Determination of responses of liquid xenon to low energy electron and nuclear recoils using the PandaX-II detector
Binbin Yan, Abdusalam Abdukerim, Wei Chen, Xun Chen, Yunhua Chen, Chen Cheng, Xiangyi Cui, Yingjie Fan, Deqing Fang, Changbo Fu, Mengting Fu, Lisheng Geng, Karl Giboni, Linhui Gu, Xuyuan Guo, Ke Han, Changda He, Di Huang, Peiyao Huang, Yan Huang, Yanlin Huang, Zhou Huang, Xiangdong Ji, Yonglin Ju, Shuaijie Li, Jianglai Liu, Zhuoqun Lei, Wenbo Ma, Yugang Ma, Yajun Mao, Yue Meng, Kaixiang Ni, Jinhua Ningand Xuyang Ning Xiangxiang Ren, Changsong Shang, Lin Si, Guofang Shen, Andi Tan, Anqing Wang, Hongwei Wang, Meng Wang, Qiuhong Wang, Siguang Wang, Wei Wang, Xiuli Wang, Zhou Wang, Mengmeng Wu, Shiyong Wu, Weihao Wu, Jingkai Xia, Mengjiao Xiao, Pengwei Xie, Rui Yan, Jijun Yang, Yong Yang, Chunxu Yu, Jumin Yuan, Ying Yuan, Jianfeng Yue, Xinning Zeng, Dan Zhang, Tao Zhang, Li Zhao, Qibin Zheng, Jifang Zhou, Ning Zhou, Xiaopeng Zhou
DDetermination of responses of liquid xenon to low energy electronand nuclear recoils using the PandaX-II detector
Binbin Yan ∗ , Abdusalam Abdukerim , Wei Chen , Xun Chen † , Yunhua Chen ,Chen Cheng , Xiangyi Cui , Yingjie Fan , Deqing Fang , Changbo Fu , Mengting Fu ,Lisheng Geng , Karl Giboni , Linhui Gu , Xuyuan Guo , Ke Han , Changda He , DiHuang , Peiyao Huang , Yan Huang , Yanlin Huang , Zhou Huang , Xiangdong Ji ,Yonglin Ju , Shuaijie Li , Jianglai Liu ‡ , Zhuoqun Lei , Wenbo Ma , Yugang Ma ,Yajun Mao , Yue Meng , Kaixiang Ni , Jinhua Ning , Xuyang Ning , XiangxiangRen , Changsong Shang , Lin Si , Guofang Shen , Andi Tan , Anqing Wang ,Hongwei Wang , Meng Wang , Qiuhong Wang , Siguang Wang , Wei Wang , XiuliWang , Zhou Wang , Mengmeng Wu , Shiyong Wu , Weihao Wu , Jingkai Xia ,Mengjiao Xiao , Pengwei Xie , Rui Yan , Jijun Yang , Yong Yang , Chunxu Yu ,Jumin Yuan , Ying Yuan , Jianfeng Yue , Xinning Zeng , Dan Zhang , Tao Zhang ,Li Zhao , Qibin Zheng , Jifang Zhou , Ning Zhou , and Xiaopeng Zhou School of Physics and Astronomy, Shanghai Jiao Tong University, MOE KeyLaboratory for Particle Astrophysics and Cosmology, Shanghai Key Laboratory forParticle Physics and Cosmology, Shanghai 200240, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800,China Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute ofModern Physics, Fudan University, Shanghai 200433, China Shanghai Jiao Tong University Sichuan Research Institute, Chengdu 610213, China Yalong River Hydropower Development Company, Ltd., 288 Shuanglin Road, Chengdu610051, China School of Physics, Sun Yat-Sen University, Guangzhou 510275, China Tsung-Dao Lee Institute, Shanghai 200240, China School of Physics, Nankai University, Tianjin 300071, China Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute ofModern Physics, Fudan University, Shanghai 200433, China School of Physics, Peking University, Beijing 100871, China School of Physics, Beihang University, Beijing 100191, China International Research Center for Nuclei and Particles in the Cosmos & Beijing KeyLaboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing100191, China School of Medical Instrument and Food Engineering, University of Shanghai forScience and Technology, Shanghai 200093, China Department of Physics, University of Maryland, College Park, Maryland 20742, USA School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240,China School of Physics and Key Laboratory of Particle Physics and Particle Irradiation(MOE), Shandong University, Jinan 250100, China Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai201210, China Center for High Energy Physics, Peking University, Beijing 100871, China a r X i v : . [ phy s i c s . i n s - d e t ] F e b Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute ofModern Physics, Fudan University, Shanghai 200433, China(PandaX-II Collaboration)Jan. 2021
Abstract
We report a systematic determination of the responses of PandaX-II, a dual phase xenon timeprojection chamber detector, to low energy recoils. The electron recoil (ER) and nuclear recoil (NR)responses are calibrated, respectively, with injected tritiated methane or
Rn source, and with
Am-Be neutron source, within an energy range from 1 −
25 keV (ER) and 4 −
80 keV (NR),under the two drift fields of 400 and 317 V/cm. An empirical model is used to fit the light yieldand charge yield for both types of recoils. The best fit models can well describe the calibration data.The systematic uncertainties of the fitted models are obtained via statistical comparison against thedata.Keywords: dark matter, liquid xenon time projection chamber, calibration, electron recoil, nu-cleon recoil, NEST2.0
