prompt-energy criterion from 1.5 < Ep< 12.0 MeV to 3.5 < Ep< 12.0 MeV. The measured number of9Li=8He was corrected with the efficiency of the augmented criterion with respect to the nominal criterion. This ratio was determined to be 74% by averaging measurements from all three halls with visible muon energy Evis
μ > 1 GeV (Evisμ is the detected energy that was deposited by a muon traversing the detector). The weighted average of the three measurements had a statistical uncertainty of 5%. The systematic uncertainty was estimated as the difference between the average and a Monte Carlo simulation, and therefore accounted for backgrounds in the measurements. The simulation usedβ spectra of9Li=8He decays calculated as those in Ref.[50]. The resulting prompt-energy spectrum from the simulation is shown in Fig.11, where it has been normalized to NLi=He. The difference in efficiency between the measurement and simulation was 6%, giving a total uncertainty of 8% for the efficiency of the augmented Ep criterion.
The 9Li=8He background was determined for three ranges of Evis
μ : 0.02–1.0 GeV, 1.0–2.5 GeV, and > 2.5 GeV. The highest energy range was defined as such because it identically defines aμsh, which was vetoed for 1 s (see TableI) and therefore contributed only Oð1Þ% of the total9Li=8He background. The lowest energy range was defined as such because it could not provide a reliable fit of 9Li=8He due to its higher R
μ and lower signal-to-back-ground ratio: relative to the middle energy range, Rμwas 14 (11) times greater and NLi=He=NDCμwas about 5 (10) times lower, in EH1 (EH3).
To obtain a more reliable estimate of the 9Li=8He back-ground of the lowest energy range, Rμwas reduced and the signal-to-background ratio was increased, by isolating the muons that produced9Li=8He. Under the assumption that the isotopes were produced along with neutrons, every μAD
without a subsequent neutron (defined as a 1.8–12 MeVevent within20–200 μs) was excluded. The measured number of 9Li=8He was corrected with the efficiency of this alteredμ
AD definition with respect to the nominal definition. Since this ratio could not be determined for the lowest energy range, the ratio for the middle energy range was used as a proxy. This ratio was determined to be about 69% (66%) in the far (near) hall(s). A 100% uncertainty was assigned to the background for the lowest energy range, corresponding to a 1σ lower bound of 35% (33%) for the efficiency of the altered μAD definition in the far (near) hall(s).
The number of9Li=8He for both the middle and lowest energy ranges in EH1 and EH2 were determined with the combined data samples of EH1 and EH2. The energy spectra of muons in EH1 and EH2 are similar[30]such that their yields of9Li=8He per muon are expected to agree to Oð1Þ%[51,52]. The Evis
μ spectra of the two near halls were observed to differ in scale by about 7%. This was due to a 7% lower average gain of the high-charge range[53]of the EH2 electronics. After scaling the Evisμ spectrum of EH2 by 7%, the difference between the near-hall spectra was Oð1Þ% across the two energy ranges. This scaling intro-duced a negligible uncertainty to the fitted number of 9Li=8He. The muon rate R
μof the combined fit was fixed to the DC-weighted average of the measured muon rates in the two near halls. Combining the uncertainties of the measured muon rates (0.3%) and numbers of DCs (1%), the weighted average had a 0.2% uncertainty. This 0.2% uncertainty of Rμ corresponded to a 27% change in the number of9Li=8He via Eq.(8)for the middle energy range. The 0.2% uncertainty had a negligible impact on the lowest energy range because its muon rate was reduced as described above. The fitted number of9Li=8He was divided among the near halls according to their measured muon rates (after scaling EH2) multiplied by their DAQ times.
Examples of fits to the time since the preceding muon without the 12B term for Evis
μ > 1.0 GeV are shown in Fig.7. The green areas represent the noncosmogenic DCs and the red areas represent the 9Li=8He DCs. For presen-tation purposes, the plots use wider bins than the actual fits. Uncertainties were from statistics, the9Li fraction r, the contribution of12B, the augmented Ep selection criterion, the alteredμADdefinition for the lowest energy range, and binning effects. The total uncertainty of the 9Li=8He background was determined from the combination of all components of uncertainty, and was dominated by stat-istical uncertainty.
