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Improved measurement of electron antineutrino disappearance at Daya Bay
View the table of contents for this issue, or go to the journal homepage for more 2013 Chinese Phys. C 37 011001
Improved measurement of electron antineutrino
disappearance at Daya Bay
∗F. P. An()1 Q. An()2 J. Z. Bai()1 A. B. Balantekin3 H. R. Band3 W. Beriguete4 M. Bishai4 S. Blyth5 R. L. Brown4 G. F. Cao()1 J. Cao()1 R. Carr6 W. T. Chan4 J. F. Chang()1 Y. Chang5 C. Chasman4 H. S. Chen()1 H. Y. Chen7 S. J. Chen()8 S. M. Chen()9 X. C. Chen()10 X. H. Chen()1 X. S. Chen()1 Y. Chen()11 Y. X. Chen()12 J. J. Cherwinka3 M. C. Chu()10 J. P. Cummings13 Z. Y. Deng()1 Y. Y. Ding()1 M. V. Diwan4 E. Draeger14 X. F. Du()1 D. Dwyer6 W. R. Edwards15,16 S. R. Ely17 S. D. Fang()8 J. Y. Fu()1 Z. W. Fu()8 L. Q. Ge()18 R. L. Gill4
M. Gonchar19 G. H. Gong()9 H. Gong()9 Y. A. Gornushkin19 W. Q. Gu()20 M. Y. Guan()1 X. H. Guo()21 R. W. Hackenburg4 R. L. Hahn4 S. Hans4 H. F. Hao( )2
M. He()1 Q. He( )22 K. M. Heeger3 Y. K. Heng( )1 P. Hinrichs3 Y. K. Hor23 Y. B. Hsiung24 B. Z. Hu7 T. Hu()1 H. X. Huang( )25 H. Z. Huang26 X. T. Huang()27
P. Huber23 V. Issakov4 Z. Isvan4 D. E. Jaffe4 S. Jetter1 X. L. Ji()1 X. P. Ji()28 H. J. Jiang()18 J. B. Jiao()27 R. A. Johnson29 L. Kang()30 S. H. Kettell4 M. Kramer15,16 K. K. Kwan()10 M. W. Kwok()10 T. Kwok()31 C. Y. Lai24 W. C. Lai()18 W. H. Lai7
K. Lau32 L. Lebanowski32 J. Lee15 R. T. Lei()30 R. Leitner33 J. K. C. Leung()31 K. Y. Leung()31 C. A. Lewis3 F. Li()1 G. S. Li()20 Q. J. Li()1 W. D. Li()1 X. B. Li()1 X. N. Li()1 X. Q. Li()28 Y. Li()30 Z. B. Li()34 H. Liang()2
C. J. Lin()15 G. L. Lin7 S. K. Lin32 Y. C. Lin( )10,18,31 J. J. Ling()4 J. M. Link23 L. Littenberg4 B. R. Littlejohn3,29 D. W. Liu17 J. C. Liu()1 J. L. Liu( )20 Y. B. Liu()1 C. Lu()22 H. Q. Lu()1 A. Luk()10 K. B. Luk15,16 Q. M. Ma()1 X. B. Ma()12
X. Y. Ma()1 Y. Q. Ma()1 K. T. McDonald22 M. C. McFarlane3 R. D. McKeown6,35 Y. Meng23 D. Mohapatra23 Y. Nakajima15 J. Napolitano36 D. Naumov19 I. Nemchenok19 H. Y. Ngai()31 W. K. Ngai17 Y. B. Nie()25 Z. Ning()1 J. P. Ochoa-Ricoux15 A. Olshevski19 S. Patton15 V. Pec33 J. C. Peng17 L. E. Piilonen23 L. Pinsky32 C. S. J. Pun()31 F. Z. Qi()1 M. Qi()8 X. Qian()6 N. Raper36 J. Ren()25 R. Rosero4 B. Roskovec33
X. C. Ruan()25 B. B. Shao()9 K. Shih()10 H. Steiner15,16 G. X. Sun( )1 J. L. Sun( )37 N. Tagg4 Y. H. Tam()10 H. K. Tanaka4 X. Tang()1 H. Themann4 Y. Torun14
S. Trentalange26 O. Tsai26 K. V. Tsang15 R. H. M. Tsang6 C. E. Tull15 Y. C. Tung24 B. Viren4 V. Vorobel33 C. H. Wang5 L. S. Wang( )1 L. Y. Wang( )1 L. Z. Wang()12
M. Wang()27 N. Y. Wang()21 R. G. Wang()1 W. Wang35 X. Wang()9 Y. F. Wang()1 Z. Wang()9 Z. Wang()1 Z. M. Wang( )1 D. M. Webber3 H. Y. Wei()9 Y. D. Wei( )30 L. J. Wen( )1 K. Whisnant38 C. G. White14 L. Whitehead32 Y. Williamson4 T. Wise3 H. L. H. Wong15,16 E. T. Worcester4 F. F. Wu6 Q. Wu( )27 J. B. Xi( )2
D. M. Xia()1 Z. Z. Xing( )1 J. Xu( )10 J. Xu( )21 J. L. Xu( )1
Received 23 October 2012, Revised 15 November 2012
∗Supported 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 NTU, NCTU, and NSC fund support from Taipei, 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
©2013 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd
Y. Xu()28 T. Xue()9 C. G. Yang()1 L. Yang()30 M. Ye( )1 M. Yeh4 Y. S. Yeh7 B. L. Young38 Z. Y. Yu()1 L. Zhan( )1 C. Zhang4 F. H. Zhang()1
J. W. Zhang( )1 Q. M. Zhang( )39 S. H. Zhang( )1 Y. C. Zhang( )2 Y. H. Zhang( )1 Y. X. Zhang( )37 Z. J. Zhang( )30 Z. P. Zhang( )2 Z. Y. Zhang( )1 J. Zhao( )1 Q. W. Zhao( )1 Y. B. Zhao( )1 L. Zheng( )2 W. L. Zhong( )1 L. Zhou( )1 Z. Y. Zhou( )25 H. L. Zhuang()1 J. H. Zou( )1
(Daya Bay Collaboration)
1 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 2University of Science and Technology of China, Hefei 230026
3University of Wisconsin, Madison, WI 4 Brookhaven National Laboratory, Upton, NY
5 National United University, Miao-Li 6 California Institute of Technology, Pasadena, CA 7 Institute of Physics, National Chiao-Tung University, Hsinchu
8Nanjing University, Nanjing 210093
9 Department of Engineering Physics, Tsinghua University, Beijing 100084 10Chinese University of Hong Kong, Hong Kong
11Shenzhen Univeristy, Shenzhen 518060 12North China Electric Power University, Beijing 102206
13Siena College, Loudonville, NY
14Department of Physics, Illinois Institute of Technology, Chicago, IL 15Lawrence Berkeley National Laboratory, Berkeley, CA 16Department of Physics, University of California, Berkeley, CA 17Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL
18Chengdu University of Technology, Chengdu 610059 19Joint Institute for Nuclear Research, Dubna, Moscow Region
20Shanghai Jiao Tong University, Shanghai 200240 21Beijing Normal University, Beijing 100875
22Joseph Henry Laboratories, Princeton University, Princeton, NJ 23Center for Neutrino Physics, Virginia Tech, Blacksburg, VA
24Department of Physics, National Taiwan University, Taipei 25China Institute of Atomic Energy, Beijing 102413
26University of California, Los Angeles, CA 27Shandong University, Jinan 250100 28School of Physics, Nankai University, Tianjin 300371
29University of Cincinnati, Cincinnati, OH 30Dongguan University of Technology, Dongguan 523808
31Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong 32Department of Physics, University of Houston, Houston, TX 33Charles University, Faculty of Mathematics and Physics, Prague
34Sun Yat-Sen (Zhongshan) University, Guangzhou 510275 35College of William and Mary, Williamsburg, VA
36Rensselaer Polytechnic Institute, Troy, NY 37China Guangdong Nuclear Power Group, Shenzhen 518028
38Iowa State University, Ames, IA 39Xi’an Jiaotong University, Xi’an 710049
Abstract: We report an improved measurement of the neutrino mixing angle θ13 from the Daya Bay Reactor Neutrino Experiment. We exclude a zero value for sin22θ13 with a significance of 7.7 standard deviations. Electron antineutrinos from six reactors of 2.9 GWth were detected in six antineutrino detectors deployed in two near (flux-weighted baselines of 470 m and 576 m) and one far (1648 m) underground experimental halls. Using 139 days of data, 28909 (205308) electron antineutrino candidates were detected at the far hall (near halls). The ratio of the observed to the expected number of antineutrinos assuming no oscillations at the far hall is 0.944±0.007(stat.)±0.003(syst.). An analysis of the relative rates in six detectors finds sin22θ
13=0.089±0.010(stat.)±0.005(syst.) in a three-neutrino framework.