The nature of dark matter (DM) remains to be one of the most intriguing physics questions today.The direct search for an important class of dark matter candidate, the weakly interacting massiveparticles (WIMPs), has been accelerated by the development in dual phase xenon time projectionchambers (TPCs), such as PandaX-II [1], XENON-1T [2], and LUX [3]. In these detectors, a WIMPmay interact with xenon nuclei via elastic scattering, depositing a nuclear recoil (NR) energy fromfew keV nr to a few tens of keV nr . γ s or β s from internal impurities and detector materials produceelectron recoil (ER) background events, which have a small probability to be identified as the NRsignals in these detectors.In a dual phase xenon TPC bounded by a cathode at the bottom in the liquid and an anodeat the top in the gas, each energy deposition will be converted into two channels, the scintillationphotons and ionized electrons. The former is the so-called S S
2) produced. Both S
1s and S
2s are collected by two arrays of photomultiplier tubes(PMTs) located at the top and bottom of the TPC. For a given event, the combination of S S S S in situ calibration.For the ER response, several injected sources were used in PandaX-II, including tritiated methane(CH T),
Rn, and
Kr. For NR calibration, an external
Am-Be (AmBe) neutron source wasused. In this paper, the detector responses are determined by fitting these data under the NEST2.0 [4]prescription.This rest of this paper is organized as follows. In Sec. 2, the detector conditions and calibrationsetups are introduced. In Sec. 3, data processing and event selection cuts are presented. The responsemodel simulation will be introduced in Sec. 4, followed by detailed discussions on the fits of the lightyield and charge yield, before the conclusion in Sec. 5.
The PandaX-II experiment, located at the China Jinping underground laboratory (CJPL) [5], wasunder operation from March 2016 to July 2019, with a total exposure of 132 ton · day for dark mattersearch. The operation was divided into three runs, Runs 9, 10, and 11 [6], during which calibrationruns were interleaved. The detector contained 580-kg liquid xenon in its sensitive volume. The liquidxenon was continuously purified through two circulation loops, each connected to a getter purifier.The internal ER sources were injected through one of the loop. Two PTFE tubes, at 1/4 and 3/4height of the TPC surrounding the inner cryostat, were used as the guide tube for the external AmBe ∗ corresponding author, [email protected] † corresponding author, [email protected] ‡ spokesperson, [email protected] ource. The TPC drift field in Run 9 was 400 V/cm and 317 V/cm in Runs 10/11, correspondingto a maximum drift time of 350 µ s and 360 µ s, respectively. The running conditions, key detectorparameters, and event selection ranges for the calibration data sets are summarized in Table. 1.Data set Run9 AmBe Run9 Tritium Runs 10/11 AmBe Runs 10/11 RnPDE 0.115 ± ± ± ± ± ± E drift (V/cm) 400 317 E extract (kV/cm) 4.56Duration (day) 6.7 27.9 48.5 11.9Number of events 2902 9387 11196 8841Drift time cut( µs ) 18-200 18-310 50-200 50-350range cut S1:3-150 PES2:100-20000 PE E rec ¡25 keV S1:3-150 PES2:100-20000 PE E rec ¡25 keV Table 1: Summary of ER and NR calibration data sets and corresponding detector configurations. PDE,EEE, and SEG, respectively, are the photon detection efficiency, electron extraction efficiency, and singleelectron gain. E drift and E extract are the drift field and extraction field. The number of events correspondto the calibration data after all cuts, which are described in Sec. 3. Tritiated methane calibration was first developed in the LUX experiment [7], which provided excellentinternal low energy β events. The tritiated methane source used in PandaX-II was procured fromAmerican Radio labeled Chemicals, Inc., with a specific activity of 0.1 Curie per mole of methane.The injection diagram is shown in Fig. 1. The tritiated methane bottle was immersed in a liquid-nitrogen cold trap, so that controllable amount of the CH T gas could diffuse through a needle valveto the 100 mL mixing volume. The gas in the mixing volume was flushed with xenon gas into thedetector.
