Neutrinoless Double Beta Decay Sensitivity of the XLZD Rare Event Observatory

Neutrinoless Double Beta Decay Sensitivity of the XLZD Rare Event Observatory The XLZD Collaboration J. Aalbers1, K. Abe2, M. Adrover3, S. Ahmed Maouloud4, D. S. Akerib5,6, A. K. Al Musalhi7, F. Alder7, L. Althueser8, D. W. P. Amaral9, C. S. Amarasinghe10, A. Ames5,6, B. Andrieu4, N. Angelides11, E. Angelino12,13, B. Antunovic14,¶, E. Aprile15, H.M. Ara´ujo11,∗J. E. Armstrong16, M. Arthurs5,6, M. Babicz3, A. Baker18,11, M. Balzer19, J. Bang20, E. Barberio21, J. W. Bargemann10, E. Barillier3, A. Basharina-Freshville7, L. Baudis3, D. Bauer11, M. Bazyk22,21, K. Beattie23, N. Beaupere22, N. F. Bell21, L. Bellagamba24, T. Benson25, A. Bhatti16, T. P. Biesiadzinski5,6, R. Biondi26, Y. Biondi27, H. J. Birch3, E. Bishop28, A. Bismark3, C. Boehm29, K. Boese26, A. Bolotnikov30, P. Br´as31, R. Braun8, A. Breskin32, C. A. J. Brew33, S. Brommer34, A. Brown35,36, G. Bruni24, R. Budnik32, S. Burdin37, C. Cai38, C. Capelli3, G. Carini30, M. C. Carmona-Benitez39, M. Carter37, A. Chauvin40, A. Chawla41, H. Chen23, J. J. Cherwinka25, Y. T. Chin39, N. I. Chott42, A. P. Cimental Chavez3, K. Clark43, A. P. Colijn44, D. J. Colling11, J. Conrad45, M. V. Converse46, R. Coronel5,6, D. Costanzo36, A. Cottle7, G. Cox47, J. J. Cuenca-Garc´ıa3, D. Curran47, D. Cussans43, V. D’Andrea13,∥, L. C.Daniel Garcia4, I. Darlington7, S. Dave7, A. David7, G. J. Davies11, M. P. Decowski44, A. Deisting48, J. Delgaudio47, S. Dey49, C. Di Donato50, L. Di Felice11, P. Di Gangi24, S. Diglio22, C. Ding20, J. E. Y. Dobson18, M. Doerenkamp40, G. Drexlin34, E. Druszkiewicz46, C. L. Dunbar47, K. Eitel27, A. Elykov27, R. Engel27, S. R. Eriksen43, S. Fayer11, N. M. Fearon49, A. D. Ferella50,13, C. Ferrari13, N. Fieldhouse49, H. Fischer35, H. Flaecher43, T. Flehmke45, M. Flierman44, E. D. Fraser37, T.M.A. Fruth29, K. Fujikawa51, W. Fulgione12,13, C. Fuselli44, P. Gaemers44, R. Gaior4, R. J. Gaitskell20, N. Gallice30, M. Galloway3, F. Gao38, N. Garroum4, A. Geffre47, J. Genovesi39, C. Ghag7, S. Ghosh5,6,52, R. Giacomobono53, R. Gibbons54,23, F. Girard4, R. Glade-Beucke35, F. Gl¨uck27, S. Gokhale30, L. Grandi55, J. Green49, J. Grigat35, M. G. D. van der Grinten33, R. Gr¨oßle27, H. Guan52, M. Guida26, P. Gyorgy48, J. J. Haiston42, C. R. Hall16, T. Hall37, R. Hammann26, V. Hannen8, S. Hansmann-Menzemer40, N. Hargittai32, E. HartiganO’Connor20, S. J. Haselschwardt56, M. Hernandez3, S. A. Hertel57, A. Higuera9, C. Hils48, K. Hiraoka51, L. Hoetzsch26, M. Hoferichter58, G. J. Homenides17, N. F. Hood59, M. Horn47, D. Q. Huang60, S. Hughes37, D. Hunt49, M. Iacovacci53, Y. Itow51, E. Jacquet11, J. Jakob8, R. S. James21, F. Joerg26,3, S. Jones36, A. C. Kaboth41, F. Kahlert52, A. C. Kamaha60, Y. Kaminaga2, M. Kara27, P. Kavrigin32, S. Kazama51, M. Keller40, P. Kemp-Russell36, D. Khaitan46, P. Kharbanda44, B. Kilminster3, J. Kim10, R. Kirk20, M. Kleifges19, M. Klute34, M. Kobayashi51, D. Kodroff23, D. Koke8, A. Kopec61, E. V. Korolkova36, H. Kraus49, S. Kravitz62, L. Kreczko43, B. von Krosigk63, V. A. Kudryavtsev36, F. Kuger35,†N. Kurita5, H. Landsman32, R. F. Lang52, C. Lawes18, J. Lee64, B. Lehnert65, D. S. Leonard64, K. T. Lesko23, L. Levinson32, A. Li59, I. Li9, S. Li66, S. Liang9, Z. Liang67, J. Lin54,23, Y. -T. Lin26, S. Lindemann35, arXiv:2410.19016v2 [physics.ins-det] 30 Apr 2025 2 S. Linden30, M. Lindner26, A. Lindote31,‡W. H. Lippincott10, K. Liu38, J. Loizeau22, F. Lombardi48, J. A. M. Lopes68,∗∗, M. I. Lopes31, W. Lorenzon56, M. Loutit43, C. Lu20, G. M. Lucchetti24, T. Luce35, S. Luitz5,6, Y. Ma59, C. Macolino50,13, J. Mahlstedt45, B. Maier34,11, P. A. Majewski33, A. Manalaysay23, A. Mancuso24, L. Manenti29, R. L. Mannino69, F. Marignetti53, T. Marley11, T. Marrod´an Undagoitia26, K. Martens2, J. Masbou22, E. Masson4, S. Mastroianni53, C. Maupin47, C. McCabe18, M. E. McCarthy46, D. N. McKinsey54,23, J. B. Mclaughlin7, A. Melchiorre50, J. Men´endez70, M. Messina13, E. H. Miller5,6, B. Milosovic14, S. Milutinovic14, K. Miuchi71, R. Miyata51, E. Mizrachi69,16, A. 