Table II lists the determined rate of background DCs due to 9Li=8He in each hall. The rate was calculated by dividing the estimated NLi=Heby TDAQεμεm and correcting for the efficiencies of the altered definitions of the Epand μAD criteria.
Since the nH- and nGd-IBD analyses used different data samples, and the efficiencies were determined with distinct
methods, there was no correlation of the 9Li=8He back-ground determinations between the nH- and nGd-IBD analyses.
B. Fast-neutron background
In addition to producing radioactive isotopes such as9Li and 8He, cosmogenic muon interactions can generate energetic neutrons via spallation. Upon reaching an AD, a neutron may scatter off a proton and then capture on hydrogen, creating a prompt-delayed coincidence. Given the high efficiency with which μWS’s are detected, the neutrons that contribute to this background predominantly originate from the rock surrounding an OWS. Because the LS volume is more accessible than the GdLS volume to the externally-produced neutrons, this background is signifi-cantly higher than for the nGd-IBD analysis.
A Monte Carlo simulation of neutrons induced from muons in the water shields was performed. An empirical parametrization for neutron production from cosmogenic muons[54]and the estimated average muon energy in an experimental hall [30] were used to generate the initial kinetic energy and zenith angle distributions of the neu-trons. The resulting prompt-energy spectra of the simulated neutrons are shown in Fig.8. The increase of events with decrease of energy in the LS volume is due to the lesser containment of the recoil protons within the LS volume: the protons that recoil from fast neutrons that capture in the LS volume are closer to the boundary of the scintillating region compared to those associated with fast neutrons that capture in the GdLS volume, and thus, are more likely to deposit less energy in scintillator.
To determine the fast neutron background spectrum, a sample of spallation neutrons was obtained by slightly
0.5 1 1.5 2 2.5 3 3.5 4 Events / 0.1s 2000 2500 3000 3500 > 1.0 GeV) vis μ Data (E He events 8 Li/ 9 Fit:
Fit: double-coincidence events
EH1+EH2
Time since the preceding muon [s]
0.5 1 1.5 2 2.5 3 3.5 4 Events / 0.1s 0 50 100 150 EH3
FIG. 7. Examples of fits of the time since the preceding muon in EH1 þ EH2 (top) and EH3 (bottom) for Evis
μ > 1.0 GeV. The green area is the noncosmogenic double-coincidence component and the red area is the9Li=8He component.
modifying the nominal IBD selection criteria: the upper prompt-energy criterion was removed and the OWS muon-event veto was excluded. Muons identified with the IWS were still vetoed to avoid confusing a spallation neutron with a muon event in an AD. In addition, the prompt event was required to occur within 300 ns after an OWS-identified muon and the delayed event at least15 μs after the muon to exclude muon decays. The OWS-identified muon events were required to occur at least1200 μs after any muon events in an AD or the IWS. The prompt recoil-energy spectrum of the OWS-identified spallation neutrons from EH1 is shown in Fig. 9. Figure 9 also shows the prompt-energy distribution of IBD candidates without the upper Ep criterion and the spectrum obtained from
the simulation. The OWS-identified and simulated spectra were normalized to the IBD candidates above 12 MeV, revealing consistent shapes.
Plotting the prompt recoil-energy spectrum in a log-log scale (see the inset of Fig. 9) shows that the low-energy portion of the spectrum up to several tens of MeV is consistent with a power law [NðEÞ ¼ N0E−a], while there is a distinct energy-dependence at higher energies. The entire spectrum could be fit after adding one degree of freedom to the power law; namely, extending the exponent to have a first-order dependence on energy:
NðEÞ ¼ N0 E E0 −a−E E0 : ð9Þ
The fit of Eq.(9) resulted in a χ2per degree of freedom close to 1 for each hall. Bin widths of 2 MeV were selected for the near halls based on the stability of the fit parameters and theχ2per degree of freedom. Due to the lower statistics of EH3, the corresponding bin width was 3 MeV. The value of a was consistent among the three halls, yielding an average of0.690 0.023. The value of E0averaged toð101.7 2.1Þ MeV for the near halls and wasð110 10Þ MeV for the far hall.