Figure 1: Tritiated methane (blue) and
Rn (red) injection system.
The injection of tritium was performed in 2016 right after Run 9, during which about 5.4 × − molof methane was loaded into the detector. The tritium events were distributed uniformly in the de-tector. Liquid xenon was constantly circulated at a speed of about 40 SLPM (standard liter of gasper minute) through the purifier. The entire calibration run lasted for 44 days, and the later dataset with an average electron lifetime of 706 µ s is used as the ER calibration data.It was realized that the hot getters were inefficient to remove tritium, whose activity plateauedat 10.2 µ Bq/kg. A distillation campaign was carried out after the calibration, which reduced thetritium activity to 0.049 ± µ Bq/kg in Runs 10/11 [6]. Rn Rn, a decay progeny of
Th, is a naturally occurring radioactive noble gas isotope. With ahalf-life of 55 s, it poses much less risk to contaminate the liquid xenon TPC, as first demonstrated n XENON100 [8]. The details of Rn calibration setup and operation in PandaX-II can be foundin Ref. [9]. The injection system consisting of a mass flow controller and a
Th source chamber withfilters upstream and downstream, is shown in Fig. 1. After
Rn was injected into the detector,the β -decay of the daughter nucleus Pb gives uniformly distributed ER events with an energyextending to zero. 11.9 days of
Rn data in 2018 are used as the low energy ER calibration forRuns 10/11.
Neutron calibration data with an AmBe ( α , n) source [10] were taken during Run 9 and Runs 10/11.The source was placed inside the external calibration tubes. Calibration runs were taken at eightsymmetric locations in each loop to evenly sample the detector. For different source locations, nosignificant difference is identified in the detector response, so the data are grouped together in theanalysis. The processing of the calibration data follows the procedure in Ref. [6]. Compared to previousanalyses [1, 11], seven unstable PMTs are inhibited from all data sets for consistency. Improvementsare made on the PMT gain calibration, quality cuts, position reconstruction, and correspondingnon-uniformity correction.The raw S S S S Xe) due to activation from the neutron source. The correction to S S τ ), and a smooth two-dimensional surface in the horizontalplane.The electron equivalent energy of each event is reconstructed as E rec = W × (cid:18) S S × SEG (cid:19) (1)where W = 13 . S S µ s) is applied to the AmBe data to avoidevents that multi-scatter and deposit part of the energy in the below-cathode region, leading tosuppressed S S > S raw >
100 PE are applied to all datasets. For the AmBe data, the upper selection cut is set at S <
150 PE ( ∼
80 keV nr ). For ER data,events with E rec <
25 keV are selected. The vertex distributions of selected events are shown inFig. 2, with FV cuts indicated. The distributions of S S Our ER and NR response models follow the prescription of NEST2.0 [4], but use our own customiza-tion. The light yield ( L y ) and charge yield ( Q y ), defined as the number of initial quanta (photonsor ionized electrons) per unit recoil energy, can be parameterized and fitted to the calibration data.We shall discuss the simulation models in Sec. 4.1 and Sec. 4.2, which will be then fitted to data inSec. 4.3 For a distribution of true recoil energy from the calibration source, each recoil energy E is convertedinto two types of quanta, scintillation photons n or ionized electrons n . For the NRs, the visibleenergy is quenched into E × L due to unmeasurable dissipation of heat in the recoil, where L isthe so-called Linhard factor with a value ranging from 0.1 to 0.25 for E less than 100 keV nr [13].For ER events, on the other hand, E converts almost entirely to photons or electrons, so effectively a) Run 9 AmBe (b) Runs 10/11 AmBe(c) Run 9 tritium (d) Runs 10/11 Radon Figure 2: Event vertex distribution in drift time vs. radius-squared for each calibration data set. TheFV region is indicated by dashed red line in each figure. (a) AmBe in Run9 (b) AmBe in Runs 10/11(c) Tritium in Run 9 (d) Radon in Runs 10/11
