Improved search for two-neutrino double electron capture on 124Xe and 126Xe using particle identification in XMASS-I

Improved search for two-neutrino double electron capture on 124Xe and 126Xe using particle... Prog. Theor. Exp. Phys. 2018, 053D03 (15 pages) DOI: 10.1093/ptep/pty053 Improved search for two-neutrino double electron 124 126 capture on Xe and Xe using particle identification in XMASS-I XMASS Collaboration 1,5 1,5 1,5 1,5 1,5 1 K. Abe , K. Hiraide , K. Ichimura , Y. Kishimoto , K. Kobayashi , M. Kobayashi , 1,5 1,5 1 1,5 1 1,5 S. Moriyama , M. Nakahata , T. Norita ,H.Ogawa , K. Sato , H. Sekiya , 1 1,5 1 1,5 1,5 2 O. Takachio , A. Takeda , S. Tasaka , M. Yamashita , B. S. Yang , N. Y. Kim , 2 3,6 3 3 3 3 4,12 Y. D. Kim , Y. Itow , K. Kanzawa ,R.Kegasa , K. Masuda , H. Takiya , K. Fushimi , 4 5 5 5 7 7,13 7 G. Kanzaki , K. Martens , Y. Suzuki ,B.D.Xu , R. Fujita , K. Hosokawa , K. Miuchi , 7 7,5 8,2 8 8 9 10 N. Oka , Y. Takeuchi , Y.H.Kim ,K.B.Lee ,M.K.Lee , Y. Fukuda , M. Miyasaka , 10 11 K. Nishijima , and S. Nakamura Kamioka Observatory, Institute for Cosmic Ray Research, the University ofTokyo, Higashi-Mozumi, Kamioka, Hida, Gifu 506-1205, Japan Center of Underground Physics, Institute for Basic Science, 70Yuseong-daero 1689-gil,Yuseong-gu, Daejeon 305-811, South Korea Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8601, Japan Institute of Socio-Arts and Sciences, The University of Tokushima, 1-1 Minamijosanjimacho Tokushima city, Tokushima 770-8502, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), the University of Tokyo, Kashiwa, Chiba 277-8582, Japan Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan Korea Research Institute of Standards and Science, Daejeon 305-340, South Korea Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan Department of Physics, Faculty of Engineering, Yokohama National University, Yokohama, Kanagawa 240- 8501, Japan Present address: Department of Physics, Tokushima University, 2-1 Minami Josanjimacho Tokushima city, Tokushima 770-8506, Japan Present address: Research Center for Neutrino Science, Tohoku University, Sendai, Miyagi 980-8578, Japan E-mail: xmass.publications7@km.icrr.u-tokyo.ac.jp Received January 10, 2018; Revised April 13, 2018; Accepted April 14, 2018; Published May 30, 2018 ................................................................................................................... We conducted an improved search for the simultaneous capture of two K -shell electrons on 124 126 the Xe and Xe nuclei with emission of two neutrinos using 800.0 days of data from the XMASS-I detector. A novel method to discriminate γ -ray/X-ray or double electron capture signals from β -ray background using scintillation time profiles was developed for this search. No significant signal was found when fitting the observed energy spectra with the expected signal and background. Therefore, we set the most stringent lower limits on the half-lives at 2.1 × 10 22 124 126 and 1.9 × 10 years for Xe and Xe, respectively, with 90% confidence level. These limits improve upon previously reported values by a factor of 4.5. ................................................................................................................... Subject Index C04, C43, D29 © The Author(s) 2018. Published by Oxford University Press on behalf of the Physical Society of Japan. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. 1. Introduction Double electron capture (ECEC) is a rare nuclear decay process where a nucleus captures two orbital electrons simultaneously. There might be two modes of the process: (Z , A) + 2e → (Z − 2, A), (1) (Z , A) + 2e → (Z − 2, A) + 2ν , (2) where Z and A are the atomic number and atomic mass number of the nucleus, respectively. Detecting the neutrinoless mode of this process (0νECEC) would provide evidence for lepton number violation and the Majorana nature of the neutrino if observed. To release the decay energy in 0νECEC, there are two proposed mechanisms: the radiative and the resonant mechanisms. In the case of the radiative mechanism, the decay energy is carried away by emitting, e.g., an internal Bremsstrahlung photon [1,2]. This process is, however, expected to have a much longer lifetime than neutrinoless double beta decay. On the other hand, an enhancement of the capture rate by a factor as large as 10 is possible if the initial and final (excited) masses of the nucleus are degenerate [3–8]. Therefore, experimental searches for 0νECEC have recently been performed for a variety of candidate nuclei [9–19]. Although two-neutrino double electron capture (2νECEC) is allowed within the Standard Model of particle physics, only a few positive experimental results for 2νECEC have been reported: geo- 130 78 chemical measurements of Ba [22,23] and a direct measurement of Kr [19,24] with half-lives 21 22 of the order of 10 –10 years. Despite the fact that the nuclear matrix element for the two-neutrino mode differs from that for the neutrinoless mode, they are related to each other through the relevant parameters in a chosen nuclear model [25]. For instance, the nucleus’ axial current coupling con- stant g and the strength of the particle–particle interaction g in the quasiparticle random-phase A pp approximation (QRPA) model are obtained from single β -decay and two-neutrino double beta decay measurements [26]. Measurements of the 2νECEC half-lives with various nuclei would shed new light on constraining these parameters. 124 126 Natural xenon contains Xe (abundance 0.095%) and Xe (0.089%), in which ECEC can be observed. Xe has the highest Q-value among all the known candidate nuclei for ECEC at + + + 2864 keV [27]. This Q-value is sufficiently large to open the β EC and β β channels. The predictions in the literature for the half-lives of Xe 2νECEC are spread over a wide range between 20 24 10 and 10 years [21,28–32] depending on the models used for calculating the corresponding nuclear matrix element and the effective value of the nucleus’ g . Although Xe can also undergo 126 124 2νECEC, the lifetime of this process for Xe is expected to be much longer than that for Xe since its Q-value is smaller at 920 keV [27]. Previous experimental searches for 2νECEC on Xe have sought the simultaneous capture of two K -shell electrons (2ν2K) using a gas proportional counter with enriched xenon and large-volume liquid xenon (LXe) detectors with natural xenon as the target. An experiment with a proportional counter containing 58.6 g of Xe (enriched to 23%) published the latest lower bound on the half- 2ν2K 124 21 life, T Xe > 2.0 × 10 years at 90% confidence level (CL) [33,34]. Large-volume LXe 1/2 detectors can also observe 2νECEC on Xe [35,36]. The XMASS experiment has conducted a search with a fiducial xenon mass of 41 kg (containing 39 g of Xe) and set the most stringent 2ν2K 124 21 lower limit of T Xe > 4.7 × 10 years [37]. The XENON100 experiment also published 1/2 a result obtained with a fiducial xenon mass of 34 kg (containing about 29 g of Xe) and set a 2ν2K 124 20 lower limit of T Xe > 6.5 × 10 years [38]. These searches were conducted with similar 1/2 2/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. Table 1. Summary of experimental searches for two-neutrino double electron capture on Xe reported to date compared with this work. 124 2ν2K 124 21 Experiment Xe target mass (g) Live time T Xe (10 years) 1/2 XMASS (this work) 311 800.0 days > 21 XMASS [37] 39 132.0 days > 4.7 Gavrilyuk et al. [34] 58.6 3220 h > 2.0 XENON100 [38] 29 224.6 days > 0.65 amounts of Xe and live times, as summarized in Table 1. In addition, the XMASS experiment set 126 2ν2K 126 21 the first experimental lower limit on the Xe 2ν2K half-life at T Xe > 4.3 × 10 years 1/2 using the same data set. 124 126 In this paper, we report the results of an improved search for Xe and Xe 2ν2K events, using data from the XMASS-I detector. We analyze a new data set taken between November 2013 and July 2016. The total live time amounts to 800.0 days and the fiducial xenon mass was enlarged to 327 kg (containing about 311 g of Xe). We developed a novel method for discriminating the 2ν2K signal from the β -ray background using LXe scintillation time profiles. 2. The XMASS-I detector XMASS-I is a large single-phase LXe detector located underground (2700 m water equivalent) at the Kamioka Observatory in Japan [39]. An active target of 832 kg of LXe is held inside a pentakis-dodecahedral copper structure that hosts 642 inward-looking 2-inch Hamamatsu R10789 photomultiplier tubes (PMTs) on its approximately spherical inner surface at a radius of about 40 cm. The photocathode coverage of the inner surface is 62.4%. Signals from each PMT are recorded with CAEN V1751 waveform digitizers with a sampling rate of 1 GHz and 10-bit resolution. The gains of the PMTs are monitored weekly using a blue LED embedded in the inner surface of the detector. The scintillation yield response is traced with a Co source [40] inserted along the central vertical axis of the detector every week or two. Through measurements with the Co source at the center of the detector volume, the photoelectron (PE) yield was determined to be ∼15 PE/keV for 122 keV γ -rays. The nonlinear response of the scintillation yield for electron-mediated events 55 241 in the detector was calibrated over an energy range from 5.9 keV to 2614 keV with Fe, Am, 109 57 137 60 232 Cd, Co, Cs, Co, and Th sources. Hereinafter, this calibrated energy is represented as keV where the subscript stands for the electron-equivalent energy. The timing offsets for the PMT ee channels owing to the differences in their cable lengths and the electronic responses were also traced by Co calibration. The LXe detector is located at the center of a cylindrical water Cherenkov detector, which is 11 m in height and 10 m in diameter. The outer detector is equipped with 72 20-inch Hamamatsu H3600 PMTs. This detector acts as an active veto counter for cosmic-ray muons as well as a passive shield against neutrons and γ -rays from the surrounding rock. Data acquisition is triggered if at least four inner-detector PMTs record a signal within 200 ns or if at least eight outer-detector PMTs register a signal within 200 ns. A 50 MHz clock is used to measure the time difference between triggers. One-pulse-per-second (1PPS) signals from the global positioning system (GPS) are fed as triggers for precise time stamping. The GPS 1PPS triggers are also used to flash the LED for the PMT gain monitoring. 