The fast neutron background and its uncertainty were both estimated as in Ref. [12]. The background was estimated as the number of events within the nominal prompt-energy selection window (1.5 < Erec < 12 MeV) in the normalized OWS-identified spectrum of each hall. The spectrum was normalized to the extended IBD spec-trum from all the ADs in a hall, between 12 and 300 MeV. The systematic uncertainty was estimated using both the OWS-identified and extended IBD spectra. First, the extended IBD spectrum of each hall was fit between 12 and 300 MeV with the power law given in Eq.(9). Then, the difference was taken between the integral of the function and the number of events in the normalized OWS-identified spectrum, with Erec between 1.5 and 12 MeV. The largest relative difference among the three halls (6% in EH3) was assigned to be the systematic uncertainty for each hall. In addition, each hall had a distinct fit uncertainty, which included the statistical uncertainty and was about 6%, 7%, and 18% for EH1, EH2, and EH3, respectively. The results are listed for each experimental hall in TableII.
There was no significant correlation between the nH- and nGd-IBD fast neutron analyses because of their different selection criteria and independent event samples.
C. Am-C calibration source background One of the calibration sources deployed from each of the three ACUs atop an AD was an241Am-13C neutron source with a detected rate of 0.7 Hz [55]. Neutrons from these sources could inelastically scatter with the nuclei in the surrounding steel (SSV, ACU enclosures, etc.) and then
Prompt Energy [MeV]
20 40 60 80 100 Entries/2 MeV 0 20 40 60 80 100 120 Simulation Total
Fast neutrons captured in LS Fast neutrons captured in GdLS
FIG. 8. Simulated prompt-recoil-energy spectra of spallation neutrons produced in the IWS or OWS by cosmogenic muons. See text for details.
Prompt Energy [MeV]
20 40 60 80 Entries/2 MeV 0 100 200 300 400 500 600 700 800 10 102 Entries/2 MeV 1 10 2 10 3 10
Data: IBD candidates Data: fast-n (normalized) MC: fast-n (normalized)
Prompt Energy [MeV]
FIG. 9. Reconstructed prompt recoil-energy spectra of fast spallation neutrons from IBD candidates in EH1 with the upper Ep limit removed (black line), OWS-identified muons (blue points), and simulation (red points). The latter two spectra were normalized to the area of the extended IBD spectrum. The green curve is the fit of the extended IBD spectrum using a first-order power law (see the text). The inset is a log-log scaling of the plot.
capture on Fe, Cr, Ni, or Mn within the steel, producingγ’s that could enter the scintillating regions and satisfy the IBD selection criteria. During the pause to install the final two ADs in the summer of 2012, two of the three Am-C sources were removed (from ACU-B and -C) from each AD in EH3, reducing this background in EH3 by about 40% relative to the previous analysis [15].
This background was estimated using a special Am-C source [56] whose neutron emission rate was approxi-mately 80 times higher than the Am-C calibration sources. The special source was positioned on the top of EH3-AD2 near ACU-B for about 10 days during the summer of 2012. Figure 10 shows the resulting distribution of the recon-structed vertical position of delayed events, which exhibits an excess at positive z (the top half of the AD). For comparison, the distribution from the adjacent EH3-AD1 (which had only an Am-C calibration source in ACU-A) is shown over the same period, exhibiting no apparent asymmetry. The distributions of the vertical position of prompt events are similar.
The number of background DCs from the special Am-C source NSpecialwas estimated by subtracting NDC of EH3-AD1 from NDC of EH3-AD2 during the same period, resulting in NSpecial¼ 137 41.6. The vertical positions of both the prompt and delayed events were required to be in the top half of each AD (zp> 0 and zd> 0).