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Zuber65 3 1Nikhef and the University of Groningen, Van Swinderen Institute, 9747AG Groningen, Netherlands 2Kamioka Observatory, Institute for Cosmic Ray Research, and Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Higashi-Mozumi, Kamioka, Hida, Gifu 506-1205, Japan 3Physik-Institut, University of Z¨urich, 8057 Z¨urich, Switzerland 4LPNHE, Sorbonne Universit´e, CNRS/IN2P3, 75005 Paris, France 5SLAC National Accelerator Laboratory, Menlo Park, CA 94025-7015, USA 6Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA 94305-4085 USA 7Department of Physics and Astronomy, University College London (UCL), London WC1E 6BT, UK 8Institute for Nuclear Physics, University of M¨unster, 48149 M¨unster, Germany 9Department of Physics and Astronomy, Rice University, Houston, TX 77005, USA 10 Department of Physics, University of California, Santa Barbara, Santa Barbara, CA 93106-9530, USA 11 Department of Physics, Imperial College London, Blackett Laboratory, London SW7 2AZ, UK 12 INAF-Astrophysical Observatory of Torino, Department of Physics, University of Torino and INFN-Torino, 10125 Torino, Italy 13 INFN-Laboratori Nazionali del Gran Sasso and Gran Sasso Science Institute, 67100 L’Aquila, Italy 14 Vinca Institute of Nuclear Science, University of Belgrade, Mihajla Petrovica Alasa 12-14. Belgrade, Serbia 15 Physics Department, Columbia University, New York, NY 10027, USA 16 Department of Physics, University of Maryland, College Park, MD 20742-4111, USA 17 Department of Physics & Astronomy, University of Alabama, Tuscaloosa, AL 34587-0324, USA 18 Department of Physics, King’s College London, London WC2R 2LS, UK 19 Institute for Data Processing and Electronics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany 20 Department of Physics, Brown University, Providence, RI 02912-9037, USA 21 ARC Centre of Excellence for Dark Matter Particle Physics, School of Physics, The University of Melbourne, VIC 3010, Australia 22 SUBATECH, IMT Atlantique, CNRS/IN2P3, Nantes Universit´e, Nantes 44307, France 23 Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720-8099, USA 24 Department of Physics and Astronomy, University of Bologna and INFN-Bologna, 40126 Bologna, Italy 25 Physical Sciences Laboratory, University of Wisconsin-Madison, Madison, WI 53589-3034, USA 26 Max-Planck-Institut f¨ur Kernphysik, 69117 Heidelberg, Germany 27 Institute for Astroparticle Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany 28 SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, UK 29 School of Physics, The University of Sydney, Camperdown, Sydney, NSW 2006, Australia 30 Brookhaven National Laboratory (BNL), Upton, NY 11973-5000, USA 31 Laborat´orio de Instrumenta¸c˜ao e F´ısica Experimental de Part´ıculas (LIP), University of Coimbra, P-3004 516 Coimbra, Portugal 32 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel 33 STFC Rutherford Appleton Laboratory (RAL), Didcot, OX11 0QX, UK 4 34 Institute of Experimental Particle Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany 35 Physikalisches Institut, Universit¨at Freiburg, 79104 Freiburg, Germany 36 School of Mathematical and Physical Sciences, University of Sheffield, Sheffield S3 7RH, UK 37 Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK 38 Department of Physics & Center for High Energy Physics, Tsinghua University, Beijing 100084, P.R. China 39 Department of Physics, Pennsylvania State University, University Park, PA 16802-6300, USA 40 Physikalisches Institut, Universit¨at Heidelberg, Heidelberg, Germany 41 Department of Physics, Royal Holloway, University of London, Egham, TW20 0EX, UK 42 South Dakota School of Mines and Technology, Rapid City, SD 57701-3901, USA 43 H.H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, UK 44 