Key words: neutrino oscillation, neutrino mixing, reactor, Daya Bay
1
Introduction
Observations of neutrinos and antineutrinos pro-duced in the sun, the atmosphere, reactors, and from particle beams provide overwhelming evidence that the flavors of neutrinos change (oscillate) [1–5]. The pre-ponderance of data support a three-neutrino framework where three flavor states (νe, νμ,ντ) are superpositions of three mass states (ν1, ν2, ν3). This mixing can be quantified using a unitary 3×3 mixing matrix described in terms of three mixing angles (θ12,θ23,θ13) and a CP violating phase (δ) [6, 7]. Neutrino oscillations are also dependent on the differences in the squares of the neu-trino masses.
The Daya Bay collaboration recently measured a non-zero value for sin2
2θ13 = 0.092 ± 0.016(stat.) ± 0.005(syst.) [8], an observation consistent with previous and subsequent experimental results [4, 9–11]. In ab-solute terms, the value of θ13 is now known with bet-ter precision than either of the other two mixing angles. Constraining the value of θ13 increases the constraints on the other mixing parameters (mixing angles and mass squared differences) through a global fit of all available oscillation data [12, 13].
For reactor-based experiments, in a three-neutrino framework, an unambiguous determination of θ13can be extracted via the survival probability of the electron an-tineutrinoνeat short distances (O(km)) from the reac-tors
Psur≈1−sin22θ13sin2(1.267Δm231L/E), (1) where Δm2
31 can be approximated by Δm 2 atm = (2.32+0−0.08.12)×10−3eV2 [14], E is the νe energy in MeV and L is the distance in meters between the νe source and the detector (baseline). The near-far arrangement of antineutrino detectors (ADs), as illustrated in Fig. 1, allows for a relative measurement by comparing the ob-servedνe rates at various distances. With functionally identical ADs, the relative rate is independent of corre-lated uncertainties, and uncorrecorre-lated reactor uncertain-ties are minimized.
The results reported here were derived using the same analysis techniques and event selection as our previous results [8], but were based on data collected between 24 December 2011 and 11 May 2012, a 2.5 fold increase in statistics. A blind analysis strategy was adopted for our previous results, with the baselines, the thermal power histories of the cores, and the target masses of the ADs hidden until the analyses were finalized. Since the base-lines and the target masses have been unveiled for the six ADs, we kept the thermal power histories hidden in this analysis until the analyses were finalized.
2
The experiment
2.1 Site
The Daya Bay nuclear power complex is located on the southern coast of China, 55 km to the northeast of Hong Kong and 45 km to the east of Shenzhen. A de-tailed description of the Daya Bay experiment can be found in [15, 16]. As shown in Fig. 1, the nuclear com-plex consists of six reactors grouped into three pairs with each pair referred to as a nuclear power plant (NPP). All six cores are functionally identical pressurized wa-ter reactors, each with a maximum of 2.9 GW thermal power [17]. The last core started commercial operation on 7 August 2011. The distance between the cores for each pair is 88 m. The Daya Bay cores are separated from the Ling Ao cores by about 1100 m, while the Ling Ao-II cores are around 500 m away from the Ling Ao cores.
Fig. 1. Layout of the Daya Bay experiment. The dots represent reactor cores, labeled as D1, D2, L1, L2, L3 and L4. Six antineutrino detectors (ADs) were installed in three experimental halls (EHs).
Three underground experimental halls (EHs) are con-nected with horizontal tunnels. For this analysis, two antineutrino detectors (ADs) were located in EH1, one in EH2, and three near the oscillation maximum in EH3 (the far hall). The overburden in equivalent meters of water (m.w.e.), simulated muon rate and average muon energy are listed in Table 1.
Table 1. Vertical overburden, muon rateRμ, and
average muon energy<Eμ> of the three EHs.
overburden (m.w.e) Rμ(Hz/m2) <Eμ>/GeV
EH1 250 1.27 57
EH2 265 0.95 58
The distances from the six ADs to the six cores are listed in Table 2. All distances have been surveyed with the Global Positioning System (GPS) and with modern theodolites utilizing two major control networks built over several months. The network surveyed using GPS is within the campus of the power plant but outside of the tunnel. The other network is inside the tunnel sys-tem, surveyed using Total Station, an electronic/optical instrument widely used in modern surveying. The dou-ble traverse survey network was laid down in a closed ring in the 7 m wide tunnels. The Total Station survey included the power plant campus to link the two control networks. The survey from the anchors at the entrance of each experimental hall to each AD was completed dur-ing the installation of each AD usdur-ing a laser tracker. The coordinates of the AD center were further deduced us-ing the AD survey data collected durus-ing AD assembly. The coordinates of the geometrical center of the reactor cores were provided by the power plant relative to four anchor points outside of each nuclear island. The survey data were processed independently by three groups with different software. The uncertainty of the baselines was determined to be 28 mm as reported in Ref. [8]. Recently another closed traverse survey was completed utilizing a different tunnel entrance and the top of the mountain. The largest baseline difference between the two surveys is 4 mm and the uncertainty in the baselines has been reduced to 18 mm. The uncertainty has seven significant contributions, the largest being 12.6 mm due to the pre-cision of the GPS survey. The second largest is 9.1 mm due to fitting uncertainties associated with the linking of the GPS and the Total Station networks. When com-bined with the uncertainties of the fission gravity cen-ter (described in Sec. 6), the baseline uncertainties were found to make a negligible contribution to the oscillation uncertainties.
Table 2. Baselines from antineutrino detectors AD1-6 to reactors D1, D2, and L1-4 in meters.
D1 D2 L1 L2 L3 L4 AD1 362 372 903 817 1354 1265 AD2 358 368 903 817 1354 1266 AD3 1332 1358 468 490 558 499 AD4 1920 1894 1533 1534 1551 1525 AD5 1918 1892 1535 1535 1555 1528 AD6 1925 1900 1539 1539 1556 1530 2.2 Antineutrino detectors
The νes are detected via the inverse β-decay (IBD) reaction,νe+p→e++n, in gadolinium-doped liquid scin-tillator (Gd-LS) [18, 19]. The coincidence of the prompt scintillation from the e+and the delayed neutron capture on Gd provides a distinctiveνe signature. The positron carries almost all of the kinetic energy of the antineu-trino, thus the positron energy deposited in the liquid
scintillator is highly correlated with the antineutrino en-ergy. The neutron thermalizes before being captured on either a proton or a gadolinium nucleus with a mean cap-ture time of∼30 μs in Gd-LS with 0.1% Gd by weight. When a neutron is captured on Gd, it releases several gamma-rays with a total energy of∼8 MeV, and is thus easily distinguished from the background coming from natural radioactivity. Only neutrons that were captured on Gd were selected as the delayed signal of an antineu-trino event in this analysis.