The intensity of the special Am-C source was scaled to the intensities of the Am-C calibration sources of each AD using“delayed-type” events, which are defined as singles that satisfy the delayed-energy criterion. The relatively low energy of the nH γ selection admitted significant radio-active contamination into this sample of events. To avoid this contamination, the higher-energy nGd delayed-type events were used. In Ref.[56], the number of nGd delayed-type events due to an Am-C source ½NAmC-dtypenGd was
estimated by the asymmetry of the vertical position dis-tribution, which was similar to that in Fig.10. The number of background DCs from each Am-C calibration source NAmC was estimated as
NAmC¼ NSpecial NAmC-dtype NSpecial-dtype nGd ; ð10Þ
where NAmC-dtype is counted over the entire 621-day data period. The nGd ratio in Eq.(10)was about 0.12 for the far hall and 0.23 for the near halls. The uncertainty of NAmC was comprised of the 30% statistical uncertainty of NSpecial and an approximate 40% systematic uncertainty shared with the nGd-IBD analysis from a difference in delayed-type event rates among the near- and far-hall ADs. This gives a total uncertainty of 50% for the Am-C background. TableIIlists the rate of Am-C background DCs, which is NAmC divided by TDAQεμεm, for each AD. The prompt-energy spectrum of the Am-C background was modeled with an exponential, which was determined from both the simulation and the data with the special Am-C source. The spectrum is shown in Fig.11.
For the nGd-IBD analysis, this background had a 45% total uncertainty. Considering the common 40% systematic uncertainty, the Am-C background determination was found to have a correlation coefficient of about 0.7 between the nH- and nGd-IBD analyses:
40% · 40%
50% · 45%¼ 0.7: ð11Þ
D. 13Cðα;nÞ16O background
The 13Cðα; nÞ16O background is from four dominant sources of alpha decays in the liquid scintillator: the227Ac (in the GdLS), 238U, and 232Th decay chains and 210Po, which is produced in the decay of 222Rn. The (α, n) background rate was roughly estimated using the rates from the nGd-IBD analysis [12] and the ratio of the nH/nGd IBD selection efficiencies. The estimate in EH3 was approximately0.02 0.01 DCs per AD per day. This estimate is expected to be conservative because of the lower activity of the LS relative to the GdLS: using the selection criteria outlined in Ref.[45], the concentration of232Th was determined to be a few hundred times greater in the GdLS while that of238U was estimated to be similar. The uncertainty of the13Cðα; nÞ16O background contrib-uted negligibly to the total uncertainty of sin22θ13 (see TableIV) and therefore, this background was neglected in this analysis.
E. Summary of correlated backgrounds The rates of the correlated backgrounds are summarized in Table II and their prompt-energy distributions are illustrated in Fig.11for EH3. The rates of nH IBDs after
-2 -1 0 1 2 Entries/0.06 m 0 20 40 60 80 100 120 140
160 Without the special Am-C With the special Am-C
d
z [m]
FIG. 10. Distribution of vertical position of delayed events for EH3-AD2 with both its Am-C calibration source and the special Am-C source (solid blue line), and EH3-AD1 with only its Am-C calibration source (dashed red line). All sources were located at the tops of the detectors: z ≈ 2.5 m.
subtracting all the backgrounds are listed for each AD in Table II.
With respect to the previous nH-IBD analysis[15], the absolute uncertainty of the dominant9Li=8He background was reduced by about 30% because of increased statistics and various improvements in the method. Reductions in the uncertainties of the fast neutron and Am-C backgrounds resulted primarily from an improved method of estimation and a fit of the full spectrum, and the removal of some Am-C sources, respectively. The overall uncertainty of backgrounds was reduced by 30%.
Comparing to the nGd-IBD analysis, the fast neutron background was about four to five times larger relative to the IBD rate in EH3, while the 9Li=8He and 241Am-13C backgrounds were equal within uncertainties, and the 13Cðα; nÞ16O background was about half as large. The absolute uncertainty of the fast neutron background was about four to five times larger relative to the IBD rate in EH3, while the uncertainties of the9Li=8He and241Am-13C backgrounds were similar, and the uncertainty of the 13Cðα; nÞ16O background was about half that of the nGd-IBD analysis. The impact of the uncertainties of the background estimations on the uncertainty of sin22θ13 is described at the end of Sec. VIII B.