Nikhef and the University of Amsterdam, Science Park, 1098XG Amsterdam, Netherlands 45 Oskar Klein Centre, Department of Physics, Stockholm University, AlbaNova, Stockholm SE-10691, Sweden 46 Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627-0171, USA 47 South Dakota Science and Technology Authority (SDSTA), Sanford Underground Research Facility, Lead, SD 57754-1700, USA 48 Institut f¨ur Physik & Exzellenzcluster PRISMA+, Johannes Gutenberg-Universit¨at Mainz, 55099 Mainz, Germany 49 Department of Physics, University of Oxford, Oxford OX1 3RH, UK 50 Department of Physics and Chemistry, University of L’Aquila, 67100 L’Aquila, Italy 51 Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, and Institute for Space-Earth Environmental Research, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan 52 Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA 53 Department of Physics “Ettore Pancini”, University of Napoli and INFN-Napoli, 80126 Napoli, Italy 54 Department of Physics, University of California, Berkeley, Berkeley, CA 94720-7300, USA 55 Department of Physics, Enrico Fermi Institute & Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA 56 Randall Laboratory of Physics, University of Michigan, Ann Arbor, MI 48109-1040, USA 57 Department of Physics, University of Massachusetts, Amherst, MA 01003-9337, USA 58 Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland 59 Department of Physics, University of California San Diego, La Jolla, CA 92093, USA 60 Department of Physics & Astronomy, University of Califonia, Los Angeles, Los Angeles, CA 90095-1547 61 Department of Physics & Astronomy, Bucknell University, Lewisburg, PA, USA 62 Department of Physics, University of Texas at Austin, Austin, TX 78712-1192, USA 63 Kirchhoff-Institut f¨ur Physik, Universit¨at Heidelberg, Heidelberg, Germany 64 IBS Center for Underground Physics (CUP), Yuseong-gu, Daejeon, Korea 65 Institut f¨ur Kern und Teilchenphysik, Technische Universit¨at Dresden, 01069 Dresden, Germany 66 Department of Physics, School of Science, Westlake University, Hangzhou 310030, P.R. China 5 67 School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong, 518172, P.R. China 68 LIBPhys, Department of Physics, University of Coimbra, 3004-516 Coimbra, Portugal 69 Lawrence Livermore National Laboratory (LLNL), Livermore, CA 94550-9698, USA 70 Departament de F´ısica Qu`antica i Astrof´ısica and Institut de Ci`encies del Cosmos, Universitat de Barcelona, 08028 Barcelona, Spain 71 Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan 72 Vatican Observatory, Castel Gandolfo, V-00120, Vatican City State 73 School of Natural Sciences, Black Hills State University, Spearfish, SD 57799-0002, USA 74 Theoretical and Scientific Data Science, Scuola Internazionale Superiore di Studi Avanzati (SISSA), 34136 Trieste, Italy 75 Department of Physics, Technische Universit¨at Darmstadt, 64289 Darmstadt, Germany 76 Department of Physics, University of California, Davis, Davis, CA 95616-5270, USA 77 INFN-Ferrara and Dip. di Fisica e Scienze della Terra, Universit`a di Ferrara, 44122 Ferrara, Italy ‡Corresponding author: [email protected] ∗Corresponding author: [email protected] †Corresponding author: F[email protected] §Corresponding author: [email protected] ¶Also at University of Banja Luka, 78000 Banja Luka, Bosnia and Herzegovina ∥Also at Also at INFN-Roma Tre, 00146 Roma, Italy ∗∗ Also at Coimbra Polytechnic - ISEC, 3030-199 Coimbra, Portugal †† Also at University of Grenada 6 Abstract. The XLZD collaboration is developing a two-phase xenon time projection chamber with an active mass of 60 to 80 t capable of probing the remaining WIMPnucleon interaction parameter space down to the so-called neutrino fog. In this work we show that, based on the performance of currently operating detectors using the same technology and a realistic reduction of radioactivity in detector materials, such an experiment will also be able to competitively search for neutrinoless double beta decay in 136Xe using a natural-abundance xenon target. XLZD can reach a 3σdiscovery potential half-life of 5.7×1027 yr (and a 90% CL exclusion of 1.3×1028 yr) with 10 years of data taking, corresponding to a Majorana mass range of 7.3–31.3 meV (4.8–20.5 meV). XLZD will thus exclude the inverted neutrino mass ordering parameter space and will start to probe the normal ordering region for most of the nuclear matrix elements commonly considered by the community. 