Each AD has three nested cylindrical volumes sep-arated by concentric acrylic vessels [20] as shown in Fig. 2. The innermost volume holds 20 t of Gd-LS with 0.1% Gd by weight and serves as the antineutrino tar-get. The middle volume is called the gamma catcher and is filled with 20 t of un-doped liquid scintillator (LS) for detecting gamma-rays that escape the target volume. The outer volume contains 37 t of mineral oil (MO) to provide optical homogeneity and to shield the inner volumes from radiation originating, for example, from the photo-multiplier tubes (PMTs) or the stainless steel vessel (SSV). There are 192 20-cm PMTs (Hama-matsu R5912) installed along the circumference of the SSV and within the mineral oil volume, in 24 columns and 8 rings. To improve optical uniformity, the PMTs are recessed in a 3-mm thick black acrylic cylindrical shield located at the equator of the PMT bulb.
Fig. 2. Schematic diagram of the Daya Bay detectors. Three automated calibration units (ACU-A, ACU-B, and ACU-C) are mounted on the top of each SSV as shown in Fig. 2. Each ACU is equipped with an LED, a68Ge source, and a combined source of241Am-13C and 60Co. The Am-C source generates neutrons at a rate of ∼0.5 Hz. The rates of the 60Co and 68Ge sources are about 100 Hz and 15 Hz, respectively. Since the AD is fully submerged in water, the ACUs are operated remotely. The sources can be deployed to better than
0.5 cm along a vertical line down to the bottom of the acrylic vessels. When not in use, the LED and sources are retracted into the ACUs that also serve as shielding for the sources.
2.3 Muon system
The muon detection system consists of a resistive plate chamber (RPC) tracker and a high-purity active water shield. The water shield consists of two optically separated regions known as the inner (IWS) and outer (OWS) water shields. There are 121 (160) PMTs in-stalled in the IWS and 167 (224) PMTs in the OWS in each near (far) hall. Each region operates as an inde-pendent water Cherenkov detector. The muon detection efficiency is 99.7% and 97% for the IWS and OWS, re-spectively [15]. In addition to detecting muons that can produce spallation neutrons or other cosmogenic back-grounds in the ADs, the pool moderates neutrons and attenuates gamma rays produced in the rock or other structural materials in and around the experimental hall. At least 2.5 m of water surrounds the ADs in every di-rection. Each pool is outfitted with a light-tight cover overlaying a dry-nitrogen atmosphere.
Each water pool is covered with an array of RPC modules [21, 22]. The 2 m×2 m modules are layered on a steel frame to minimize dead areas. The assembly is mounted on rails and can be retracted to provide access to the water pool. There are four layers of bare RPCs inside each module, with one layer of readout strips as-sociated with each layer of bare RPCs. The strips have a “switchback” design with an effective width of 25 cm, and are stacked in alternating orientations providing a spatial resolution of∼8 cm.
2.4 Trigger and readout
Each detector unit (AD, IWS, OWS, and RPC) is read out with a separate VME crate. All PMT read-out crates are physically identical, differing only in the number of instrumented readout channels. The front-end electronics board (FEE) receives raw signals from up to sixteen PMTs, sums the charge from all input chan-nels, identifies over-threshold chanchan-nels, records their tim-ing information, and measures the charge of each over-threshold pulse with a 40 MHz sampling rate [23]. The FEE in turn sends the number of channels over threshold and the integrated charge to the trigger system. When a trigger is issued, the FEE reads out the charge and timing information within 1 μs for each over-threshold channel, as well as the average ADC value over a 100 ns time-window immediately preceding the over-threshold condition (preADC).
Triggers are primarily created internally within each PMT readout crate based on the number of over-threshold channels (NHIT) as well as the summed charge
(E-Sum) from each FEE [24]. The system is also capa-ble of accepting external trigger requests, for example, from the calibration system. The trigger system blocks triggers when either the trigger data-buffer or an FEE data-buffer is nearly full. The number of blocked trig-gers is recorded and read out for calculating the dead time offline.
3
Data characteristics, calibration and
modelling
3.1 Data set
The data used in this analysis were collected from 24 December 2011 through to 11 May 2012. Table 3 sum-marizes the experimental livetime for each hall. Total data acquisition (DAQ) time measures the number of hours that the DAQ was collecting data, with about 2% of the DAQ time devoted to detector calibration. Stan-dard data running (Physics Data or Physics DAQ time) accounted for more than 93% of the calendar time. We further rejected about 60 hours of physics data from each hall due to excessive coherent electromagnetic pickup, PMT high voltage (HV) trips, electronic or DAQ prob-lems, or requirements of simultaneous operation in all three halls. The resulting data set (good run data or good run time) was used for analysis.
Table 3. Summary of experimental livetime in hours.
EH1 EH2 EH3
total calendar time 3322.1 3322.1 3322.1
total DAQ time 3195.4 3179.5 3171.6
physics DAQ time 3117.9 3122.0 3093.6
good run time 3061.1 3057.1 3030.5
The detector halls operated independently with a common centralized clock and GPS timing system. The analysis presented here required simultaneous operation of all three detector halls, to minimize systematic effects associated with potential reactor power excursions. Si-multaneous operation was defined as Physics Data within a given hour existing for all three detector halls. The data samples used in this analysis differed by 1% in time for the three halls. A more rigorous requirement that demands synchronization among the three halls on the scale of seconds was tested with no change to the re-ported results.
3.2 Triggered detector rates
Triggers were formed based either on the number of PMTs with signals above a ∼0.25 photoelectron (p.e.) threshold (NHIT triggers), or the charge sum of the PMTs (E-Sum triggers). AD triggers with NHIT >45 or E-Sum 65 p.e. correspond to an event energy thresh-old of∼0.4 MeV [15]. The corresponding trigger rate per
AD was <280 Hz with a negligible trigger inefficiency for IBD candidates.
The νe candidates were selected in the offline anal-ysis using the coincidence of a prompt signal from the e+ and a delayed signal due to neutron capture on Gd. A prompt-type (delayed-type) signal was defined as an event with energy in the range of 0.7–12 MeV (6– 12 MeV). The rates of prompt-type and delayed-type sin-gles that are separated in time by at least 200μs from any additional signals with an energy >0.7 MeV were of particular interest for background studies and detector stability monitoring. They are shown in Fig. 3. A veto was applied to reject events within−2 to 200 μs relative to a muon (defined in Sec. 4.1). The data were cor-rected for the corresponding inefficiencies. These rates were used to estimate the accidental background rate as described in Sec. 5.1.
The observed rate of low energy signals decreased with time. The detectors in EH1 initiated data taking on 15 August 2011 and the AD in EH2 started on 5 Novem-ber 2011. As such, these detectors (AD1-3) had reached a steady state by 24 December 2011, while the rates in AD4-6 in EH3 exhibited decaying behavior, as shown in Fig. 3.
Fig. 3. Singles rates for the six ADs. The top panel shows the prompt candidates and the bot-tom panel shows the delayed candidates.