Due to the sharing of uncertainty components between the nGd- and nH-IBD analyses, the Am-C background determinations had a correlation coefficient of about 0.7, while the 9Li=8He and fast neutron background determi-nations were uncorrelated, and the 13Cðα; nÞ16O back-ground was neglected in this analysis.
VII. DETECTION EFFICIENCY
The expected number of selected IBDs from one AD was determined according to Eq.(1), in which the efficiency-weighted number of target protons was calculated
considering antineutrino interactions in the GdLS, LS, and acrylic volumes v:
Nε¼ εμεm XGdLS;LS;acry v Np;vεEp;vεT;vεEd;v εD; ð12Þ whereεμandεmare the muon-veto and multiplicity selection efficiencies of the AD, Npis the number of target protons of the AD, εE
p and εEd are the prompt- and delayed-energy
selection efficiencies, andεTandεDare the coincidence-time and -distance selection efficiencies, respectively. The PMT flash selection efficiency (Sec.IV B 1) is not included due to its negligible inefficiency.
The number of target protons was determined for each AD from measurements made prior to AD deployment. The muon-veto, multiplicity, and distance selection efficiencies were determined with data. The prompt- and delayed-energy, and time selection efficiencies were determined with a simulation using a predicted antineutrino spectrum such as described in Sec.III. The simulation framework of Daya Bay is based on GEANT4[57]and has been validated with comparisons to data[45].
In comparing the IBD rates among the far hall and near halls, efficiencies and uncertainties common to all the ADs are irrelevant. The AD-uncorrelated uncertainties of the efficiencies, which reflect the identicalness of the ADs, were determined by comparing data among all eight ADs. The uncertainties of εμ and εm were negligible (see Sec.IV B). The remaining quantities in Eq.(12)and their uncertainties, are discussed in this section. The contribution from IBDs in the MO is described in Sec.VII E.
A. Prompt-energy selection
The first selection criterion applied to AD events (after rejecting PMT flashes) was Erec> 1.5 MeV. Ultimately, this selection affected only prompt events because of the more stringent requirement applied to delayed events. The prompt-energy selection efficiency and its uncertainty were determined with simulation in which the energy scale was aligned to that of the data (see Sec.IVA). The efficiency was defined as the number of IBD reactions N that satisfied the prompt-energy criterion divided by the total number of IBD reactions:
εEp¼
NðEp> 1.5 MeVÞ NIBD
: ð13Þ
The higher-energy requirement of Ep< 12 MeV was estimated to contribute negligibly to the inefficiency and uncertainty, as suggested by Fig.11. The efficiency in the LS volume was lower than that in the GdLS volume because a larger fraction of the annihilationγ’s deposited energy outside the scintillating volumes. This fraction was largest for IBDs occurring in the acrylic elements. The net efficiency of all volumes was about 90%.
Prompt Energy [MeV]
2 3 4 5 6 7 8 9 10 11 12 Entries/0.3 MeV 1 10 2 10 3 10 4 10 Far hall IBD candidates Accidentals He 8 Li/ 9 Fast neutrons Am-C
FIG. 11. Reconstructed prompt-energy distributions of the measured double coincidences after IBD selection (black points) and estimated backgrounds, for the sum of all ADs in EH3.
The AD-uncorrelated uncertainty of the efficiency was estimated as the change in efficiency after shifting the energy scale by 0.5%. The relative change in efficiency was about 0.1%. The 0.5% shift is an estimate of the AD-uncorrelated uncertainty of the energy scale that was determined by comparing the fitted means of the nH-IBD γ and 212Bi α peaks of all eight ADs. For reference, the estimated uncertainty of the energy scale in the GdLS volume was 0.2% [12].