3/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. 3. Expected signal and simulation The process of 2νECEC on Xe is 124 − 124 Xe + 2e → Te + 2ν . (3) 124 124 If two K -shell electrons in the Xe atom are captured simultaneously, a daughter atom of Te is formed with two vacancies in the K -shell and this atom relaxes by emitting atomic X-rays and/or Auger electrons. Our Monte Carlo simulations of the atomic de-excitation signal are based on the atomic relaxation package in Geant4 [41,42]. On the assumption that the X-rays and Auger electrons emitted in the 2ν2K event are like those generated by two single K -shell vacancies, the signal simulation begins with two Te atoms with a single K -shell vacancy. In such a case, the total energy deposition is given by twice the K -shell binding energy of Te (2K = 63.63 keV). On the other hand, the energy of the two electron holes in the K -shell of Te is calculated to be 64.46 keV [43], which only varies by 0.8 keV. Since the energy resolution of the 2ν2K signal peak is estimated to be 3.2 keV after all the detector responses mentioned below are accounted for, we judge that this difference is negligible in our analysis. The results actually do not change even if the peak position of the simulated signal is artificially shifted by this amount. According to the simulation, 77% of 2ν2K events emit two K -shell X-rays, 21% of events emit a single K -shell X-ray, and the remaining 1.6% of events emits no K -shell X-ray. These probabilities are consistent with those expected from the fluorescence yield for the K -shell of Te, ω = 0.875 [44]. Auger electron cascades are also simulated. The energy deposition from the recoil of the daughter nucleus is ∼30 eV at most, which is negligible. Simulated de-excitation events are generated uniformly throughout the detector volume. The nonlinearity of scintillation yield is accounted for using the nonlinearity model from Doke et al. [45] with a further correction obtained from the γ -ray calibrations. The absolute energy scale of the simulation is adjusted at 122 keV. The time profile of the scintillation is also modeled based on the γ -ray calibrations [46]. Propagation of scintillation photons in LXe is also simulated. Optical parameters of the LXe such as absorption and scattering lengths for the scintillation are tuned by source calibration data at various positions. The group velocity of the scintillation light in the LXe follows from LXe’s refractive index (∼11 cm/ns for 175-nm light [47]). Charge and timing responses of the PMTs are also modeled in the simulation based on the calibrations with the LED and the γ -ray sources. Finally, waveforms of the PMT signal are simulated using the template of a single-PE waveform obtained from the LED calibration data. 4. Data set The data used in the present analysis were collected between 20 November 2013 and 20 July 2016. The data set was divided into four periods depending on the detector conditions at that time, as summarized in Table 2. Period 1 started two weeks after the introduction of LXe into the detector. At 131m 129m the beginning of the run, we observed neutron-activated peaks from Xe and Xe that were created when the LXe was stored outside the water shield. We also performed the Cf calibration data collection twice in this period. Runs within 10 days after each calibration were excluded from 252 131m the data set. We ended period 1 60 days after the second Cf calibration because the Xe and 129m 252 Xe peaks caused by the Cf disappeared. Period 2 then ran until continuous gas circulation at a flow rate of ∼1.5 L/min with a getter purifier was introduced. Period 3 was ended so that the xenon could be purified by vaporizing it once to remove possible non-volatile impurities dissolved in LXe. During the purification process, LXe was extracted from the detector and therefore the xenon was 4/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. Table 2. Summary of the data set used in this analysis. Period Start date–end date Live time (days) Gas circulation Comment 1 20 Nov 2013–13 May 2014 124.0 None Activated 2 13 May 2014–13 Mar 2015 249.1 None 3 13 Mar 2015–29 Mar 2016 338.1 ∼1.5 L/min 4 14 Apr 2016–20 Jul 2016 88.8 ∼1.5 L/min Activated exposed to and activated by thermal neutrons outside the water shield. The purification process took 7 days and period 4 started immediately after completing the introduction of LXe into the detector. We selected periods of operation under what we call normal data taking conditions with a stable temperature (172.6–173.0 K) and pressure (0.162–0.164 MPa absolute) of the LXe in the detector. After further removing periods of operation that include excessive PMT noise, unstable pedestal levels, or abnormal trigger rates, the total live time became 800.0 days. 5. Event reduction and classification The event-reduction process comprises four steps: pre-selection, the fiducial volume selection, Bi identification, and particle identification. 5.1. Pre-selection Pre-selection requires that no outer-detector trigger is associated with an event, that the time elapsed since the previous inner-detector event (dT ) is at least 10 ms, and that the standard deviation of pre the inner-detector hit timing distribution in the event is less than 100 ns. The last two requirements remove events caused by after-pulses in the PMTs following bright events. The dT cut eliminates pre events by chance coincidence at a probability of 3.0% on average, which was estimated from the fraction of the GPS 1PPS events that are rejected by this cut. The chance coincidence probability is counted as dead time, and the live time mentioned above is obtained after subtracting this dead time. 5.2. Fiducial volume selection To select events that occurred within the fiducial volume, an event vertex is reconstructed based on a maximum-likelihood evaluation of the observed light distribution in the detector [39]. We select events whose reconstructed vertex has a radial distance of less than 30 cm from the center of the detector. The fiducial mass of natural xenon in that volume is 327 kg, containing 311 g of Xe and 291gof Xe. 5.3. Bi identification Rn emanates from the detector’s surface and contaminates the LXe within the detector. Thus, its 214 214 214 daughters, Bi and Pb, become one of the major sources of β -ray background. Bi can be 214 214 tagged using the Bi– Po delayed coincidence (T = 164 μs) and is used as a good control 1/2 sample of pure β -ray events in the relevant energy range. To remove the Bi events, events whose time difference from the subsequent event (dT ) is less than 1 ms are rejected from the 2ν2K signal post sample. This cut reduces the Bi background by a factor of ∼70, while consequently discarding only 0.4% of all other events. The counterpart sample, i.e., events with 0.015 ms < dT < 1 ms, post 214 214 214 is referred to as the Bi sample and is used to constrain the Bi and Pb backgrounds. 5/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. -50 0 50 100 150 Time (ns) 241 241 Fig. 1. An example waveform recorded in a PMT from the Am calibration data. The Am source was placed at z = 20 cm. Red dashed curves represent decomposed single-PE pulses. 5.4. Particle identification The scintillation time profiles of LXe can be used for particle identification. We use them to eliminate both the α-ray and β -ray backgrounds from the 2ν2K signal sample. After the fiducial volume selection, the largest source of background in the relevant energy range is β -rays coming from radioactive impurities within the LXe. 2ν2K or γ -ray events can be discriminated from these β -ray events by utilizing the energy dependence of the scintillation decay time for electron- induced events. The scintillation decay time increases from 28 ns to 48 ns as the kinetic energy of an electron increases from 3 keV to 1 MeV, as summarized in Fig. 3 of Ref. [46]. In the case of the 2ν2K or γ -ray events, the X-ray or γ -ray is converted into multiple low-energy electrons in the LXe; this shortens the effective scintillation decay time by a few ns from that of an event caused by a single electron with the same deposited energy. In particular, events caused by 2ν2K or γ -rays with energy close to twice the K -shell binding energy are easily distinguishable from the β -ray events by this effective scintillation decay time. The particle-identification parameter β CL is formulated as follows. First, waveforms in each PMT are decomposed into single-PE pulses using the single-PE waveform template [46]. Figure 1 shows an example of a waveform recorded in a PMT from the Am calibration data. Decomposed single- PE pulses are also shown in the figure. The timings of the decomposed single-PE pulses in all the PMTs are sorted chronologically after correcting for the time-of-flight of scintillation photons. The single-PE pulses in the first 20 ns are excluded from the following calculation to avoid systematic uncertainties in the leading edge of the scintillation time profile. The variable β CL is defined as n−1 (− ln P) β CL = P × , (4) i! i=0 n−1 where n is the total number of single-PE pluses after truncating the first 20 ns, P = CL , i=0 and CL (i = 0, 1, 2, ... , n − 1) is the CL of each pulse timing under the assumption that the event is caused by a β -ray. The probability-density function of the pulse-timing distribution for a β -ray event including its energy and position dependences is modeled from measurements in the Bi data sample over the energy range between 30 and 200 keV . This formula is in general used to ee combine p-values from a set of independent tests for a certain hypothesis [48]. Figure 2 shows distributions of the variable β CL for the Bi sample in the energy range from 241 214 30 to 200 keV along with the Am 59.5 keV γ -ray events. While the β -ray events in the Bi ee 6/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 ADC counts PTEP 2018, 053D03 K. Abe et al. 