The muon rates in the water Cherenkov detectors (IWS and OWS) were closely monitored, as shown in Fig. 4. IWS and OWS events were selected with NHIT >12. The event rates were different for the three halls due to differing muon rates in each hall and different sizes of the far hall and the near halls.
3.3 Instrumental backgrounds
A small number of AD PMTs spontaneously emit light, due to discharge within the base. These
instru-mental backgrounds are referred to as flasher events. For Daya Bay, the reconstructed energy of such events covers a wide range, from sub-MeV to 100 MeV. Two features were typically observed when a PMT flashed: the ob-served charge fraction for a given PMT was very high, and PMTs on the opposite side of the AD saw a large fraction of light from the flashed PMT. The charge pat-tern of a typical flasher event is shown in Fig. 5.
Fig. 4. Muon rates in the inner (IWS) and outer water shield (OWS) in the three experimental halls.
Fig. 5. Topology of a typical flasher event. Such events are distinctive, characterized by a single channel with substantially more charge than in surrounding PMTs, as well as excessive charge on the opposite side of the AD.
To reject flasher events, two variables, named MaxQ and Quad, were created based on the distinctive charge pattern. MaxQ is the largest fraction of the total de-tected charge seen by a single PMT (the “hottest” PMT). There are twenty-four columns of PMTs in an AD that can be divided into four quadrants. With the hottest PMT centered in the first quadrant, Quad was defined as Q3/(Q2+Q4), where Qiis the charge sum of the PMTs in the i-th quadrant. A flasher event identification vari-able (FID) was constructed based on MaxQ and Quad:
FID=log10[(MaxQ/0.45)2+(Q uad)2
Figure 6 shows the discrimination of flasher events for the delayed signal of the IBD candidates. The dis-tributions for all six ADs agree well for IBD candidates (FID<0); however, there is some variation for flasher candidates (FID>0). For the IBD analysis as well as other analyses, the rejection of flasher events was done at the beginning of the data reduction.
Fig. 6. Discrimination of flasher events (FID>0) and IBD delayed signals (FID<0). The delayed signals of IBDs have the same distribution for all six ADs while the flashers are different. The FID
<0 distributions have been scaled to equal area.
The discrimination power decreases for low energy events or events very close to PMTs. For the rejected events with FID ∼ 0, we studied the charge pattern, the energy distribution, the capture time, and the dis-tance between the vertices of the prompt and the de-layed signals, and found that some were consistent with real IBD events. By counting such events, the ineffi-ciency of the IBD selection due to the flasher rejection was estimated to be 0.02% with an uncorrelated uncer-tainty of 0.01%. The background contamination of se-lected IBD candidates was evaluated to be <10−4. Fur-thermore, such contamination was counted as accidental background (Sec. 5.1) and was subtracted. Special runs were conducted with reduced high voltage for selected PMTs to cross-check the identified PMTs that exhibited flashing. Due to the high efficiency of the FID, all AD PMTs were kept in operation, including those identified as flashing PMTs.
3.4 Energy reconstruction
In general, the energy response of the AD can depend on time, position in the fiducial volume (non-uniformity), particle species, and their energies (non-linearity). The goal of energy reconstruction was to correct for these dependencies in order to minimize the uncertainties in the AD energy scale. To achieve this goal, each AD was calibrated using LEDs, 68Ge, and 241Am-13C/60Co sources. LEDs were utilized for PMT gain calibration, while the energy calibration parameter (p.e. per MeV)
was determined with a 60Co source deployed at the de-tector center. The sources were deployed once per week to check and correct for any time dependence. Occa-sionally a PMT’s output was noisy and was temporar-ily turned off during physics data taking. The energy calibration corrected such situations. The energy cali-bration parameter for each AD is shown in Fig. 7 as a function of time. The small jumps correspond to the temporary turn-off of noisy PMTs. The energy resolu-tion was (7.5/E(MeV)+0.9)% for all 6 ADs.
Fig. 7. Calibration parameter versus time for each AD. A scan along the vertical axis utilizing the 60Co source from each of the three ACUs was used to obtain non-uniformity correction functions. The non-uniformity was also studied with spallation neutrons generated by cosmic muons, and alphas produced by natural radioac-tivity present in the liquid scintillator. The neutron en-ergy scale was set by comparing60Co events with neutron capture on Gd events from the Am-C source at the de-tector center. Additional details of energy calibration, reconstruction, and vertex reconstruction can be found in Ref. [15].
The AD energy scale uncertainty was studied by com-paring the energy peaks in all ADs using neutron capture on gadolinium from IBD and muon spallation products, alphas from Polonium decay in the Gd-LS, and each of the calibration sources. Asymmetries of the six ADs’ re-sponse are shown in Fig. 8. For each type of event, we defined the asymmetry as
Asymmetryi=E i− Ei/6 Ei/6 , (3)
where Eiis the fitted mean energy of the studied type of event of the i-th AD. The energy scale uncertainty was set at 0.5% in Ref. [15] based on extensive side-by-side studies of AD1 and AD2. Extending this to six ADs, asymmetries for all types of events in all the ADs fall within a band of 0.5%. As such, we kept the same un-certainty, uncorrelated among ADs.
Fig. 8. Asymmetries in energy response for all six ADs. The sources 68Ge, 60Co, and Am-C were deployed at the detector center. The60Co data were used for energy calibration. The alpha parti-cles from polonium decay and neutron capture on gadolinium of IBD and spallation neutrons were uniformly distributed within each detector. Dif-ferences between these sources are due to spa-tial non-uniformity of the detector response. The same set of data points is shown in the lower panel as a function of energy, which demonstrates that all six ADs have similar energy non-linearity.
3.5 Detector simulation
A Geant4 [25] based computer simulation (Monte Carlo, MC) of the detectors and readout electronics was used to study the detector response. It consisted of five components: kinematic generator, detector simula-tion, electronics simulasimula-tion, trigger simulation and read-out simulation. The MC was carefully tuned to match observed detector distributions, such as PMT timing, charge response, and energy non-linearity.
The antineutrino generator read from a database that stored the reactor antineutrino spectra from each core at each detector. The database was binned in daily incre-ments and accounted for fuel evolution. The flux was scaled later based on the actual reactor power. The cos-mic muons in the underground laboratory were simu-lated using a digitized topographic map of the site and Muon Simulation Code [26] (MUSIC), which calculated the energy loss and multiple scattering due to the rock overburden. The muon generator for Geant4 read ran-domly from a library of muon events generated with MU-SIC. The software generators for the calibration sources and the simulation of the decay sequences for natural ra-dionuclides found in our detectors were customized based on data from the ENDF database [27].
All physical processes in Geant4 relevant to the Daya Bay simulation were validated. In the validation pro-cess, we found that the gamma spectra of neutron cap-ture and muon capcap-ture on many nuclei were incorrectly modeled. Since a systematic correction was complex, we implemented corrections on a case by case basis. The most important one was the neutron capture on gadolin-ium where we used a customized module based on the measured gamma spectrum [28]. Furthermore, the sim-ulation of thermal neutron scattering was improved by considering the molecular binding energy of the scatter-ing nuclei.
The gadolinium and other elemental concentrations of the liquid scintillator were measured and incorporated into the MC. All relevant optical properties of the de-tector components were derived from measurements, in-cluding the attenuation lengths and refractive indices of all liquids as well as the acrylic components, time con-stants and photon emission spectra of Gd-LS, LS, and mineral oil, and the reflectivity of the reflectors as well as other detector materials. Photon absorption and re-emission processes in the liquid scintillator were modeled based on measurements in order to properly simulate the propagation of optical photons and contributions from the Cherenkov process.