1. Introduction The observation of neutrinoless double beta decay (0νββ) would have far-reaching consequences in Particle Physics and Cosmology. Forbidden by the Standard Model (SM) of Particle Physics, it implies the violation of lepton number as a global conservation law and may establish the Majorana nature of the neutrino [1, 2]. If the decay is mediated by the exchange of a light Majorana neutrino, the corresponding half-life is inversely proportional to the square of the effective Majorana neutrino mass, ⟨mββ⟩, (T0ν 1/2)−1=g4 AG0ν|M0ν|2⟨mββ⟩2 m2 e ,(1) where meis the electron mass, gAthe axial-vector coupling constant, G0νthe phase space factor, and M0νthe nuclear matrix element (NME) [3]. Several experimental techniques have been deployed and more are planned to search for this rare decay in a variety of isotopes [3, 4], with the current best lower limits (at 90% CL) on the 0νββ decay half-life (T0ν 1/2) set in the 1026 yr range, and ⟨mββ⟩ ≤ (28 −180) meV [5, 6]. The two-phase (liquid/gas) xenon time projection chamber (TPC) is the leading technology in the field of direct search for dark matter in the form of Weakly Interacting Massive Particles (WIMPs) [7–9], but it can also be used to search for 0νββ decay in 134Xe and 136Xe [10–13]. Efforts are underway to scale up this technology to tens of tonnes of target mass [14,15], sufficient to probe the remaining WIMP-nucleon interaction parameter space down to the “neutrino fog” [16–18]. The XENON-LUX-ZEPLIN-DARWIN (XLZD) collaboration was formed to consolidate the expertise and resources of the teams using this technology with the goal of building such a detector. The XLZD experiment will lead the dark matter direct-detection field for years to come, but with its large mass, low background and high sensitivity it will also be able to study many other physics channels, such as alternative dark matter candidates and neutrino properties, serving as a rare event observatory [15, 19]. Amongst these, XLZD will be able to competitively search for 0νββ in 136Xe, reaching or even surpassing the sensitivity of current and planned dedicated experiments using this isotope [5,20,21]. 7 In this work, we present the 136Xe 0νββ half-life sensitivity projections for XLZD using the expected performance and background rates of the experiment based on those of the current generation of detectors, in particular LUX-ZEPLIN (LZ) and XENONnT. We explore the dependence of this sensitivity on the active xenon mass, muon flux at the host laboratory, and possible 136Xe enrichment or depletion scenarios. The paper is organized as follows: in Section 2 we describe the XLZD experiment; in Section 3 we discuss the expected performance of the detector in the most relevant parameters for this search, and the various backgrounds which can impact it, developing two performance scenarios which are used for the sensitivity estimates; Section 4 describes the metrics used for calculating the 90% CL exclusion and 3σdiscovery half-life sensitivities, with the results for the half-life and Majorana mass reach being presented in Section 5; Section 6 offers conclusions from this work. 2. The XLZD experiment The indicative design for the detector at the core of XLZD is a cylindrical, two-phase xenon TPC with an active liquid mass of 60 t of natural xenon in a 1:1 height/diameter ratio, corresponding to approximately 3 m in both