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 βCL βCL Fig. 2. The particle-identification parameter β CL for the Bi β -ray events in the energy range from 30 to 200 keV (left) and the Am 59.5 keV γ -ray events (right). The distributions of the observed data (black ee points) and the simulated events (red curves) are normalized to the unit area. 5 5 10 10 4 4 10 10 3 3 10 10 2 2 10 10 10 10 1 1 40 60 80 100 120 140 160 180 200 40 60 80 100 120 140 160 180 200 Energy (keV ) Energy (keV ) ee ee Fig. 3. Energy spectra after each event reduction step for the observed data (left) and the simulated 2ν2K sample assuming T = 4.7 × 10 years (right). From top to bottom, energy distributions after the pre- 1/2 selection (black solid), fiducial volume selection (red solid), Bi rejection (blue dashed nearly overlaps with red solid), and β -like event rejection (magenta points) steps are shown. sample are distributed between 0 and 1, the distribution of the 59.5 keV γ -ray events in the Am sample peaks at β CL = 0. Events with β CL less than 0.05 are classified as the β -depleted sample, and the rest is referred to as the β -enriched sample. When selecting events with β CL less than 0.05, 42% of the 2ν2K signal events are selected, while only 6% of the β -ray events from the Bi decay in this energy range are selected. Thus, the signal-to-noise ratio is improved by a factor of 7 by this selection. The cut position is tuned based on the simulated data to maximize the sensitivity for the 2ν2K signal. α-ray events often occur in the grooves of the inner surface of the detector, so that only some of their energy is detected. These events are sometimes incorrectly reconstructed within the fiducial volume [49]. Above 30 keV , α-ray events can be clearly separated from β -ray or γ -ray events ee using the scintillation decay time. Therefore, the waveforms from all PMTs are summed up to form a total waveform of the event after correcting for the relative gain and timing of each PMT. Then, the falling edge of that total waveform is fitted with an exponential function to obtain the decay time for each event. Events with fitted decay times of less than 30 ns are deemed α-ray events and are rejected. Figure 3 shows the energy spectra plotted after each event-reduction step for the observed data and the simulated 2ν2K sample. For the simulated 2ν2K sample, T = 4.7 × 10 years is assumed. 1/2 7/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 Entries/2keV Probability density ee Entries/2keV Probability density ee PTEP 2018, 053D03 K. Abe et al. 6. Spectrum fitting 6.1. Chi-squared definition To extract the 2ν2K signal from the observed data, the energy spectra for the β -depleted samples, β -enriched samples, and Bi samples are simultaneously fitted to the expected signal and back- ground spectra. The energy range from 30 to 200 keV is used for fitting. The chi-squared value is ee defined as χ =−2ln L N N N sample period N data sys bin (1 − p ) exp ijk l data data = 2 n (p ) − n + n ln + , (5) exp ijk ijk ijk n (p ) σ ijk l i=1 j=1 k=1 l=1 exp data where n and n (p ) are the observed and expected number of events in the ith sub-sample, jth ijk ijk period, and k th energy bin, respectively. N = 3, N = 4, N = 85, and N are the sample period bin sys number of sub-samples, periods, energy bins, and constrained systematic parameters, respectively. p and σ are a scaling parameter for the nominal value and its relative error, respectively. l l 6.2. Expected background We consider three types of backgrounds: radioactive isotopes (RIs) in the LXe, neutron activation of xenon, and external backgrounds. 222 214 214 85 39 14 136 For the internal RIs, the Rn daughters ( Bi and Pb), Kr, Ar, C, and Xe are consid- 214 214 ered. The Bi activity during each period is determined from the fitting to the Bi sample and the 214 214 222 85 Pb activity in each period follows from this Bi activity as both originate from Rn. While Kr decays by β -decay (Q = 687 keV, T = 10.8 years) predominantly into the ground state of Rb, β 1/2 0.434% of their decays go into the 514-keV excited state of Rb followed by a nuclear relaxation γ -ray (T = 1.014 μs). Kr contamination in the detector is measured at 0.26 ± 0.06 mBq by the 1/2 coincidence of β -ray and γ -ray events. In this analysis, the Kr activity in each period is fitted with this constraint. We have also found argon contamination in the xenon through measurements of the sampled xenon gas using gas chromatography–mass spectrometry (GC–MS). The argon is thought to have adsorbed to the detector material when we conducted a leakage test of the LXe chamber using argon gas in 2013. Ar undergoes β -decay (Q = 565 keV, T = 269 years). By comparing β 1/2 the energy spectra for periods 2 and 3 of the data set, we found a reduction in event rate below ∼150 keV in the β -enriched sample. The difference in the energy spectra between two periods ee is consistent with the β -decay of C(Q = 156 keV, T = 5730 years). Hence, we assume β 1/2 that impurities containing carbon were reduced by gas circulation through the getter although its chemical form is not known. Finally, natural xenon contains Xe with an isotopic abundance of 136 21 8.9%, and Xe undergoes 2νββ decay (Q = 2.46 MeV, T = 2.2 × 10 years [50,51]). ββ 1/2 Although the LXe detector is shielded against environmental neutrons by water, some of the detector components such as the cable feed-through box, calibration system, and cryogenic system lie outside the water shield and are filled with xenon gas [39]. The volume of xenon gas outside 5 3 the water shield is estimated to be 2.6 × 10 cm at the standard temperature of 273.15 K and pressure of 10 Pa. This xenon is activated by thermal neutron capture and returned to the LXe in the 125 125m 125 127 127m 129m 131m 133 133m detector. The resulting 13 RIs, Xe, Xe, I, Xe, Xe, Xe, Xe, Xe, Xe, 135 135m 137 137 Xe, Xe, Xe, and Cs, are also considered. Their activities are calculated based on the isotopic abundance of xenon and the cross sections of thermal neutron capture. Among those isotopes, 8/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. Table 3. Summary of systematic parameters and their uncertainties used as constraints in the spectrum fitting. Item Fractional uncertainty Period dependence 222 214 214 Rn daughters ( Bi and Pb) Unconstrained Assumed Kr ±23% Assumed Ar Unconstrained Assumed C Unconstrained Assumed Thermal neutron flux ±27% Assumed 131m Additional Xe Unconstrained Assumed Additional Xe Unconstrained Assumed 238 232 γ -ray backgrounds from PMTs ±9.4% ( U), ±24% ( Th), Not assumed 60 40 ±11% ( Co), ±17% ( K) 124 126 Isotopic abundance ±8.5% ( Xe), ±12% ( Xe) Not assumed Fiducial volume ±4.5% Not assumed β CL acceptance for γ -ray ±30% Not assumed β CL acceptance for β -ray ±8.0% Not assumed Energy scale (β -depleted sample) ±2.0% Assumed Energy scale (β -enriched sample) ±2.0% Assumed 125 125 125 125m I is the most considerable background in this analysis. The I is produced from Xe and Xe 124 125 created by thermal neutron capture on Xe with a total cross section of 165±11 barn [52]. I 125 125 decays by 100% electron capture via an excited state of Te into the ground state of Te with a total energy deposition of 67.5 keV. The flux of thermal neutrons (E < 0.5 eV) in the Kamioka mine −5 2 has been measured to be (0.8–1.4)×10 /cm /s [53,54]. In this analysis, the thermal neutron flux 125 131m 133 during each period is fitted under the constraint of these measurements. I, Xe, and Xe are the main RIs relevant to this analysis and the entire energy range of the beta-depleted samples has the power to constrain the thermal neutron flux. Activations of xenon by neutrons emitted from the (α, n) reaction or spontaneous fission in the detector material are negligible. In addition, occasional neutron activations of the LXe appear in periods 1 and 4 due to the Cf calibration and the purification work. The data taken just after the Cf calibration, which were excluded from this analysis, showed 131m 133 clear event rate increases in the energy range between 30 and 200 keV due to Xe and Xe. 131m 133 To accommodate these backgrounds, we introduce additional quantities of Xe and Xe in the fitting. For the external backgrounds, a detailed evaluation of radioactive backgrounds from each detector material has been conducted previously [49]. In the present data set, a small contribution of γ -ray 238 232 60 40 backgrounds from impurities in the PMTs is expected. U, Th, Co, and K are considered, and the uncertainties in their activities are accounted for in the fitting. 6.3. Systematic uncertainties Systematic uncertainties in the background yields, exposure, event selections, and energy scales are considered in the fitting, as listed in Table 3. The upper part of Table 3 summarizes the systematic parameters used to determine the activities of RI backgrounds in the spectrum fitting. The Kr activity, thermal neutron flux, and γ -ray backgrounds from the PMTs are constrained by the external measurements as described in the previous section since this spectrum fitting does not have the sensitivity for an independent evaluation. The isotopic composition of the LXe was measured with a mass spectrometer, and the result was consistent with that of natural xenon in air [37]. The uncertainties in the measurement, ±8.5% for 9/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. 