The details of the electronics simulation can be found in Ref. [29]. Using the timing and number of p.e. gen-erated in PMTs, an analog signal pulse for each PMT was generated and tracked through the digitization pro-cess, taking into account the non-linearity, dark rate, pre-pulsing, after-pre-pulsing, and ringing of the waveform. The simulated analog pulse was then used as input to a trig-ger system simulation for each sub-detector.
4
Event selection
4.1 IBD selection
Two conditions were implemented prior to the IBD selection. First, flasher events were rejected (Sec. 3.3). Second, all AD triggers within a (−2 μs, 200 μs) time-window with respect to a water shield muon candidate (μWS) were rejected, where a μWS was defined as any signal with NHIT >12 in either the inner or outer wa-ter shield. This allowed for the removal of most of the superfluous triggers that followed a muon, as well as trig-gers associated with muon-induced spallation products. The veto time-window was extended to 2μs earlier than the muon to avoid the time alignment issue among dif-ferent detectors. Events in an AD within ±2 μs of a μWS with energy >20 MeV or >2.5 GeV were classified as AD muons (μAD) or showering muons (μsh), respec-tively. Longer veto windows were applied for such events to further reject cosmogenic backgrounds.
The energy of the prompt and delayed candidates were required to satisfy 0.7 MeV< Ep< 12.0 MeV and 6.0 MeV< Ed<12.0 MeV, respectively, and Δt = td−tp must have satisfied a 1 <Δt<200 μs coincidence, where tp and td are the times of the prompt and delayed sig-nals. A multiplicity cut required no additional candidate with E >0.7 MeV in the interval 200 μs before tp, 200μs after td, or between tp and td. The prompt-delayed pair was vetoed if the delayed candidate satisfied any of the conditions−2 μs<td−tμWS<600 μs (water shield muon), 0 < td−tμAD< 1000 μs (AD muon), or 0 < td−tμsh< 1 s (AD showering muon). The prompt energy, delayed en-ergy and capture-time distributions for data and MC are shown in Figs. 9–11, respectively.
Fig. 9. Prompt energy spectrum from AD1. IBD selection required 0.7<Ep<12.0 MeV. The spec-trum of accidental backgrounds, determined from the distribution of all prompt-type signals, was subtracted.
Fig. 10. Delayed energy spectrum from AD1. IBD selection required 6.0<Ed<12.0 MeV. The spec-trum of accidental backgrounds, determined from the distribution of all delayed-type signals, was subtracted.
The data are generally in good agreement with the MC. The apparent difference between data and MC in
the prompt energy spectrum in Fig. 9 is primarily due to nonlinearity of the detector response. Since all ADs had similar nonlinearity (as shown in the bottom panel of Fig. 8), and the energy selection cuts cover a larger range than the actual distribution, the discrepancies between MC and data introduced negligible uncertainties to the rate analysis. Therefore, this nonlinearity correction was not implemented in this analysis.
4.2 Efficiencies and uncertainties
For a relative measurement, the absolute efficiencies and correlated uncertainties do not factor into the error budget. In that regard, only the relative efficiencies and uncorrelated uncertainties matter. Extraction of abso-lute efficiencies and correlated uncertainties was done in part to better understand our detector, and was a natural consequence of evaluating the uncorrelated uncertainties. Absolute efficiencies associated with the prompt energy, delayed energy, capture time, Gd-capture fraction, and spill-in effects were evaluated with the Monte Carlo. Effi-ciencies associated with the muon veto, multiplicity cut, and livetime were evaluated using data. In general, the uncorrelated uncertainties were not dependent on the de-tails of our simulation.
Table 4 summarizes the absolute efficiencies and the systematic uncertainties. The uncertainties of the abso-lute efficiencies were correlated among the ADs. No rela-tive efficiency, except the muon veto efficiency μand the average multiplicity cut efficiency m, were corrected. All differences between the functionally identical ADs were taken as uncorrelated uncertainties.
Table 4. Summary of absolute efficiencies, and cor-related and uncorcor-related systematic uncertainties. For our relative measurement, the absolute effi-ciencies as well as the correlated uncertainties ef-fectively cancel. Only the uncorrelated uncertain-ties contribute to the final error in our relative measurement.
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 fraction 83.8% 0.8% <0.1%
spill-in 105.0% 1.5% 0.02%
livetime 100.0% 0.002% <0.01%
combined 78.8% 1.9% 0.2%
The absolute efficiency of the prompt energy cut (0.7 < Ep< 12.0 MeV) was determined to be 99.88%. The energy spectrum is shown in Fig. 9. Inefficiency was mainly caused by interactions inside the inner acrylic ves-sel, indicated by the vertex distribution of the rejected
prompt signal below 0.7 MeV. While the uncertainty in the energy scale is below 0.5% for events at the detector center or uniformly distributed in the target volume, it is larger for events at the edge. The asymmetries of the energy among ADs could be as large as 2% for events at the radius of ACU-C, studied with60Co source [15]. Taking 2% uncertainty in the energy scale for events near the inner acrylic vessel, the uncorrelated uncertainty of the efficiency due to the prompt energy cut was eval-uated to be 0.01%. Given that the positron threshold was calibrated with the68Ge source, the uncertainty of this absolute efficiency comes from the difference of non-linearity and non-uniformity between the data and MC. The correlated uncertainty was estimated to be 0.1%.
The absolute efficiency of the delayed energy cut (6.0 < Ed< 12.0 MeV) was determined to be 90.9%. As shown in Fig. 10, the fraction of events in the 6–7 MeV region was 5.3% of that in 6–12 MeV for MC. For selected IBD data, this fraction was 5.6%. Assuming the same relative difference between MC and data in the 0–6 MeV region, the difference of absolute efficiency between the MC and data was evaluated to be 0.6%, which is taken as the correlated uncertainty. By varying the cut at 6 MeV and counting the number of events in the selected sam-ple, we found that the 0.5% asymmetry of the energy scale in ADs, shown in Fig. 8, leads to a 0.12% uncorre-lated efficiency uncertainty. The low energy tail around 6 MeV is relatively flat and the MC and data agree well. Both MC and data studies yield the same uncorrelated efficiency uncertainty.
The spill-in enhancement resulted when neutrons from IBD interactions outside the target volume were captured by a Gd nucleus in the target volume. It was defined as the ratio of all IBD interactions that lead to a neutron capture on Gd to IBD interactions within the target volume leading to a neutron capture on Gd. From MC, it was evaluated to be 105.0%. By modeling the rel-ative difference in acrylic vessel thickness, acrylic density and liquid density in MC, the relative uncertainty of the spill-in efficiency was evaluated to be 0.02%. The corre-lated uncertainty of the spill-in efficiency was evaluated with MC. The modeling of molecular binding energy of the scattering nuclei has a large impact on the simulation of thermal neutron scattering, and thus on the absolute spill-in efficiency. The thermal neutron scattering pro-cess is correlated with the neutron capture time. The agreement between data and MC is shown in the inset of Fig. 11. By comparing the results of simulation with two different models of molecular binding energy as well as without binding energy, we conservatively estimated the correlated uncertainty of the spill-in efficiency to be 1.5%.