dimensions [19]. A more ambitious scenario is also foreseen in case of a favourable xenon supply market, with an active mass of 80 t in a configuration which maintains the TPC diameter but increases its height to about 4 m. With an abundance of 8.9% in natural xenon, this corresponds to 5.3 t and 7.1 t of 136Xe isotope in each of these mass stages. Interactions in the active xenon volume lead to the production of a prompt scintillation signal (termed ‘S1’) and a delayed electroluminescence signal (‘S2’) produced by the ionization electrons drifted upwards to the surface and extracted to the thin gas layer by electric fields defined by the anode, gate, and cathode electrode grids. In the typical configuration of this type of detector, both signals will be detected by two arrays of photosensors, at the top and bottom of the TPC. The standard choice for photosensors in liquid xenon TPCs has been photomultiplier tubes (PMTs) optimised to detect the xenon vacuum ultraviolet (VUV) light, although VUV-optimised Silicon Photomultipliers (SiPMs) or a hybrid configuration of both technologies are also being considered for XLZD. From these signals it is possible to accurately reconstruct the multiplicity, location(s), energy, and recoiling species for the interaction [22,23]. A field cage surrounding the active volume ensures a uniform vertical field and presents a highly reflective polytetrafluoroethylene (PTFE) [24] surface to maximise the collection of light from the S1 scintillation signal (which drives the energy threshold in such detectors). The entire inner TPC will be installed in a double-walled vacuum cryostat for thermal insulation. In a design similar to that of LZ [25], the XLZD TPC will be surrounded by two veto systems: the volume of xenon between the TPC field-cage and the inner cryostat wall (dubbed the “xenon skin”) will be instrumented with PMTs, and an outer detector 8 (OD) will surround the cryostat with near 4πcoverage. Several design options are being considered for the OD, from the use of liquid scintillator tanks [25] to a water-based Cherenkov detector [26], or a water-based liquid scintillator (WbLS) that would bridge the two media (see Ref. [19] for a more detailed discussion on these options). The goal of these two veto systems is to tag neutron and γ-ray backgrounds of radiogenic or cosmogenic origin with high efficiency [25–27]. To shield against cosmic-ray radiation, XLZD must be operated deep underground. Several world-renowned laboratories have indicated interest in hosting the experiment and are being considered for the final installation: Boulby [28], Kamioka [29], LNGS [30], SNOLAB [31] and SURF [32]. They offer varying levels of reduction of the cosmic muon flux, which in the case of 0νββ search has direct impact in the 137Xe background, as discussed in Section 3. In Section 5 we discuss the impact on the 0νββ sensitivity of operating XLZD at each of these laboratories. The TPC and veto systems will be installed in a large water tank to shield the experiment from environmental γ-rays and neutrons mainly emitted from the walls of the laboratory due to trace amounts of 238U and 232Th in the rock. Simulations have shown that a 4 m water equivalent (w.e.) of shielding on all sides can make these sources of background negligible for both WIMP and 0νββ searches, resulting in a water tank with 12 m in diameter and height [33]. Many complex ancillary systems are required to support the operation of these detectors, but their description is beyond the scope of this work. More details on these systems can be found in Ref. [19]. 