124 126 Xe and ±12% for Xe, are treated as a systematic error. The uncertainties in the LXe density and the detector live time are negligible. The uncertainties in the event selections and energy scales are estimated from comparisons between data and simulated samples for the Am (59.5 keV γ -ray) and Co (122 keV γ -ray) calibration data at various positions within the fiducial volume. The radial position of the reconstructed vertex for the calibration data differs from that for the simulated result by ±4.5 mm near the fiducial volume boundary, which causes ±4.5% uncertainty in the fiducial LXe volume. From the difference in the β CL distribution between the calibration data and simulated samples, the uncertainty in the acceptance of the β CL cut for the γ -ray events is found to be ±30%. In the same manner, the uncertainty in the rejection power of the β CL cut for β -ray events is evaluated to be ±8.0% from the comparison of the β CL distributions for the Bi sample in the energy range from 30 to 200 keV . By comparing the peak position of the γ -ray calibration data and simulated ee samples at various source positions and in different periods, the uncertainty in energy scale for the γ -ray events is estimated to be ±2.0%. Since we observe a small difference in the peak position of the γ -ray calibration data between the β -depleted and β -enriched samples, the energy scales for the β -depleted and β -enriched samples are treated independently. 7. Results and discussion Figure 4 shows the energy spectra for the β -depleted samples, β -enriched samples, and Bi samples. The observed spectra are overlaid with the best-fit 2ν2K signal and background spectra. The best-fit -4 Period1 (124.0 days) Period2 (249.1 days) Period3 (338.1 days) Period4 (88.8 days) x10 131m Xe 2ν2K Xe -3 x10 39 85 Ar Kr Pb 0.5 -4 x10 Bi 50 100 150 50 100 150 50 100 150 Energy (keV ) Energy (keV ) Energy (keV ) Energy (keV ) ee ee ee ee Fig. 4. Energy spectra for the β -depleted samples (top), β -enriched samples (middle), and Bi samples (bottom). The observed data spectra (points) are overlaid with the best-fit 2ν2K signal and background spectra 125 131m (colored stacked histograms). Colored histograms are the 2ν2K signal (red filled), I (green hatched), Xe 133 14 39 85 214 (red hatched), Xe (blue hatched), C (orange filled), Ar (magenta filled), Kr (blue filled), Pb (cyan 214 136 filled), Bi (green filled), Xe 2νββ (brown filled), and external backgrounds (gray filled). 10/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 β-enriched sample β-depleted sample Bi sample (events/day/kg/keV ) (events/day/kg/keV ) (events/day/kg/keV ) ee ee ee PTEP 2018, 053D03 K. Abe et al. Period1 Period2 Period3 Period4 0.4 0.3 0.2 0.1 0.8 0.6 0.4 0.2 0.3 0.2 0.1 0 200 400 600 800 1000 Days from 1 Jan 2014 214 85 39 14 Fig. 5. Time variation of the fitted activities of Bi, Kr, Ar, and C in the active 832-kg LXe volume. The left and right edges of the horizontal error bars represent the start and end of each period, respectively. Period1 Period2 Period3 Period4 1.5 0.5 0.15 0.1 0.05 0.15 0.1 0.05 1.02 0.98 0 200 400 600 800 1000 Days from 1 Jan 2014 131m 133 Fig. 6. Time variation of the fitted thermal neutron flux, additional activities of Xe, Xe in the active 832-kg LXe volume, and energy scales for the β -enriched (black circle) and β -depleted samples (red rectangle). The left and right edges of the horizontal error bars represent the start and end of each period, respectively. 2 214 result gives χ /ndf = 1073/999. The bottom figures determine the activities of Bi in LXe and 214 39 14 constrain the Pb activities. The middle figures determine the Ar and C activities while the amount of Kr is constrained by the independent β –γ coincidence measurement. The variation in 214 85 39 14 time of the fitted activities of Bi, Kr, Ar, and C in the active 832-kg LXe volume are shown in Fig. 5. The Rn concentration in LXe increased by ∼50% after gas circulation was initiated at the beginning of period 3. It is surmised that Rn emanating from detector materials in the xenon gas volume mixes into the LXe by the gas circulation. An increase of the Ar concentration in period 3 is thought to occur in the same manner. On the other hand, the C concentration decreased with gas circulation. Figure 6 shows the variation in time of the fitted thermal neutron flux, additional activities of 131m 133 Xe and Xe in the active 832-kg LXe volume, and energy scales. The fitted thermal neutron −6 2 131m flux is stable over the entire data set at ∼8×10 /cm /s. The larger amounts of Xe in periods 1 11/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 14 39 85 214 Thermal n flux 133 131m C (mBq) Ar (mBq) Kr (mBq) Bi (mBq) Energy scale Xe (mBq) Xe (mBq) -5 -2 -1 x10 (cm s ) PTEP 2018, 053D03 K. Abe et al. -4 -4 x10 x10 Period1 (124.0 days) Period2 (249.1 days) 1.5 1.5 1 1 2ν 2K Xe 0.5 0.5 0 0 40 60 80 100 40 60 80 100 Energy (keV ) Energy (keV ) ee ee -4 -4 x10 x10 Period3 (338.1 days) Period4 (88.8 days) 1.5 1.5 1 1 0.5 0.5 0 0 40 60 80 100 40 60 80 100 Energy (keV ) Energy (keV ) ee ee Fig. 7. Closeup figures of energy spectra between 30 and 100 keV for the β -depleted samples. The observed ee spectra (points) are overlaid with the best-fit 2ν2K signal and background spectra (colored stacked histograms). 125 133 14 Colored histograms are the 2ν2K signal (red filled), I (green hatched), Xe (blue hatched), C (orange 39 85 214 136 filled), Ar (magenta filled), Kr (blue filled), Pb (cyan filled), Xe 2νββ (brown filled), and external backgrounds (gray filled). and 4 are explained by the neutron activation of LXe while storing the LXe outside the water shield 252 133 and caused by the Cf calibrations. Increases in the Xe yield in periods 1 and 4 are not significant 131m compared with the increases in the Xe yield. The fitted energy scales for the β -enriched and β -depleted samples vary within ±2%, which is consistent with the evaluation before fitting. Closeup figures of energy spectra between 30 and 100 keV for the β -depleted samples are shown ee 125 125 in Fig. 7. The peak found at 67.5 keV is attributable to the I decay. The event rate of the I ee decay is constrained by the thermal neutron flux. Figure 8 shows the normalized profile likelihood L/L as a function of the inverse of the Xe max 2ν2K half-life, where L is the maximum value of the likelihood. No significant excess over the max expected background is found in the signal region. We calculate the 90% CL limit from the relation limit L(ξ )dξ = 0.9, (6) L(ξ )dξ 2ν2K where ξ = 1/T . This leads to 1/2 2ν2K 124 22 T Xe > = 2.1 × 10 years. (7) 1/2 limit The fact that we do not observe significant excess above the background allows us to give a constraint on 2ν2K on Xe in the same manner: 2ν2K 126 22 T Xe > 1.9 × 10 years (8) 1/2 at 90% CL. 12/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 (events/day/kg/keV ) (events/day/kg/keV ) ee ee (events/day/kg/keV ) (events/day/kg/keV ) ee ee PTEP 2018, 053D03 K. Abe et al. 0.8 0.6 0.4 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 -22 -1 T (x10 year ) 1/2 Fig. 8. Normalized profile likelihood L/L as a function of the inverse of the Xe 2ν2K half-life. The max vertical line indicates the 90% quantile from which the lower limit on the half-life is derived. XMASS(This work) XMASS(2016) Gavrilyuk et al. 10 XENON100 QRPA QRPA SU(4) PHFB PHFB MCM τσ Singh Shukla Suhonen Hirsch Aunola Rumyantsev Fig. 9. Comparison of the experimental 90% CL exclusion limits on the Xe 2ν2K half-life overlaid with the theoretical calculations [21,28–32]. The lower and upper edges of the theoretical predictions correspond to g = 1.26 and g = 1, respectively. A A Figure 9 shows a comparison of the experimental 90% CL exclusion limits on the Xe 2ν2K half-life overlaid with the theoretical calculations [21,28–32] for comparison. The present result gives a lower limit stronger by a factor of 4.5 over our previous result, and gives the most stringent experimental constraint reported to date. For the theoretical predictions, the reported 2νECEC half- lives are converted to 2ν2K half-lives, divided by the branching ratio for the two electrons being captured from the K -shell, P = 0.767 [55]. The lower and upper edges of the bands correspond 2K to g = 1.26 and g = 1, respectively. A A Note that the predicted half-lives will be longer if quenching of g is larger. These experimental results rule out part of the relevant range of the reported half-life predictions, and future experiments with multi-ton LXe targets will have improved sensitivity to further explore this parameter space. 8. Conclusion 124 126 We have conducted an improved search for 2ν2K on Xe and Xe using 800.0 days of data from XMASS-I. For this search, a novel method to discriminate γ -ray/X-ray or 2ν2K signals from β -ray 13/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 Profile likelihood Xe 2ν2K half-life (years) PTEP 2018, 053D03 K. Abe et al. backgrounds using LXe scintillation time profiles was developed. With spectrum fitting in the energy range from 30 to 200 keV , no significant 2ν2K signal appeared over the expected background. ee Therefore, we set the most stringent lower limits on the half-lives for these processes at 2.1 × 10 124 22 126 years for Xe and 1.9 × 10 years for Xe at 90% CL. Acknowledgements We gratefully acknowledge the cooperation of the Kamioka Mining and Smelting Company. This work was supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology, Grants-in-Aid for Scientific Research (19GS0204, 26104004, and 16H06004), the joint research program of the Institute for Cosmic Ray Research (ICRR), the University of Tokyo, and partially by a National Research Foundation of Korea Grant funded by the Korean Government (NRF-2011-220-C00006). References [1] R. G. Winter, Phys. Rev. 100, 142 (1955). [2] M. Doi and T. Kotani, Prog. Theor. Phys. 89, 139 (1993). [3] J. D. Vergados, Nucl. Phys. B 218, 109 (1983). [4] J. Bernabeu, A. De Rujula, and C. 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Available at: https://www-nds.iaea.org/publications/indc/indc-nds-0440/. [53] A. Minamino, Master Thesis, University of Tokyo (2004). [54] W. Ootani, Master Thesis, University of Tokyo (1994). [55] M. Doi and T. Kotani, Prog. Theor. Phys. 87, 1207 (1992). 15/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Progress of Theoretical and Experimental Physics Oxford University Press