The Gd capture fraction was defined as the ratio of the number of Gd capture events produced by IBD
reac-tions to all IBD reacreac-tions in the Gd-LS. It was evaluated to be 83.8%. The spill-out deficit, ∼2.2% by compar-ing the Gd capture fraction of the Am-C neutron source at the detector center and IBD events in MC, was in-cluded in the absolute Gd capture fraction. Spill-out is analogous to spill-in, except that IBD neutrons produced within the target volume were captured outside the tar-get volume. By measuring the difference in the neutron capture time of each AD, the relative Gd-concentration variation was constrained and the Gd capture fraction variation was determined to be within 0.1%. By com-paring Am-C source data with MC, as well as spallation neutrons, the correlated uncertainty on Gd capture frac-tion was estimated to be 0.8%.
Fig. 11. Neutron capture time from AD1. IBD se-lection required 1< td−tp< 200 μs. In order to compare data with MC, a cut on the prompt energy (Ep> 3 MeV) was applied to suppress accidental backgrounds. A zoomed-in plot for 1<td−tp<30 μs is shown in the inset.
The efficiency of the capture time cut (1 < Δt < 200μs) was evaluated to be 98.6% with 0.2% of events with Δt < 1 μs and 1.2% events with Δt > 200 μs. The correlated efficiency uncertainty was evaluated to be 0.12%, according to the difference in the measured capture time between Am-C data and MC. The uncorre-lated uncertainty comes from the Gd-concentration vari-ation and possible trigger time-walk effect, and it was evaluated to be 0.01%.
The muon veto efficiencies were determined using data. For each type of muon candidate (μWS, μAD and μsh), the start and end time of the veto window were well defined. Overlapping veto windows were merged to avoid double counting. As a result, each livetime window was precisely calculated as the unvetoed time interval between two isolated veto windows. The total livetime was obtained by summing all the individual livetime win-dows. The muon veto efficiency μ was defined as the fraction of the livetime after a muon veto in the total
DAQ livetime. For each experimental hall the muon rates were stable as shown in Fig. 4. The muon veto ef-ficiencies differed due to different muon candidate rates. The multiplicity cut required no additional > 0.7 MeV signals (singles) in the time range from 200 μs before the prompt signal to 200 μs after the delayed signal. The singles rate Rs can be taken as the rate of prompt-type signals shown in Fig. 3. The efficiency of the multiplicity cut is a product of three components. The probability of no singles in the 200μs before the prompt signal is given by exp(−R200), where R200= Rs·200 μs. The probability of no singles between the prompt and delayed signal is given as
200μs 0
exp(−Rst)f (t)dt, where f (t) is the probability density function of the capture time of a neutron on Gd, and can be simplified as 1− Rstcap+ O(10−5), where tcap is the mean neutron capture time in 200μs. The average of the mean cap-ture time of the six ADs was 33.46 μs, obtained from data. The uncorrelated uncertainty was determined by the difference of the mean capture times among ADs. The probability of no singles in 200μs after the delayed signal must be calculated for two cases since the window may be truncated by an AD muon that would obscure any potential single. If the single livetime window was Ts<200 μs, the efficiency was
1−e(−RsTs) RsTs
, and if Ts>200 μs, the efficiency was
1−200μs Ts e−R200+ 1 RsTs (1−e−R200).
Because the second term depends on the length of the single livetime window, the multiplicity cut efficiency must be calculated for every single livetime window. As a consequence, the muon veto efficiency and the multi-plicity were coupled. The combined efficiency is
μm= i i mT i s /TDAQ, (4) where i
m is the multiplicity cut efficiency in the i-th sin-gle livetime Ti
s, and TDAQ is the analyzed good run time. The muon veto efficiency μ and the average multiplic-ity cut efficiency mcalculated with Eq. (4) are listed in Table 5 and corrected for each AD.
The target mass uncertainty was discussed exten-sively in Ref. [15]. The correlated uncertainty 0.47% largely comes from the hydrogen-carbon ratio of the tar-get liquid, which is canceled out in the near-far relative measurement by using the same batch of Gd-LS. The time variation of the target mass, e.g. due to tempera-ture variation, is monitored by the liquid level with sev-eral independent sensors in the overflow tanks on the top
of the AD lid [30]. The variation of the target mass for the analyzed data set is shown in Fig. 12. The±0.02% range is the target mass uncertainty evaluated during fill-ing [15]. To accurately evaluate the mass of Gd-LS trans-ferred into detectors, a 20-t filling tank was equipped with load cells to measure the mass of the filling tank before and after filling. The above uncertainty is domi-nated by the load cell drift during the filling operation. As such, the uncorrelated uncertainty is set to be 0.03%.
Fig. 12. Target mass variation for each AD over the analyzed time period. The vertical double ar-row indicates the total uncorrelated uncertainty in the target mass evaluated during filling.
5
Backgrounds
5.1 Accidental backgrounds
The accidental background is defined as any pair of otherwise uncorrelated signals that happen to satisfy the IBD selection criteria. For any given signal with an ob-served energy between 6 and 12 MeV (delayed-type sig-nal), the probability of forming an accidental background is the product of two components, the probability of a prompt-type signal within 1–200μs before the delayed-type signal, 1−exp(−R·199 μs), and the probability of no singles within 200μs before the prompt-type signal and 200μs after the delayed-type signal, exp(−R · 400 μs). R is the rate of prompt-type singles. Since the rate of prompt-type and delayed-type singles changed over time, the accidental background was calculated every four hours and summed as follows:
Nacc.bkg.=
i
Nie−Ri·400 μs(1−e−Ri·199 μs), (5) where Ni and Ri are the number of delayed-type and prompt-type singles rates in the i-th four-hour period, respectively. The statistical uncertainty was dominated by Ni, and was approximated as
δN(stat.) acc.bkg.≈ Nacc.bkg. iNi . (6)
Table 5. Summary of signal and background. The background and IBD rates have been corrected for the muon veto efficiencyμand the average multiplicity cut efficiencym.
AD1 AD2 AD3 AD4 AD5 AD6
IBD candidates 69121 69714 66473 9788 9669 9452
expected IBDs 68613 69595 66402 9922.9 9940.2 9837.7
DAQ livetime/days 127.5470 127.3763 126.2646
μ 0.8231 0.8198 0.8576 0.9813 0.9813 0.9810
m 0.9738 0.9742 0.9753 0.9737 0.9734 0.9732
accidentals (per day) 9.73±0.10 9.61±0.10 7.55±0.08 3.05±0.04 3.04± 0.04 2.93±0.03 fast-neutron (per day) 0.77±0.24 0.77±0.24 0.58±0.33 0.05±0.02 0.05±0.02 0.05±0.02
9Li/8He (per AD per day) 2.9±1.5 2.0±1.1 0.22±0.12
Am-C correlated (per AD per day) 0.2±0.2
(α, n) background (per day) 0.08±0.04 0.07±0.04 0.05±0.03 0.04±0.02 0.04±0.02 0.04±0.02 IBD rate (per day) 662.47±3.00 670.87±3.01 613.53±2.69 77.57±0.85 76.62±0.85 74.97±0.84
The expected rates of accidental backgrounds are listed in Table 5, after correcting for the muon veto efficiency and the multiplicity cut efficiency in the IBD selection.
An alternate method to determine the accidental backgrounds, the off-window method, was developed. By definition, the accidental background within the IBD co-incidence time window (1μs<Δt<200 μs) should be the same as in any other window (toff+1μs<Δt<toff+200μs), where toff is an arbitrary time offset.