3. Detector modeling and backgrounds At this early (pre-conceptual) stage of the design of XLZD, we assume a performance similar to that of the currently running xenon-based experiments XENONnT and LZ. We describe below the main assumptions regarding the detector parameters that are most relevant for the NDBD search. These assumptions will be revisited as the design evolves. The energy resolution of the detector at the 0νββ decay energy (Qββ = 2457.83 ± 0.37 keV [34]) is a key parameter, as it drives the leakage of events from nearby background γ-ray lines into the signal region (see Section 3.1). Detectors based on the two-phase xenon TPC design have demonstrated sub-1% (σ) relative energy resolution in this energy region, with XENON1T reporting 0.80% [35] and LZ 0.67% [36]. LZ attained this resolution by using only the unsaturated S2 signal collected in the bottom PMT array and applying granular temporal and spatial corrections to the S1 and S2 pulses, obtained from calibration and background signals (alpha decays in the 222Rn chain, 131mXe and 83mKr decays, and pulses from single extracted electrons). In this study we consider a slightly more optimistic resolution of 0.65%, which we believe is within reach for XLZD using a similar approach. We define the Region-of-Interest (ROI) for 0νββ search as ±1σaround the Qββ peak, corresponding to a 32 keV-wide interval, 9 (2441.8–2473.8 keV). High-energy γ-ray lines around Qββ, from 214Bi and 208Tl from trace radioactivity in the detector materials, will be used to determine and monitor the energy scale and resolution (see Section 3.1). The ability to reject multiple interactions in the same event is also critical, as it allows to significantly reduce the γ-ray background from external sources with energy in the 0νββ ROI: MeV-scale γ-rays are likely to produce one or more Compton scatters before being absorbed, leading to multiple-site (MS) events. By contrast, 0νββ decays are essentially point-like to a large degree and thus single-site (SS), with the emitted electrons having short tracks, each on the scale of 1 mm in the dense liquid. Critically, the extremely low energy threshold of these detectors makes this rejection very efficient. Bremsstrahlung photons emitted by the fast 0νββ electrons can nevertheless travel far enough for the decay to be viewed as a multiple interaction, and thus lead to some loss in signal efficiency. In this study we consider SS/MS separation only in the vertical (z) axis, and assume that interactions 3 mm or further apart can be rejected. This choice of threshold follows what has been considered in the literature for two-phase xenon TPCs [11, 37], and is further supported by preliminary results from the LZ detector, which show that a separation of 2 mm is possible throughout the full detector depth with a applied 193 V/cm drift field [38]. Analysis of Monte Carlo simulations performed for the DARWIN detector [13] using a 3 mm SS/MS discrimination resolution shows that it should be possible to reject 90% of the γ-ray background in the ROI while maintaining 85% efficiency for signal events. Moreover, it also provides some rejection capability (23%) for electron backgrounds in the ROI (from βdecays and solar neutrino interactions, see Sections 3.2 – 3.4), leveraging the emission of bremsstrahlung photons by these electrons. Additional capability to identify multiple interactions in the horizontal (xy) plane would contribute to further improvements in the sensitivity, but we do not explore it in this work. The additional veto systems surrounding the detector help to further extend the capability of detecting multiple interaction events. Coincident energy depositions in the skin or the OD may be caused directly by the particle that interacts in the TPC (on its way in or out) or by other particles emitted simultaneously. In this study we assume that events in which >100 keV is deposited in either of the veto systems in prompt coincidence with an interaction in the TPC can be excluded. 