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Abstract

Prog. Theor. Exp. Phys. 2018, 053D03 (15 pages) DOI: 10.1093/ptep/pty053 Improved search for two-neutrino double electron 124 126 capture on Xe and Xe using particle identification in XMASS-I XMASS Collaboration 1,5 1,5 1,5 1,5 1,5 1 K. Abe , K. Hiraide , K. Ichimura , Y. Kishimoto , K. Kobayashi , M. Kobayashi , 1,5 1,5 1 1,5 1 1,5 S. Moriyama , M. Nakahata , T. Norita ,H.Ogawa , K. Sato , H. Sekiya , 1 1,5 1 1,5 1,5 2 O. Takachio , A. Takeda , S. Tasaka , M. Yamashita , B. S. Yang , N. Y. Kim , 2 3,6 3 3 3 3 4,12 Y. D. Kim , Y. Itow , K. Kanzawa ,R.Kegasa , K. Masuda , H. Takiya , K. Fushimi , 4 5 5 5 7 7,13 7 G. Kanzaki , K. Martens , Y. Suzuki ,B.D.Xu , R. Fujita , K. Hosokawa , K. Miuchi , 7 7,5 8,2 8 8 9 10 N. Oka , Y. Takeuchi , Y.H.Kim ,K.B.Lee ,M.K.Lee , Y. Fukuda , M. Miyasaka , 10 11 K. Nishijima , and S. Nakamura Kamioka Observatory, Institute for Cosmic Ray Research, the University ofTokyo, Higashi-Mozumi, Kamioka, Hida, Gifu 506-1205, Japan Center of Underground Physics, Institute for Basic Science, 70Yuseong-daero 1689-gil,Yuseong-gu, Daejeon 305-811, South Korea Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8601, Japan Institute of Socio-Arts and Sciences, The University of Tokushima, 1-1 Minamijosanjimacho Tokushima city, Tokushima 770-8502, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), the University of Tokyo, Kashiwa, Chiba 277-8582, Japan Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan Korea Research Institute of Standards and Science, Daejeon 305-340, South Korea Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan Department of Physics, Faculty of Engineering, Yokohama National University, Yokohama, Kanagawa 240- 8501, Japan Present address: Department of Physics, Tokushima University, 2-1 Minami Josanjimacho Tokushima city, Tokushima 770-8506, Japan Present address: Research Center for Neutrino Science, Tohoku University, Sendai, Miyagi 980-8578, Japan E-mail: xmass.publications7@km.icrr.u-tokyo.ac.jp Received January 10, 2018; Revised April 13, 2018; Accepted April 14, 2018; Published May 30, 2018 ................................................................................................................... We conducted an improved search for the simultaneous capture of two K -shell electrons on 124 126 the Xe and Xe nuclei with emission of two neutrinos using 800.0 days of data from the XMASS-I detector. A novel method to discriminate γ -ray/X-ray or double electron capture signals from β -ray background using scintillation time profiles was developed for this search. No significant signal was found when fitting the observed energy spectra with the expected signal and background. Therefore, we set the most stringent lower limits on the half-lives at 2.1 × 10 22 124 126 and 1.9 × 10 years for Xe and Xe, respectively, with 90% confidence level. These limits improve upon previously reported values by a factor of 4.5. ................................................................................................................... Subject Index C04, C43, D29 © The Author(s) 2018. Published by Oxford University Press on behalf of the Physical Society of Japan. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. 1. Introduction Double electron capture (ECEC) is a rare nuclear decay process where a nucleus captures two orbital electrons simultaneously. There might be two modes of the process: (Z , A) + 2e → (Z − 2, A), (1) (Z , A) + 2e → (Z − 2, A) + 2ν , (2) where Z and A are the atomic number and atomic mass number of the nucleus, respectively. Detecting the neutrinoless mode of this process (0νECEC) would provide evidence for lepton number violation and the Majorana nature of the neutrino if observed. To release the decay energy in 0νECEC, there are two proposed mechanisms: the radiative and the resonant mechanisms. In the case of the radiative mechanism, the decay energy is carried away by emitting, e.g., an internal Bremsstrahlung photon [1,2]. This process is, however, expected to have a much longer lifetime than neutrinoless double beta decay. On the other hand, an enhancement of the capture rate by a factor as large as 10 is possible if the initial and final (excited) masses of the nucleus are degenerate [3–8]. Therefore, experimental searches for 0νECEC have recently been performed for a variety of candidate nuclei [9–19]. Although two-neutrino double electron capture (2νECEC) is allowed within the Standard Model of particle physics, only a few positive experimental results for 2νECEC have been reported: geo- 130 78 chemical measurements of Ba [22,23] and a direct measurement of Kr [19,24] with half-lives 21 22 of the order of 10 –10 years. Despite the fact that the nuclear matrix element for the two-neutrino mode differs from that for the neutrinoless mode, they are related to each other through the relevant parameters in a chosen nuclear model [25]. For instance, the nucleus’ axial current coupling con- stant g and the strength of the particle–particle interaction g in the quasiparticle random-phase A pp approximation (QRPA) model are obtained from single β -decay and two-neutrino double beta decay measurements [26]. Measurements of the 2νECEC half-lives with various nuclei would shed new light on constraining these parameters. 124 126 Natural xenon contains Xe (abundance 0.095%) and Xe (0.089%), in which ECEC can be observed. Xe has the highest Q-value among all the known candidate nuclei for ECEC at + + + 2864 keV [27]. This Q-value is sufficiently large to open the β EC and β β channels. The predictions in the literature for the half-lives of Xe 2νECEC are spread over a wide range between 20 24 10 and 10 years [21,28–32] depending on the models used for calculating the corresponding nuclear matrix element and the effective value of the nucleus’ g . Although Xe can also undergo 126 124 2νECEC, the lifetime of this process for Xe is expected to be much longer than that for Xe since its Q-value is smaller at 920 keV [27]. Previous experimental searches for 2νECEC on Xe have sought the simultaneous capture of two K -shell electrons (2ν2K) using a gas proportional counter with enriched xenon and large-volume liquid xenon (LXe) detectors with natural xenon as the target. An experiment with a proportional counter containing 58.6 g of Xe (enriched to 23%) published the latest lower bound on the half- 2ν2K 124 21 life, T Xe > 2.0 × 10 years at 90% confidence level (CL) [33,34]. Large-volume LXe 1/2 detectors can also observe 2νECEC on Xe [35,36]. The XMASS experiment has conducted a search with a fiducial xenon mass of 41 kg (containing 39 g of Xe) and set the most stringent 2ν2K 124 21 lower limit of T Xe > 4.7 × 10 years [37]. The XENON100 experiment also published 1/2 a result obtained with a fiducial xenon mass of 34 kg (containing about 29 g of Xe) and set a 2ν2K 124 20 lower limit of T Xe > 6.5 × 10 years [38]. These searches were conducted with similar 1/2 2/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. Table 1. Summary of experimental searches for two-neutrino double electron capture on Xe reported to date compared with this work. 124 2ν2K 124 21 Experiment Xe target mass (g) Live time T Xe (10 years) 1/2 XMASS (this work) 311 800.0 days > 21 XMASS [37] 39 132.0 days > 4.7 Gavrilyuk et al. [34] 58.6 3220 h > 2.0 XENON100 [38] 29 224.6 days > 0.65 amounts of Xe and live times, as summarized in Table 1. In addition, the XMASS experiment set 126 2ν2K 126 21 the first experimental lower limit on the Xe 2ν2K half-life at T Xe > 4.3 × 10 years 1/2 using the same data set. 124 126 In this paper, we report the results of an improved search for Xe and Xe 2ν2K events, using data from the XMASS-I detector. We analyze a new data set taken between November 2013 and July 2016. The total live time amounts to 800.0 days and the fiducial xenon mass was enlarged to 327 kg (containing about 311 g of Xe). We developed a novel method for discriminating the 2ν2K signal from the β -ray background using LXe scintillation time profiles. 2. The XMASS-I detector XMASS-I is a large single-phase LXe detector located underground (2700 m water equivalent) at the Kamioka Observatory in Japan [39]. An active target of 832 kg of LXe is held inside a pentakis-dodecahedral copper structure that hosts 642 inward-looking 2-inch Hamamatsu R10789 photomultiplier tubes (PMTs) on its approximately spherical inner surface at a radius of about 40 cm. The photocathode coverage of the inner surface is 62.4%. Signals from each PMT are recorded with CAEN V1751 waveform digitizers with a sampling rate of 1 GHz and 10-bit resolution. The gains of the PMTs are monitored weekly using a blue LED embedded in the inner surface of the detector. The scintillation yield response is traced with a Co source [40] inserted along the central vertical axis of the detector every week or two. Through measurements with the Co source at the center of the detector volume, the photoelectron (PE) yield was determined to be ∼15 PE/keV for 122 keV γ -rays. The nonlinear response of the scintillation yield for electron-mediated events 55 241 in the detector was calibrated over an energy range from 5.9 keV to 2614 keV with Fe, Am, 109 57 137 60 232 Cd, Co, Cs, Co, and Th sources. Hereinafter, this calibrated energy is represented as keV where the subscript stands for the electron-equivalent energy. The timing offsets for the PMT ee channels owing to the differences in their cable lengths and the electronic responses were also traced by Co calibration. The LXe detector is located at the center of a cylindrical water Cherenkov detector, which is 11 m in height and 10 m in diameter. The outer detector is equipped with 72 20-inch Hamamatsu H3600 PMTs. This detector acts as an active veto counter for cosmic-ray muons as well as a passive shield against neutrons and γ -rays from the surrounding rock. Data acquisition is triggered if at least four inner-detector PMTs record a signal within 200 ns or if at least eight outer-detector PMTs register a signal within 200 ns. A 50 MHz clock is used to measure the time difference between triggers. One-pulse-per-second (1PPS) signals from the global positioning system (GPS) are fed as triggers for precise time stamping. The GPS 1PPS triggers are also used to flash the LED for the PMT gain monitoring. 