Figure 3: S S E nr and equal- E rec lines for the NR and ER events, respectively.5 = 1. Now the number of quanta can be expressed as n q ≡ n + n = E LWn = L y E , n = Q y E (2)In NEST2.0, L y is parameterized as an empirical function of E L , and L y and Q y are connectedthrough Eqn. 2. The intrinsic (correlated) fluctuations in n and n is encoded in our simulationby an energy dependent Gaussian smearing function f ( E L ) as n e = Gaus( n , f ( E L ) × n ) n ph = n q − n e , (3)in which Gaus( µ, σ ) is a Gaussian random distribution with µ and σ as the mean and 1 σ value, and f can be adjusted to the data (see Fig. 4). ] ee Visible energy [keV F l u c t u a ti on ( % ) Run 9 TritiumRuns 10/11 Radon (a) ER ] ee Visible energy [keV F l u c t u a ti on ( % ) Run 9 AmBeRuns 10/11 AmBe (b) NR
Figure 4: The empirical fluctuation parameter f as a function visible energy for the ER (left) and NR(right) data, both in electron equivalent energy keV ee The detector model is used to convert n ph and n e to detected S S
2. For the R11410-20 PMTsused in PandaX-II, the double-photoelectron emission probability by the 178 nm scintillation photons p is measured to be 0 . ± .
02 from the data [6]. Therefore, the number of detected photons( N dph ) can be simulated as is N dph = Binom( n ph , PDE / (1 + p )) (4)in which Binom( N, p ) refers to a binomial distribution with N throws and a probability p , andPDE / (1 + p ) is the binomial probability to detect a photon. N dph is randomly distributed ontothe two arrays of PMTs (55 each) according to the measured top/bottom ratio from the data ( ∼ p , leading to the number of photoelectrons N PE = N dph + Binom( N dph , p ) . (5) S σ SPE of 33% [14] S N PE , σ SPE × √ N PE ) . (6)Each S S n e by using detector parameters from the data. For eachevent, the drift time t drift is randomized according to the data distribution, leading to an electronsurvival probability s = exp( − t drift /τ ) with the electron lifetime τ obtained from the data. So atthe liquid level, the number of electrons is N (cid:48) e = Binom( n e , s ) . (7)Then the number of extracted electron N (cid:48)(cid:48) e and S N (cid:48)(cid:48) e = Binom( N (cid:48) e , EEE) ,S N (cid:48)(cid:48) e × SEG , σ SE × (cid:112) N (cid:48)(cid:48) e ) , (8) n which σ SE ∼ . S S f ( S
1) and f ( S S S S d = S × f , S d = S × f . (9)Finally, the data selection efficiency is parameterized as a Fermi-Dirac function (cid:15) ( S d ) = 11 + exp( S d − p p ) , (10)where p and p will be determined by fitting to calibration data. Note that our selection efficiencyon S S In this section, the ER and NR response models will be fitted against the calibration data in S S As an initial approximation, L y can be fitted from the medians of the calibration data distributionas L y ( E rec /L ) = S × E rec /L , (11)where E rec (Eqn. 1) is the reconstructed energy including all detector effects, and the E rec L is theestimate of E . The true L y can be parameterized as L y ( E ) = L y ( E ) + (cid:88) n =0 c n P n ( E ) , (12)in which P n ( E ) is the n th order Legendre polynomial functions, and c n can be fitted to data.For a given model, a two-dimensional probability density function (PDF) in ( S S
2) is producedwith a large statistics simulation described in Secs. 4.1 and 4.2 using the following sets of parameters:a) PDE, EEE and SEG constrained by their Gaussian priors (Table 1), with the anti-correlationbetween PDE and EEE embedded (see Ref. [16]), b) parameters for (cid:15) ( S d ) in Eqn. 10, with a flatsampling of p ∈ (2 ,
5) and p ∈ (0 , L y in Eqn. 12, with c n ( n = 0 , , , ,
4) uniformly sampled from − n e , the electron lifetime, p , and the baseline suppression nonlinearities.To compare the data with the PDF, a standard unbinned log likelihood function is defined in thespace of ( S S