3.1. External γ-rays The most important backgrounds in the search for 0νββ in 136Xe arise from high-energy γ-rays emitted in the decay of 214Bi (2448 keV) and 208Tl (2615 keV), which are part of the decay chains of 238U and 232Th, respectively. These long-lived isotopes are present in trace amounts in the materials used to build the detector and in the surrounding environment – most notably in the laboratory rock. We assume that the water tank used for XLZD will be large enough to efficiently shield it against high-energy γ-rays from the rock, rendering this particular source of background negligible. 16 Table 2. Underground laboratory depth, muon flux, and projected rates of 137Xe production [55] and of subsequent decays leading to SS-like events in the 0νββ ROI (considering the nominal scenario, see Section 3.5) for the different sites being considered for installing XLZD (listed in order of increasing SS ROI rate). Production rates for Boulby and Kamioka are scaled from LNGS using the respective muon flux ratios. The water equivalent depth and muon flux for Boulby refer to a new proposed laboratory at 1300 m and are interpolated from measurements at the existing 1100 m laboratory and the projections for a 1400 m laboratory studied in Ref. [56]. Depth µflux 137Xe rate SS ROI rate Site [m] [m w.e.] [/(m2·d)] [/(t·yr)] [evt/(t·yr·keV)] SNOLAB 2070 5890 <0.3 0.007 1.29×10−6 SURF 1490 4300 4.6 0.142 2.72×10−5 Boulby 1300 3330 14.6 0.404 7.73×10−5 LNGS 1400 3800 29.7 0.822 1.57×10−4 Kamioka 1000 2700 128 3.54 6.78×10−4 abundance xenon, which has a 136Xe abundance of only 8.9%; moreover, 136Xe has the lowest neutron capture cross section amongst all naturally occurring isotopes [55], which results in a much smaller 137Xe production as the other isotopes effectively shield the 136Xe. In this study we use the recently estimated production rates for DARWIN at LNGS, SURF and SNOLAB [55], while the rates for Kamioka and a proposed new facility at 1300 m depth at Boulby are estimated by scaling the LNGS projections by the relative muon fluxes. These production rates are summarised in Table 2, along with the rates of SS-like events in the 0νββ ROI estimated with a simulation of 137Xe decays. We note that the new 137Xe production rate estimate for DARWIN at LNGS, and used here, is a factor of approximately 8 smaller compared to that used in the DARWIN 0νββ sensitivity study [13, 15], as noted in Refs. [55, 57], with direct impact on the sensitivity. The rate of this background could be further reduced by vetoing events for a given number of 137Xe half-lives following the passage of a muon, or using a delayed coincidence between the muon and the 136Xe(n, γ)137Xe process (which produces a γ-ray cascade adding up to 4025 keV [58]) to minimise the false-vetoing rate and consequently the detector dead time in laboratories with higher muon flux. Ref. [55] reports that 95% of the 136Xe captures are with neutrons produced by muons crossing the TPC itself, with the neutron capture occurring shortly after the passage of the muon (up to microseconds). The deposition of hundreds of MeV by a high-energy muon in an ultra-sensitive detector such as a LXe-TPC, optimised for keV-scale interactions, is an extremely disruptive event which can affect the optical readout of the detector for an extended period lasting up to seconds. This implies that the use of a delayed coincidence will not be efficient for most of the 137Xe production. On the other hand, vetoing the detector after each muon has a large impact on the experiment live-time for the shallower 17 laboratories: e.g., vetoing for one 137Xe half-life (3.82 min) at Boulby would result in a 76% live-time fraction. Given that 137Xe is not dominant except in Kamioka, we conservatively assume that no veto will be applied to reduce this background. Cosmic-ray muons reaching the underground laboratory also lead to the production of lighter radioisotopes by nuclear spallation, i.e. the fragmentation of xenon nuclei to create radioactive nuclei. Some of these radioisotopes decay with a total energy in the 0νββ decay ROI, and may have long half-lives of