3/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. 3. Expected signal and simulation The process of 2νECEC on Xe is 124 − 124 Xe + 2e → Te + 2ν . (3) 124 124 If two K -shell electrons in the Xe atom are captured simultaneously, a daughter atom of Te is formed with two vacancies in the K -shell and this atom relaxes by emitting atomic X-rays and/or Auger electrons. Our Monte Carlo simulations of the atomic de-excitation signal are based on the atomic relaxation package in Geant4 [41,42]. On the assumption that the X-rays and Auger electrons emitted in the 2ν2K event are like those generated by two single K -shell vacancies, the signal simulation begins with two Te atoms with a single K -shell vacancy. In such a case, the total energy deposition is given by twice the K -shell binding energy of Te (2K = 63.63 keV). On the other hand, the energy of the two electron holes in the K -shell of Te is calculated to be 64.46 keV [43], which only varies by 0.8 keV. Since the energy resolution of the 2ν2K signal peak is estimated to be 3.2 keV after all the detector responses mentioned below are accounted for, we judge that this difference is negligible in our analysis. The results actually do not change even if the peak position of the simulated signal is artificially shifted by this amount. According to the simulation, 77% of 2ν2K events emit two K -shell X-rays, 21% of events emit a single K -shell X-ray, and the remaining 1.6% of events emits no K -shell X-ray. These probabilities are consistent with those expected from the fluorescence yield for the K -shell of Te, ω = 0.875 [44]. Auger electron cascades are also simulated. The energy deposition from the recoil of the daughter nucleus is ∼30 eV at most, which is negligible. Simulated de-excitation events are generated uniformly throughout the detector volume. The nonlinearity of scintillation yield is accounted for using the nonlinearity model from Doke et al. [45] with a further correction obtained from the γ -ray calibrations. The absolute energy scale of the simulation is adjusted at 122 keV. The time profile of the scintillation is also modeled based on the γ -ray calibrations [46]. Propagation of scintillation photons in LXe is also simulated. Optical parameters of the LXe such as absorption and scattering lengths for the scintillation are tuned by source calibration data at various positions. The group velocity of the scintillation light in the LXe follows from LXe’s refractive index (∼11 cm/ns for 175-nm light [47]). Charge and timing responses of the PMTs are also modeled in the simulation based on the calibrations with the LED and the γ -ray sources. Finally, waveforms of the PMT signal are simulated using the template of a single-PE waveform obtained from the LED calibration data. 4. Data set The data used in the present analysis were collected between 20 November 2013 and 20 July 2016. The data set was divided into four periods depending on the detector conditions at that time, as summarized in Table 2. Period 1 started two weeks after the introduction of LXe into the detector. At 131m 129m the beginning of the run, we observed neutron-activated peaks from Xe and Xe that were created when the LXe was stored outside the water shield. We also performed the Cf calibration data collection twice in this period. Runs within 10 days after each calibration were excluded from 252 131m the data set. We ended period 1 60 days after the second Cf calibration because the Xe and 129m 252 Xe peaks caused by the Cf disappeared. Period 2 then ran until continuous gas circulation at a flow rate of ∼1.5 L/min with a getter purifier was introduced. Period 3 was ended so that the xenon could be purified by vaporizing it once to remove possible non-volatile impurities dissolved in LXe. During the purification process, LXe was extracted from the detector and therefore the xenon was 4/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. Table 2. Summary of the data set used in this analysis. Period Start date–end date Live time (days) Gas circulation Comment 1 20 Nov 2013–13 May 2014 124.0 None Activated 2 13 May 2014–13 Mar 2015 249.1 None 3 13 Mar 2015–29 Mar 2016 338.1 ∼1.5 L/min 4 14 Apr 2016–20 Jul 2016 88.8 ∼1.5 L/min Activated exposed to and activated by thermal neutrons outside the water shield. The purification process took 7 days and period 4 started immediately after completing the introduction of LXe into the detector. We selected periods of operation under what we call normal data taking conditions with a stable temperature (172.6–173.0 K) and pressure (0.162–0.164 MPa absolute) of the LXe in the detector. After further removing periods of operation that include excessive PMT noise, unstable pedestal levels, or abnormal trigger rates, the total live time became 800.0 days. 5. Event reduction and classification The event-reduction process comprises four steps: pre-selection, the fiducial volume selection, Bi identification, and particle identification. 5.1. Pre-selection Pre-selection requires that no outer-detector trigger is associated with an event, that the time elapsed since the previous inner-detector event (dT ) is at least 10 ms, and that the standard deviation of pre the inner-detector hit timing distribution in the event is less than 100 ns. The last two requirements remove events caused by after-pulses in the PMTs following bright events. The dT cut eliminates pre events by chance coincidence at a probability of 3.0% on average, which was estimated from the fraction of the GPS 1PPS events that are rejected by this cut. The chance coincidence probability is counted as dead time, and the live time mentioned above is obtained after subtracting this dead time. 5.2. Fiducial volume selection To select events that occurred within the fiducial volume, an event vertex is reconstructed based on a maximum-likelihood evaluation of the observed light distribution in the detector [39]. We select events whose reconstructed vertex has a radial distance of less than 30 cm from the center of the detector. The fiducial mass of natural xenon in that volume is 327 kg, containing 311 g of Xe and 291gof Xe. 5.3. Bi identification Rn emanates from the detector’s surface and contaminates the LXe within the detector. Thus, its 214 214 214 daughters, Bi and Pb, become one of the major sources of β -ray background. Bi can be 214 214 tagged using the Bi– Po delayed coincidence (T = 164 μs) and is used as a good control 1/2 sample of pure β -ray events in the relevant energy range. To remove the Bi events, events whose time difference from the subsequent event (dT ) is less than 1 ms are rejected from the 2ν2K signal post sample. This cut reduces the Bi background by a factor of ∼70, while consequently discarding only 0.4% of all other events. The counterpart sample, i.e., events with 0.015 ms < dT < 1 ms, post 214 214 214 is referred to as the Bi sample and is used to constrain the Bi and Pb backgrounds. 5/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. -50 0 50 100 150 Time (ns) 241 241 Fig. 1. An example waveform recorded in a PMT from the Am calibration data. The Am source was placed at z = 20 cm. Red dashed curves represent decomposed single-PE pulses. 5.4. Particle identification The scintillation time profiles of LXe can be used for particle identification. We use them to eliminate both the α-ray and β -ray backgrounds from the 2ν2K signal sample. After the fiducial volume selection, the largest source of background in the relevant energy range is β -rays coming from radioactive impurities within the LXe. 2ν2K or γ -ray events can be discriminated from these β -ray events by utilizing the energy dependence of the scintillation decay time for electron- induced events. The scintillation decay time increases from 28 ns to 48 ns as the kinetic energy of an electron increases from 3 keV to 1 MeV, as summarized in Fig. 3 of Ref. [46]. In the case of the 2ν2K or γ -ray events, the X-ray or γ -ray is converted into multiple low-energy electrons in the LXe; this shortens the effective scintillation decay time by a few ns from that of an event caused by a single electron with the same deposited energy. In particular, events caused by 2ν2K or γ -rays with energy close to twice the K -shell binding energy are easily distinguishable from the β -ray events by this effective scintillation decay time. The particle-identification parameter β CL is formulated as follows. First, waveforms in each PMT are decomposed into single-PE pulses using the single-PE waveform template [46]. Figure 1 shows an example of a waveform recorded in a PMT from the Am calibration data. Decomposed single- PE pulses are also shown in the figure. The timings of the decomposed single-PE pulses in all the PMTs are sorted chronologically after correcting for the time-of-flight of scintillation photons. The single-PE pulses in the first 20 ns are excluded from the following calculation to avoid systematic uncertainties in the leading edge of the scintillation time profile. The variable β CL is defined as n−1 (− ln P) β CL = P × , (4) i! i=0 n−1 where n is the total number of single-PE pluses after truncating the first 20 ns, P = CL , i=0 and CL (i = 0, 1, 2, ... , n − 1) is the CL of each pulse timing under the assumption that the event is caused by a β -ray. The probability-density function of the pulse-timing distribution for a β -ray event including its energy and position dependences is modeled from measurements in the Bi data sample over the energy range between 30 and 200 keV . This formula is in general used to ee combine p-values from a set of independent tests for a certain hypothesis [48]. Figure 2 shows distributions of the variable β CL for the Bi sample in the energy range from 241 214 30 to 200 keV along with the Am 59.5 keV γ -ray events. While the β -ray events in the Bi ee 6/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 ADC counts PTEP 2018, 053D03 K. Abe et al. 