2) as − L = N (cid:88) i =1 − P ( S i , S i )) (13)in which P ( S i , S i ) is the probability density for a given calibration data point i , and N is the totalnumber of events for each calibration data set. An independent parameter scan is carried out to determine the best fit model for each calibrationdata set. The best fit corresponds to the PDF which gives the minimum − L . For illustration,the centroids and 90% quantiles of the best fit models from the four data sets are overlaid in Fig. 3,where good agreements with the data are observed.The parameter space allowable by the calibration data is determined based on the likelihoodratio approach in Ref. [17]. For each set of fixed parameters, 1000 mock data runs are produced withequal but Poisson fluctuated statistics as the calibration data. The test statistic for each mock runis defined as the difference between the log likelihood calculated using this fixed point PDF, and theglobal minimum value from the parameter scan,∆ L = − L fixed − ( − L min ) . (14)The distributions of ∆ L for the mock data generated from the best fit parameters for the fourcalibration data sets are shown in Fig. 5. The blue dashed regions refer to the 90% integrals from ero, beyond which the difference between the mock data set and its own PDF becomes less likely.It is verified that the 90% boundary values for ∆ L at other parameter space points are similar.Therefore, ∆ L of the real data is tested around the best fit, and the allowable space is defined by the90% boundaries in Fig. 5. The corresponding allowable range of distributions in recoil energy, S S L D
90% integral (a) AmBe in Run 9 L D
90% integral (b) AmBe in Runs 10/11 L D
90% integral (c) Tritium in Run 9 L D
90% integral (d) Radon in Runs 10/11
Figure 5: The distribution of ∆ L for mock calibration data sets generated at the best fit parameterpoints. The shaded regions indicate the 90% integrals. The resulting best fit Q y and L y for the NR and ER events are shown in Fig. 7, overlaid withthe world data, as well as the native NEST2.0 predictions [4]. The shaded bands indicate the 90%allowable model space, with uncertainties due to detector parameters and statistics of the calibrationdata naturally incorporated. Our NR models cover a wide energy range from 4 to 80 keV nr . At thetwo drift fields (400 V/cm and 317 V/cm), our best NR models are consistent as expected. Forthe Q y distribution with recoil energy from 4 to 15 keV nr , there is significant spread among theworld data, in which our Q y appears to be in better agreement with Ref. [18] (Xenon-1T 2019), butlower than the others. The NEST2.0 global fit, presumably mostly driven by data from Ref. [19](LUX DD), has a higher Q y than ours. The global data agreement improves significantly above 15keV nr . L y of our NR models, on the other hand, appear to be in agreement with most of the worlddata, except some slight tension at above 25 keV nr with Ref. [20] (Manzur 2010), which bears largeuncertainties by itself.For the ER models, Q y ( L y ) for Run 9 is higher (lower) than that for Runs 10/11. Such abehavior can also be expected since the initial ionized electrons are less likely to be recombined instronger drift field. Our model at 400 V/cm is in reasonable agreement with Ref. [21] (Xenon100) atsimilar drift field, but is in some tension with Refs. [22, 23] (neriX 480 V/cm, Lin 424 V/cm). Our Q y ( L y ) at 317 V/cm is generally lower (higher) than the world data, including that from Ref. [19](LUX) taken at 180 V/cm (and that from Ref. [18] at 81 V/cm, not drawn), as well as the nativeNEST2.0 predictions. Given the uncertainties in all these measurement, however, more systematicstudies and comparisons are warranted.Regardless of the global comparison, it should be emphasized that for PandaX-II, models deter-mined from in situ calibrations are the most self-consistent models to be used in the dark mattersearch data. Our best fit models presented here have therefore been adopted in the analysis inRef. [6].