1. Variation with baseline
The L=E-dependence of neutrino oscillation [see Eq. (3)] implies that the shape of the neutrino energy spectrum changes with baseline L. Therefore, the efficiency of the prompt-energy criterion varies with baseline. The impact of this dependence on the multiple reactor-detector pairs at Daya Bay was estimated by applying oscillation to a predicted reactor antineutrino spectrum as a function of baseline. At each baseline[36], the IBD selection efficiency was determined with simulation samples for the GdLS, LS, and acrylic volumes. The simulation accounted for energy deposited outside the scintillator volumes, and the non-linearity[12], nonuniformity, and resolution of the detector energy-response. The oscillation parameter values were the same as those in Sec.III. The resulting variation in the IBD selection efficiency as a function of baseline is illustrated for the LS region in Fig.12. The shape of the curve is due to the span of the data in the L=E domain. For the near halls (smaller L), more oscillation occurred for lower energy antineutrinos, which decreased the number of IBD reac-tions with prompt energy below threshold and thus, increased the efficiency. For illustration, the mean energy of a prompt event without oscillation was 3.626 MeV while
the corresponding energy in EH1 (EH2) due to antineu-trinos from the two (four) nearby reactors with oscillation was 3.630 (3.632) MeV. These numbers are representative of the first 4 (8) points in Fig.12. For the far hall (larger L), more oscillation occurred at median antineutrino energies and about equally at higher and lower energies, resulting in a net decrease in efficiency.
In the fit for sin22θ13 (Sec. VIII B), the IBD selection efficiencies in the GdLS, LS, and acrylic volumes of each AD were multiplied by a correction factor for each reactor baseline (6 reactors × 8 ADs ¼ 48 baselines) [36]. The fit was first performed without correction factors. The resulting value of sin22θ13was then used to generate a set of correction factors and then fit again. This iterative approach was tested using Asimov data samples generated according to Eq.(1)
with known values of sin22θ13. Several values of sin22θ13 were tested and all fits converged consistently with negligible bias. No additional uncertainty was assigned. Although several iterations were performed, the value of sin22θ13 converged within the precision reported in this article after only one iteration. The results of the fits without corrections were about 4% larger than the true values for the Asimov data samples and the converged value for the measured data. This variation of the IBD selection efficiency was estimated to be an order of magnitude smaller for the nGd-IBD analysis, which required Ep> 0.7 MeV.
B. Coincidence-time selection
The efficiency of the coincidence-time selection was different for each detector volume v due to the different densities and neutron-capture cross sections of the materi-als. The efficiency was defined as
εT ¼
Nð1 < tc < 400 μs; Ep> 1.5 MeVÞ NðEp> 1.5 MeVÞ
; ð14Þ and was determined with simulation. The efficiency in the LS volume was about 85% and that in the GdLS volume was about 99% due to the shorter neutron-capture time of nGd. These values were validated with data.
The neutron-capture time was studied in the GdLS and LS volumes by fitting for the mean neutron-capture time with the following formulas:
NGdðtÞ ¼ N0;Gd· ð1 þ αÞτ1 Gd e−t=τGd− α1 τ0e −t=τ0 þ C1 NLSðtÞ ¼ N0;LS· 1 τLS e−t=τLSþ C 2; ð15Þ
whereα balances two terms, the first corresponding to the capture of a neutron at thermal energies [Oð0.025Þ eV] with time constantτGd, and the second representing the difference in capture cross section between thermal and IBD neutron energies [Oð0.015Þ MeV], with effective time constant τ0. The capture-time spectrum in LS is due almost solely to nH which can be represented by a single exponential. This is
Baseline [m]
0 500 1000 1500 2000 2500
Efficiency Correction Factor
0.995 0.996 0.997 0.998 0.999 1 1.001 1.002 1.003 1.004
FIG. 12. An example of the relative variation of the IBD selection efficiency with baseline using the value of sin22θ13 presented in this article. This correction curve is for the LS region. The red circles denote the 48 reactor-detector pairs. Their error bars and the error band are identically defined by the uncertainty of sin22θ13.
![TABLE I. IBD selection criteria for the nH and nGd [12] analyses. See text for details.](https://thumb-ap.123doks.com/thumbv2/9libinfo/7690327.143254/6.918.77.446.113.399/table-ibd-selection-criteria-ngd-analyses-text-details.webp)