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 βCL βCL Fig. 2. The particle-identification parameter β CL for the Bi β -ray events in the energy range from 30 to 200 keV (left) and the Am 59.5 keV γ -ray events (right). The distributions of the observed data (black ee points) and the simulated events (red curves) are normalized to the unit area. 5 5 10 10 4 4 10 10 3 3 10 10 2 2 10 10 10 10 1 1 40 60 80 100 120 140 160 180 200 40 60 80 100 120 140 160 180 200 Energy (keV ) Energy (keV ) ee ee Fig. 3. Energy spectra after each event reduction step for the observed data (left) and the simulated 2ν2K sample assuming T = 4.7 × 10 years (right). From top to bottom, energy distributions after the pre- 1/2 selection (black solid), fiducial volume selection (red solid), Bi rejection (blue dashed nearly overlaps with red solid), and β -like event rejection (magenta points) steps are shown. sample are distributed between 0 and 1, the distribution of the 59.5 keV γ -ray events in the Am sample peaks at β CL = 0. Events with β CL less than 0.05 are classified as the β -depleted sample, and the rest is referred to as the β -enriched sample. When selecting events with β CL less than 0.05, 42% of the 2ν2K signal events are selected, while only 6% of the β -ray events from the Bi decay in this energy range are selected. Thus, the signal-to-noise ratio is improved by a factor of 7 by this selection. The cut position is tuned based on the simulated data to maximize the sensitivity for the 2ν2K signal. α-ray events often occur in the grooves of the inner surface of the detector, so that only some of their energy is detected. These events are sometimes incorrectly reconstructed within the fiducial volume [49]. Above 30 keV , α-ray events can be clearly separated from β -ray or γ -ray events ee using the scintillation decay time. Therefore, the waveforms from all PMTs are summed up to form a total waveform of the event after correcting for the relative gain and timing of each PMT. Then, the falling edge of that total waveform is fitted with an exponential function to obtain the decay time for each event. Events with fitted decay times of less than 30 ns are deemed α-ray events and are rejected. Figure 3 shows the energy spectra plotted after each event-reduction step for the observed data and the simulated 2ν2K sample. For the simulated 2ν2K sample, T = 4.7 × 10 years is assumed. 1/2 7/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 Entries/2keV Probability density ee Entries/2keV Probability density ee PTEP 2018, 053D03 K. Abe et al. 6. Spectrum fitting 6.1. Chi-squared definition To extract the 2ν2K signal from the observed data, the energy spectra for the β -depleted samples, β -enriched samples, and Bi samples are simultaneously fitted to the expected signal and back- ground spectra. The energy range from 30 to 200 keV is used for fitting. The chi-squared value is ee defined as χ =−2ln L N N N sample period N data sys bin (1 − p ) exp ijk l data data = 2 n (p ) − n + n ln + , (5) exp ijk ijk ijk n (p ) σ ijk l i=1 j=1 k=1 l=1 exp data where n and n (p ) are the observed and expected number of events in the ith sub-sample, jth ijk ijk period, and k th energy bin, respectively. N = 3, N = 4, N = 85, and N are the sample period bin sys number of sub-samples, periods, energy bins, and constrained systematic parameters, respectively. p and σ are a scaling parameter for the nominal value and its relative error, respectively. l l 6.2. Expected background We consider three types of backgrounds: radioactive isotopes (RIs) in the LXe, neutron activation of xenon, and external backgrounds. 222 214 214 85 39 14 136 For the internal RIs, the Rn daughters ( Bi and Pb), Kr, Ar, C, and Xe are consid- 214 214 ered. The Bi activity during each period is determined from the fitting to the Bi sample and the 214 214 222 85 Pb activity in each period follows from this Bi activity as both originate from Rn. While Kr decays by β -decay (Q = 687 keV, T = 10.8 years) predominantly into the ground state of Rb, β 1/2 0.434% of their decays go into the 514-keV excited state of Rb followed by a nuclear relaxation γ -ray (T = 1.014 μs). Kr contamination in the detector is measured at 0.26 ± 0.06 mBq by the 1/2 coincidence of β -ray and γ -ray events. In this analysis, the Kr activity in each period is fitted with this constraint. We have also found argon contamination in the xenon through measurements of the sampled xenon gas using gas chromatography–mass spectrometry (GC–MS). The argon is thought to have adsorbed to the detector material when we conducted a leakage test of the LXe chamber using argon gas in 2013. Ar undergoes β -decay (Q = 565 keV, T = 269 years). By comparing β 1/2 the energy spectra for periods 2 and 3 of the data set, we found a reduction in event rate below ∼150 keV in the β -enriched sample. The difference in the energy spectra between two periods ee is consistent with the β -decay of C(Q = 156 keV, T = 5730 years). Hence, we assume β 1/2 that impurities containing carbon were reduced by gas circulation through the getter although its chemical form is not known. Finally, natural xenon contains Xe with an isotopic abundance of 136 21 8.9%, and Xe undergoes 2νββ decay (Q = 2.46 MeV, T = 2.2 × 10 years [50,51]). ββ 1/2 Although the LXe detector is shielded against environmental neutrons by water, some of the detector components such as the cable feed-through box, calibration system, and cryogenic system lie outside the water shield and are filled with xenon gas [39]. The volume of xenon gas outside 5 3 the water shield is estimated to be 2.6 × 10 cm at the standard temperature of 273.15 K and pressure of 10 Pa. This xenon is activated by thermal neutron capture and returned to the LXe in the 125 125m 125 127 127m 129m 131m 133 133m detector. The resulting 13 RIs, Xe, Xe, I, Xe, Xe, Xe, Xe, Xe, Xe, 135 135m 137 137 Xe, Xe, Xe, and Cs, are also considered. Their activities are calculated based on the isotopic abundance of xenon and the cross sections of thermal neutron capture. Among those isotopes, 8/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. Table 3. Summary of systematic parameters and their uncertainties used as constraints in the spectrum fitting. Item Fractional uncertainty Period dependence 222 214 214 Rn daughters ( Bi and Pb) Unconstrained Assumed Kr ±23% Assumed Ar Unconstrained Assumed C Unconstrained Assumed Thermal neutron flux ±27% Assumed 131m Additional Xe Unconstrained Assumed Additional Xe Unconstrained Assumed 238 232 γ -ray backgrounds from PMTs ±9.4% ( U), ±24% ( Th), Not assumed 60 40 ±11% ( Co), ±17% ( K) 124 126 Isotopic abundance ±8.5% ( Xe), ±12% ( Xe) Not assumed Fiducial volume ±4.5% Not assumed β CL acceptance for γ -ray ±30% Not assumed β CL acceptance for β -ray ±8.0% Not assumed Energy scale (β -depleted sample) ±2.0% Assumed Energy scale (β -enriched sample) ±2.0% Assumed 125 125 125 125m I is the most considerable background in this analysis. The I is produced from Xe and Xe 124 125 created by thermal neutron capture on Xe with a total cross section of 165±11 barn [52]. I 125 125 decays by 100% electron capture via an excited state of Te into the ground state of Te with a total energy deposition of 67.5 keV. The flux of thermal neutrons (E < 0.5 eV) in the Kamioka mine −5 2 has been measured to be (0.8–1.4)×10 /cm /s [53,54]. In this analysis, the thermal neutron flux 125 131m 133 during each period is fitted under the constraint of these measurements. I, Xe, and Xe are the main RIs relevant to this analysis and the entire energy range of the beta-depleted samples has the power to constrain the thermal neutron flux. Activations of xenon by neutrons emitted from the (α, n) reaction or spontaneous fission in the detector material are negligible. In addition, occasional neutron activations of the LXe appear in periods 1 and 4 due to the Cf calibration and the purification work. The data taken just after the Cf calibration, which were excluded from this analysis, showed 131m 133 clear event rate increases in the energy range between 30 and 200 keV due to Xe and Xe. 131m 133 To accommodate these backgrounds, we introduce additional quantities of Xe and Xe in the fitting. For the external backgrounds, a detailed evaluation of radioactive backgrounds from each detector material has been conducted previously [49]. In the present data set, a small contribution of γ -ray 238 232 60 40 backgrounds from impurities in the PMTs is expected. U, Th, Co, and K are considered, and the uncertainties in their activities are accounted for in the fitting. 