If toff is large enough to avoid real correlated events (such as for IBD, fast neutron (Sec. 5.2), and9
Li/8He decay (Sec. 5.3)), the accidental backgrounds can be estimated by counting the coincidences in the off-window. To reduce the statistical uncertainty, multiple non-overlapping off-windows were examined. The mean number of selected coincidences in these off-windows was taken as the expected accidental background. The relative differences between the results from the off-window method and the calculations using
Fig. 13. Distance between the prompt signal and delayed signal. The dots show the IBD candi-dates in data and the open circles are accidental candidates selected with the off-window method, both in their absolute rates. The histogram shows the simulated IBD events, with rate normalized to data.
Eq. (5) were consistent given the statistical uncertainties for all six ADs.
The accidental background was also validated by comparing the distributions of distance between the re-constructed vertices for the prompt and delayed signals of the IBD candidates and accidentals selected by the off-window method, as shown in Fig. 13. The prompt and delayed vertices of accidentals were uncorrelated, thus giving a broad distribution, while the two vertices for IBD events were correlated, giving a distribution peaked at a short distance. For distances greater than 2 m, the IBD candidate and off-window distributions agree well. 5.2 Fast neutron backgrounds
Energetic neutrons created by cosmic rays entering an AD could mimic IBD by recoiling off a proton before being captured on Gd. Since the visible energy of the re-coil proton ranged well past that of the IBD events (up to several hundred MeV as shown in Fig. 14), we esti-mated the number of fast-neutron background events in the IBD sample by extrapolating the prompt energy (Ep) distribution between 12 and 100 MeV down to 0.7 MeV. Two different extrapolation methods were used. By as-suming the recoil proton energy spectrum follows a flat distribution, the mean number of events per energy bin of the distribution from 12 to 100 MeV was used to esti-mate the number of fast-neutron events between 0.7 and 12 MeV. In addition, the data from 12 to 100 MeV were fit with a first-order polynomial function (f (E)=a+bE). The best-fit parameters were used to estimate the num-ber of fast-neutron events between 0.7 and 12 MeV. The fast neutron background in the IBD sample was assigned to be equal to the mean value of the two extrapolation methods. The systematic error was determined from their differences and the fitting uncertainties.
As a check, we studied the fast neutrons associated with tagged muons. The prompt energy of the fast neu-tron tagged by the IWS muon will be contaminated if
the muon clips the edge or corner of an AD. Further-more, the fast neutron backgrounds in the IBD candi-date pool mostly originated from OWS muons (defined as OWS PMT multiplicity > 12 and without an IWS trigger) or muons passing through rock, since the muon detection efficiency of the IWS was very high (99.7%). The fast neutrons tagged by the OWS muons or RPC-only muons (RPC-only detected by RPC) had a prompt en-ergy spectrum similar to the fast neutron backgrounds in the IBD sample. After rejecting flasher events, we se-lected fast-neutron-like events by requiring exactly two signals within 200 μs after an OWS muon or an RPC-only muon. The time interval and the energy selections of the prompt-delayed pair were the same as the IBD selections, except that the prompt energy was relaxed to be 0.7 < Ep<100 MeV. We combined the samples from EH1 and EH2 to create the fast neutron prompt energy spectrum shown in the inset of Fig. 14. The observed distribution validates our extrapolation method for esti-mating the fast neutron background.
Fig. 14. Prompt energy spectrum of IBD candi-dates with the upper limit relaxed. The energy spectrum of the fast neutron backgrounds tagged by the OWS muons or RPC-only muons is shown in the inset.
Two additional methods were used to provide fur-ther cross checks and estimates for the fast neutron back-ground. These two methods are consistent with the re-sult by extrapolating the IBD prompt energy spectrum within the assigned uncertainty.
First, a muon with a large PMT multiplicity in the IWS and OWS has an increased probability to produce a fast neutron in an AD, presumably since track length correlates with PMT multiplicity. Such a correlation has been observed in data. Also, muon detection inefficiency was associated with low PMT multiplicity. By extrapo-lating the fast neutron rate produced by muons with a sum of PMT multiplicities between 24 and 48 in the IWS
and OWS to the range 0 and 24, we were able to esti-mate the fast neutron background slipping into the IBD sample due to the inefficiency of the muon detection.
Second, we collected different fast neutron samples based on muons going through different detector vol-umes (nIWS
f : fast neutron from an IWS tagged muon; nOWS
f : fast neutron from an OWS muon; n rock
f : fast neu-tron from a muon going through nearby rock) and esti-mated these samples separately. The nrock
f was estimated by selecting RPC-only muons. MC simulation suggested that the fast neutron backgrounds tagged by RPC-only muons account for one-third of the rock neutron back-ground. The fast neutron background (nf) is described as nf=n IWS f (1−ξIWS)+n OWS f (1−ξOWS)+n rock f , (7)
where ξIWS is the muon detection efficiency of the IWS and ξOWS is that of the OWS.
5.3 9Li/8He backgrounds
The rate of correlated background from the β-n cas-cade of the cosmogenic 9Li/8He decays was evaluated from the distribution of the time since the last muon, which can be described as [31]
f (t)=Ba λa ·e−t/λa+Bb λb ·e−t/λb+NIBD T e −t/T , (8) where Baand Bbare the number ofβ-n events for9Li and 8
He, respectively. T is the mean time between muons, 1 λa = 1 T + 1 τa and 1 λb = 1 T + 1 τb with τa = 0.257 s and τb= 0.172 s being the known decay time constants for 9Li and 8
He, respectively. The muon rate Rμ= 1/T de-pends on the muon selection criteria.
To reduce the impact of accidental backgrounds on our measurement of9Li and8He, we made the following modification to our IBD selection criteria:
1) 0.7 < Ep < 12.0 MeV changed to 3.5 < Ep < 12.0 MeV.
2) 1<Δt<200 μs changed to 1<Δt<100 μs. 3) μsh veto time changed from 1 s to 1000μs. The measured9Li/8He rate was corrected for the rela-tive efficiency with respect to the IBD selection criteria. Assuming that 9Li was predominant over 8He (as ob-served in a previous experiment [3] and consistent with our observations), and based on the 9
Li β spectrum, this efficiency was evaluated to be about 72%. The re-duced capture time window has an efficiency of 94%. The residual accidental backgrounds were thus reduced to <0.05/day at the near sites, and <0.01/day at the far site.
To reduce the number of minimum ionizing muons in these data samples, we assumed that most of the9Li and 8He production was accompanied with neutron genera-tion, and thus rejected AD tagged muon events with no
follow-on neutron (defined as >1.8 MeV signal within a 10–200μs window). The muon samples with and with-out reduction were both prepared for the 9Li and 8He background estimation. The data were sub-divided into six groups in visible muon energy (0.02–0.5, 0.5–1.5, 1.5– 2.5, 2.5–3.5, 3.5–4.5, and >4.5 GeV). Taking EH1 as an example, the corresponding muon rates in each energy bin were (10.0, 10.9, 0.23, 0.042, 0.016, 5.6e-3 Hz). Note that the maximum visible energy was around 5 GeV be-cause of the saturation of the PMTs. An example of a fit to the time-since-last muon distribution using Eq. (8) for determining the number of 9Li and 8He events for Eμ>4.5 GeV is shown in Fig. 15. Though only four seconds are shown in the figure, the fit range was actu-ally from 1 ms to 40 s. Fitting over such a large range helped to insure that Rμ was accurate. Because of the 1000μs μADveto, the fitted Rμwas slightly smaller than the directly measured value.