10 20 30 40 50 60 70 80 ] nr Energy[keV / b i n n r e V DataModel (a) Run 9 AmBe energy
S1[PE] P E / b i n DataModel (b) Run 9 AmBe S S2[PE] P E / b i n DataModel (c) Run 9 AmBe S ] nr Energy[keV / b i n n r e V DataModel (d) Runs 10/11 AmBe energy
S1[PE] P E / b i n DataModel (e) Runs 10/11 AmBe S S2[PE] P E / b i n DataModel (f) Runs 10/11 AmBe S Energy[keV] / b i n ee . e V DataModel (g) Run 9 CH T energy
S1[PE] P E / b i n DataModel (h) Run 9 CH T S S2[PE] P E / b i n DataModel (i) Run 9 CH T S Energy[keV] / b i n ee . e V DataModel (j) Runs 10/11
Rn energy
S1[PE] P E / b i n DataModel (k) Runs 10/11 Rn S S2[PE] P E / b i n DataModel (l) Runs 10/11 Rn S Figure 6: The comparison of calibration data (points) and model (shaded bands = 90% allowable) in therecoil energy, S
1, and S
2, in Run 9 and Runs 10/11. For the
Rn energy distribution (j), the decreaseat high energy end is due to the 150 PE S nr Energy [keV0246810121416182022 ] n r [ e l ec t r on s / k e V y Q PandaX-II 400V/cmPandaX-II 317V/cmXenon-1T 2019 82V/cmLUX DD 2016 180V/cmManzur 2010 1kV/cmManzur 2010 4kV/cmNEST2.0 400V/cmNEST2.0 317V/cm (a) Q y of NR nr Energy [keV0246810121416182022 ] n r [ pho t on s / k e V y L PandaX-II 400V/cmPandaX-II 317V/cmXenon1T 2019 82V/cmLUX DD 2016 180V/cmNEST2.0 400V/cmNEST2.0 317V/cm
Manzur 2010 0kV/cmneriX 2018 490V/cmneriX 2018 190V/cm (b) L y of NR er Energy [keV102030405060708090 ] e r [ e l ec t r on s / k e V y Q PandaX-II 400V/cmPandaX-II 317V/cmneriX 480V/cm 2017LUX 180V/cm 2016Xenon100 366V/cm 2018NEST2.0 400V/cmNEST2.0 317V/cm (c) Q y of ER er Energy [keV01020304050607080 ] e r [ pho t on s / k e V y L PandaX-II 400V/cmPandaX-II 317V/cmBaudis 450V/cm 2013neriX 480V/cm 2017NEST2.0 400V/cmNEST2.0 317V/cm
Lin 424V/cm 2015LUX 180V/cm 2016Xenon100 366V/cm 2018 (d) L y of ER Figure 7: Charge yield Q y (a) and light yield L y (b) of the NR and Q y (c) and L y (d) of the ER obtainedfrom the PandaX-II data: blue=400 V/cm, red=317 V/cm. Overlaid world data include: NR fromRefs. [19, 20, 24–27], and ER from Refs. [7, 22, 23, 28], as indicated in the legend. The native NEST2.0predictions are drawn in black curves, solid (317 V/cm), and dashed (400 V/cm). The XENON1Tresponses [18] are not included in the ER figures since the operation field (81 V/cm) is significantlydifferent from the PandaX-II conditions, and for visual clarity.10 Conclusion
We report the ER and NR responses from the PandaX-II detector based on all calibration dataobtained during the operation at two different drift fields (400 V/cm and 317 V/cm). The empiricalbest fits to the data and model uncertainties are obtained, yielding good agreements between the dataand our models. In comparison to those presented in Refs. [16,29], the models in this work cover theentire PandaX-II data taking period, with a more extend energy range between 4 to 80 keV nr (NR)and 1 to 25 keV ee (ER). At the two drift fields, our NR models are in agreement, and our ER modelsexhibit a relative shift. Both behaviors are consistent with expectation.Our models are also compared to the world data. Our NR models lie within the large globalspread. For the ER response, our model yields a higher (lower) L y ( Q y ) in comparison to most ofthe world data, indicating some unaccounted systematic uncertainties in our or others’ measurements.These discrepancies encourage continuous calibration effort and further investigations of systematicsin the data. Finally, the analysis approach presented here is general and can be applied to similarnoble liquid TPC experiments. This project is supported in part by a grant from the Ministry of Science and Technology ofChina (No. 2016YFA0400301), grants from National Science Foundation of China (Nos. 12090060,11525522, 11775141 and 11755001), and Office of Science and Technology, Shanghai Municipal Gov-ernment (grant No. 18JC1410200). We thank supports from Double First Class Plan of the ShanghaiJiao Tong University. We also thank the sponsorship from the Chinese Academy of Sciences Cen-ter for Excellence in Particle Physics (CCEPP), Hongwen Foundation in Hong Kong, and TencentFoundation in China. Finally, we thank the CJPL administration and the Yalong River HydropowerDevelopment Company Ltd. for indispensable logistical support and other help.
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