6.3. Systematic uncertainties Systematic uncertainties in the background yields, exposure, event selections, and energy scales are considered in the fitting, as listed in Table 3. The upper part of Table 3 summarizes the systematic parameters used to determine the activities of RI backgrounds in the spectrum fitting. The Kr activity, thermal neutron flux, and γ -ray backgrounds from the PMTs are constrained by the external measurements as described in the previous section since this spectrum fitting does not have the sensitivity for an independent evaluation. The isotopic composition of the LXe was measured with a mass spectrometer, and the result was consistent with that of natural xenon in air [37]. The uncertainties in the measurement, ±8.5% for 9/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 PTEP 2018, 053D03 K. Abe et al. 124 126 Xe and ±12% for Xe, are treated as a systematic error. The uncertainties in the LXe density and the detector live time are negligible. The uncertainties in the event selections and energy scales are estimated from comparisons between data and simulated samples for the Am (59.5 keV γ -ray) and Co (122 keV γ -ray) calibration data at various positions within the fiducial volume. The radial position of the reconstructed vertex for the calibration data differs from that for the simulated result by ±4.5 mm near the fiducial volume boundary, which causes ±4.5% uncertainty in the fiducial LXe volume. From the difference in the β CL distribution between the calibration data and simulated samples, the uncertainty in the acceptance of the β CL cut for the γ -ray events is found to be ±30%. In the same manner, the uncertainty in the rejection power of the β CL cut for β -ray events is evaluated to be ±8.0% from the comparison of the β CL distributions for the Bi sample in the energy range from 30 to 200 keV . By comparing the peak position of the γ -ray calibration data and simulated ee samples at various source positions and in different periods, the uncertainty in energy scale for the γ -ray events is estimated to be ±2.0%. Since we observe a small difference in the peak position of the γ -ray calibration data between the β -depleted and β -enriched samples, the energy scales for the β -depleted and β -enriched samples are treated independently. 7. Results and discussion Figure 4 shows the energy spectra for the β -depleted samples, β -enriched samples, and Bi samples. The observed spectra are overlaid with the best-fit 2ν2K signal and background spectra. The best-fit -4 Period1 (124.0 days) Period2 (249.1 days) Period3 (338.1 days) Period4 (88.8 days) x10 131m Xe 2ν2K Xe -3 x10 39 85 Ar Kr Pb 0.5 -4 x10 Bi 50 100 150 50 100 150 50 100 150 Energy (keV ) Energy (keV ) Energy (keV ) Energy (keV ) ee ee ee ee Fig. 4. Energy spectra for the β -depleted samples (top), β -enriched samples (middle), and Bi samples (bottom). The observed data spectra (points) are overlaid with the best-fit 2ν2K signal and background spectra 125 131m (colored stacked histograms). Colored histograms are the 2ν2K signal (red filled), I (green hatched), Xe 133 14 39 85 214 (red hatched), Xe (blue hatched), C (orange filled), Ar (magenta filled), Kr (blue filled), Pb (cyan 214 136 filled), Bi (green filled), Xe 2νββ (brown filled), and external backgrounds (gray filled). 10/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 β-enriched sample β-depleted sample Bi sample (events/day/kg/keV ) (events/day/kg/keV ) (events/day/kg/keV ) ee ee ee PTEP 2018, 053D03 K. Abe et al. Period1 Period2 Period3 Period4 0.4 0.3 0.2 0.1 0.8 0.6 0.4 0.2 0.3 0.2 0.1 0 200 400 600 800 1000 Days from 1 Jan 2014 214 85 39 14 Fig. 5. Time variation of the fitted activities of Bi, Kr, Ar, and C in the active 832-kg LXe volume. The left and right edges of the horizontal error bars represent the start and end of each period, respectively. Period1 Period2 Period3 Period4 1.5 0.5 0.15 0.1 0.05 0.15 0.1 0.05 1.02 0.98 0 200 400 600 800 1000 Days from 1 Jan 2014 131m 133 Fig. 6. Time variation of the fitted thermal neutron flux, additional activities of Xe, Xe in the active 832-kg LXe volume, and energy scales for the β -enriched (black circle) and β -depleted samples (red rectangle). The left and right edges of the horizontal error bars represent the start and end of each period, respectively. 2 214 result gives χ /ndf = 1073/999. The bottom figures determine the activities of Bi in LXe and 214 39 14 constrain the Pb activities. The middle figures determine the Ar and C activities while the amount of Kr is constrained by the independent β –γ coincidence measurement. The variation in 214 85 39 14 time of the fitted activities of Bi, Kr, Ar, and C in the active 832-kg LXe volume are shown in Fig. 5. The Rn concentration in LXe increased by ∼50% after gas circulation was initiated at the beginning of period 3. It is surmised that Rn emanating from detector materials in the xenon gas volume mixes into the LXe by the gas circulation. An increase of the Ar concentration in period 3 is thought to occur in the same manner. On the other hand, the C concentration decreased with gas circulation. Figure 6 shows the variation in time of the fitted thermal neutron flux, additional activities of 131m 133 Xe and Xe in the active 832-kg LXe volume, and energy scales. The fitted thermal neutron −6 2 131m flux is stable over the entire data set at ∼8×10 /cm /s. The larger amounts of Xe in periods 1 11/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 14 39 85 214 Thermal n flux 133 131m C (mBq) Ar (mBq) Kr (mBq) Bi (mBq) Energy scale Xe (mBq) Xe (mBq) -5 -2 -1 x10 (cm s ) PTEP 2018, 053D03 K. Abe et al. -4 -4 x10 x10 Period1 (124.0 days) Period2 (249.1 days) 1.5 1.5 1 1 2ν 2K Xe 0.5 0.5 0 0 40 60 80 100 40 60 80 100 Energy (keV ) Energy (keV ) ee ee -4 -4 x10 x10 Period3 (338.1 days) Period4 (88.8 days) 1.5 1.5 1 1 0.5 0.5 0 0 40 60 80 100 40 60 80 100 Energy (keV ) Energy (keV ) ee ee Fig. 7. Closeup figures of energy spectra between 30 and 100 keV for the β -depleted samples. The observed ee spectra (points) are overlaid with the best-fit 2ν2K signal and background spectra (colored stacked histograms). 125 133 14 Colored histograms are the 2ν2K signal (red filled), I (green hatched), Xe (blue hatched), C (orange 39 85 214 136 filled), Ar (magenta filled), Kr (blue filled), Pb (cyan filled), Xe 2νββ (brown filled), and external backgrounds (gray filled). and 4 are explained by the neutron activation of LXe while storing the LXe outside the water shield 252 133 and caused by the Cf calibrations. Increases in the Xe yield in periods 1 and 4 are not significant 131m compared with the increases in the Xe yield. The fitted energy scales for the β -enriched and β -depleted samples vary within ±2%, which is consistent with the evaluation before fitting. Closeup figures of energy spectra between 30 and 100 keV for the β -depleted samples are shown ee 125 125 in Fig. 7. The peak found at 67.5 keV is attributable to the I decay. The event rate of the I ee decay is constrained by the thermal neutron flux. Figure 8 shows the normalized profile likelihood L/L as a function of the inverse of the Xe max 2ν2K half-life, where L is the maximum value of the likelihood. No significant excess over the max expected background is found in the signal region. We calculate the 90% CL limit from the relation limit L(ξ )dξ = 0.9, (6) L(ξ )dξ 2ν2K where ξ = 1/T . This leads to 1/2 2ν2K 124 22 T Xe > = 2.1 × 10 years. (7) 1/2 limit The fact that we do not observe significant excess above the background allows us to give a constraint on 2ν2K on Xe in the same manner: 2ν2K 126 22 T Xe > 1.9 × 10 years (8) 1/2 at 90% CL. 12/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 (events/day/kg/keV ) (events/day/kg/keV ) ee ee (events/day/kg/keV ) (events/day/kg/keV ) ee ee PTEP 2018, 053D03 K. Abe et al. 0.8 0.6 0.4 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 -22 -1 T (x10 year ) 1/2 Fig. 8. Normalized profile likelihood L/L as a function of the inverse of the Xe 2ν2K half-life. The max vertical line indicates the 90% quantile from which the lower limit on the half-life is derived. XMASS(This work) XMASS(2016) Gavrilyuk et al. 10 XENON100 QRPA QRPA SU(4) PHFB PHFB MCM τσ Singh Shukla Suhonen Hirsch Aunola Rumyantsev Fig. 9. Comparison of the experimental 90% CL exclusion limits on the Xe 2ν2K half-life overlaid with the theoretical calculations [21,28–32]. The lower and upper edges of the theoretical predictions correspond to g = 1.26 and g = 1, respectively. A A Figure 9 shows a comparison of the experimental 90% CL exclusion limits on the Xe 2ν2K half-life overlaid with the theoretical calculations [21,28–32] for comparison. The present result gives a lower limit stronger by a factor of 4.5 over our previous result, and gives the most stringent experimental constraint reported to date. For the theoretical predictions, the reported 2νECEC half- lives are converted to 2ν2K half-lives, divided by the branching ratio for the two electrons being captured from the K -shell, P = 0.767 [55]. The lower and upper edges of the bands correspond 2K to g = 1.26 and g = 1, respectively. A A Note that the predicted half-lives will be longer if quenching of g is larger. These experimental results rule out part of the relevant range of the reported half-life predictions, and future experiments with multi-ton LXe targets will have improved sensitivity to further explore this parameter space. 8. Conclusion 124 126 We have conducted an improved search for 2ν2K on Xe and Xe using 800.0 days of data from XMASS-I. For this search, a novel method to discriminate γ -ray/X-ray or 2ν2K signals from β -ray 13/15 Downloaded from https://academic.oup.com/ptep/article-abstract/2018/5/053D03/5021518 by Ed 'DeepDyve' Gillespie user on 21 June 2018 Profile likelihood Xe 2ν2K half-life (years) PTEP 2018, 053D03 K. Abe et al. backgrounds using LXe scintillation time profiles was developed. 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Published: May 30, 2018

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