Fig. 15. An example of fitting for 8He/9Li backgrounds. Instead of allowing the 9Li to 9Li plus 8He ratio to float, we scanned it from 0 to 1 in steps of 0.01. For each scan point, a maximum likelihood fit was done, where only NLi+He, NIBD, and Rμ were allowed to float. Also, only the results with a global maximum likelihood among scan points were regarded as best fit values. The global maximum likelihood confirmed that 9Li was dominant in the8He/9Li backgrounds. The binning effect was in-cluded in the uncertainty estimation by changing the bin width of the time-since-last muon distribution.
The best-fit results are shown in Fig. 16. Since the statistics were quite low in EH3, we also predicted the 9Li yield in EH3 from the EH1 and EH2 yields by as-suming that the9Li yields with the same visible energy at different sites were identical, as shown in the bot-tom panel in Fig. 16. The measured values agreed with the prediction within statistics. Another check was done by predicting the EH3 9Li yield assuming that it fol-lows an E0.74
μ power law, where Eμis the simulated aver-age muon energy (See Table 1), and normalizing to EH1
and EH2 measurements. Again the fitted EH39Li yield agreed with the prediction within statistics. By consid-ering binning effects, differences between the results with and without muon reduction, and the difference between the predicted EH3 result and the measured result, we as-signed a 50% systematic uncertainty to the final result.
Fig. 16. The fitted 9Li yield as a function of the visible energy of parent muons for three experi-mental halls. The open circles represent the fit with all muons included. Due to high muon rate, the fit is done only forEμ> 2.5 GeV. The filled circles are the results obtained by requiring a neu-tron following the muon as described in the text. In the bottom panel the prediction from the near site measurements is shown as a solid line.
5.4 (α, n) backgrounds
The 13C(α, n)16O background was determined by measuring alpha-decay rates in situ and then using the MC to calculate the neutron yield. We identified four sources of alpha decays, the 238U, 232Th, 227Ac decay chains and 210
Po. The decay chains are β-α cascades with half lives of 164.3μs, 0.3 μs, and 1.781 ms, respec-tively. Fig. 17 displays the correlation of the prompt-delayed energy distributions for various time intervals corresponding to these cascade decays: 1–3μs at upper left (group A are212Bi-212Po decays from the 232Th de-cay chain), 10–160μs at upper right (group B are IBD events where the neutron captures on hydrogen. Group C are214Bi-214Po decays from the238U decay chain, and group D are 219Rn-215Po decays from the 227Ac decay chain). In the 1–2 ms region at lower left, only group D and some accidental coincidence events remain.
Fig. 17. Correlations of prompt and delayed energy for cascade decay chains of contaminants within the ADs. At upper left are events with a time correlation between 1 and 3μs, 10 to 160 μs is at upper right, 1–2 ms is at lower left, with the combined distributions at lower right.
210Po was produced by the decay of 222Rn. Its 5.3 MeV alpha produced 0.5 MeV of visible energy in an AD. The spatial distribution suggests that the210Po background was due in part to an accumulation on the wall of the inner acrylic vessel.
Geant4 was used to model the energy deposition pro-cess. Based on the (α, n) cross sections archived in JENDL [32], the neutron yield as a function of α energy was calculated and summed. Finally, with the in-situ measured alpha-decay rates and MC determined neu-tron yields, the 13C(α, n) 16O rate was calculated, as listed in Table 5. The uncertainties come from the selec-tion efficiencies of the Bi-Po and Rn-Po chain measure-ments, the possible deviation from equilibrium of the 238U, 232Th, and 227Ac decay chains, the fitting to de-termine the210Po activity, and the simulation of (α, n) reactions. During the Gd-LS synthesis,238U,232Th, and Ra were removed by radio-purification. They may con-tribute∼30% of the alphas of the whole chain. Thus a 30% uncertainty was assigned for the possible deviation from equilibrium, which was the largest component in the uncertainties. A 10% uncertainty was assigned to the neutron yield by comparing the MC simulation with an analytical calculation. Together with the other two components,∼50% uncertainties were estimated for the (α, n) backgrounds, slightly different for each AD due to different alpha components in them.
5.5 Correlated backgrounds from Am-C source During data taking, the Am-C sources sat inside the ACUs on top of each AD. Neutrons emitted from these sources would occasionally mimic IBD events by scat-tering inelastically with nuclei in the shielding material (emitting gamma rays) before being captured on a metal nuclei, such as Fe, Cr, Mn or Ni (releasing more gamma rays). It was possible for the gamma-rays from both
Fig. 18. Energy spectrum for events near the top of the three ADs in the far hall show three peaks consistent with neutron capture on 56Fe and58Ni/54Fe/53Cr.
processes to enter the scintillating region and satisfy the IBD selection requirements. Fig. 18 shows the energy spectrum in the three ADs at the far site of these de-layed candidates from the Am-C sources. The rate in MC was normalized to data. There is good agreement between the data and MC.
Figure 19 shows an asymmetry of delayed-type events along the z axis as was seen by ADs in the far hall. We es-timated the delayed-type events from the Am-C sources by subtracting the number of delayed-type singles in the Z < 0 region from the Z >0 region. The Am-C correlated background rate was estimated by MC simulation nor-malized with the Am-C delayed-type event rate obtained from the data,
Rcorr=Rn−like data Ncorr−MC
Nn−like MC
, (9)
where Ncorr−MC and Nn−like MCare the number of corre-lated background and number of delayed-type events in MC respectively, and Rn−like data is the Am-C delayed-type event rate from data. Even though the agreement in shape between data and MC is excellent for Am-C delayed-type events, we assigned 100% uncertainty to the estimated background due to the Am-C sources to account for any potential uncertainty in the neutron scat-tering/capture cross sections used in the simulation.
Fig. 19. Z distribution of delayed-type events. The excess in the top half of the ADs (Z > 0) comes from the Am-C sources in the ACUs.
6
Side-by-side comparison in EH1
Relative uncertainties were studied with data by com-paring two side-by-side antineutrino detectors. A de-tailed comparison using three months of data from the ADs in EH1 has been presented elsewhere [15]. An up-dated comparison of the prompt energy spectra of IBD events for the ADs in EH1 using 231 days of data (23 September 2011 to 11 May 2012) is shown in Fig. 20 after correcting for efficiencies and subtracting background.
A bin-by-bin ratio of the AD1 and AD2 spectra is also shown. The ratio of the total IBD rates in AD1 and AD2 was measured to be 0.987±0.004(stat.)±0.003(syst.), con-sistent with the expected ratio of 0.982. The deviation of the ratio from unity was primarily due to differences in the baselines of the two ADs with a slight dependence on the individual reactor on/off status. It was shown that AD2 has a 0.3% lower energy response than AD1 for uniformly distributed events, resulting in a slight tilt to the distribution shown in the bottom panel of Fig. 20. The distribution of the data points denoted by open cir-cles was created by scaling the AD2 energy by 0.3%. The bin-by-bin ratio with scaled AD2 energy agrees well with a flat distribution.
Fig. 20. The energy spectra for the prompt signal of IBD events in AD1 and AD2 are shown in the top panel, along with the bin-by-bin ratio in the bottom panel (solid circles). In the bottom panel, the dashed line represents the ratio of the total rates for the two ADs, and the open circles show the ratio with the AD2 energy scaled by +0.3%.
7
Reactor antineutrino flux
Reactor antineutrinos result primarily from the beta decay of the fission products of four main isotopes,235U, 239Pu, 238U, and 241Pu. The ¯ν
e flux of each reactor (S(E)) was predicted from the simulated fission rate (Fi) and the antineutrino spectrum per fission (Si) [33–38] of each isotope [39],
S(E)=
i
FiSi(E), (10) where i sums over the four isotopes. The fission rate was determined from the fission fraction fi, the energy