several hours or even days. KamLANDZen [59] reported a xenon spallation rate of isotopes decaying in their wider [2350– 2700] keV ROI of (3.5±0.6)×10−3/(t·d) at the Kamioka laboratory (which has a muon flux of 128 /(m2·d), the highest amongst the candidate laboratories for hosting XLZD). Most of the isotopes observed by KamLAND decay with the emission of a positron and additional γ-rays, leading to multi-interaction events which will be easily tagged in XLZD and its vetoes. Those isotopes that undergo β−decay (around 15%) could in principle be more challenging, but the emitted electron is always accompanied by one or more γ-rays, which will also result in a very high tagging efficiency in XLZD. Given the much narrower (one-tenth) 0νββ decay ROI of XLZD and its excellent capability to identify multi-site events with high efficiency, we expect this background to be negligible. Installation of XLZD in a laboratory other than Kamioka would result in a further reduction of at least a factor of 4. KamLAND-Zen uses xenon enriched in 136Xe (91%) and 134Xe (9%), but recent simulations for DARWIN show that the production rates for the isotopes observed in KamLAND-Zen are similar in natural xenon [55]. Nevertheless, spallation in natural xenon will result in a wider set of radioisotopes; further simulations are underway to more accurately estimate this background. 3.5. Performance scenarios We consider two scenarios with different detector performance and background considerations for the sensitivity projections presented in this work, which are summarised in Table 3. The nominal scenario is based on the performance already achieved by currently running detectors, installation at LNGS and a realistic reduction of the γ-ray background from detector materials (as discussed in Section 3.1). We also consider a more optimistic scenario, with slight improvements in detector performance, installation at SURF, and a more ambitious reduction of the external γ-ray background. We believe such a scenario is achievable with a very thorough material screening campaign, design and engineering innovations, and further improvements to photosensor radioactivity – aided by new analysis techniques such as the use of track topology information (e.g. S2 pulse shape deconvolution). The two active mass configurations (60 t and 80 t) being considered by XLZD are studied under both of these scenarios, resulting in a total of four configurations. Figure 3 shows the background energy spectra of SS events in the inner region of a 60 t XLZD, considering the nominal scenario. 8B solar neutrinos dominate the internal backgrounds for all possible installation sites except Kamioka (at LNGS the 18 Table 3. Summary of the background assumptions and detector performance parameters used in the two scenarios considered for the sensitivity projections in this study. Irreducible backgrounds from 8B neutrinos and 136Xe 2νββ are constant. Scenario Parameter Nominal Optimistic 222Rn concentration [µBq/kg] 0.1 BiPo tagging efficiency [%] 99.95 99.99 External γ-ray [% LZ] 25 10 Installation site LNGS SURF Energy resolution [%] 0.65 0.60 SS/MS vert. separation [mm] 3 2 137Xe contribution is at the same level of 8B); the effect of 222Rn is negligible even with the conservative 99.95% BiPo efficiency considered in this scenario; the power of the excellent energy resolution in minimising the contamination from 2νββ in the ROI is evident. Moreover, this figure clearly shows the impact that the use of external vetoes has on the 208Tl Compton plateau in the 0νββ ROI. Vetoed 208Tl events can nevertheless be used to determine and monitor the energy resolution of the detector, as is done in LZ [36], with close to 106SS events expected in the 208Tl peak in the active volume of the 60 t stage of XLZD over 10 years of data taking in the nominal scenario (104in the inner 30 t). 4. Sensitivity calculation We calculate the 136Xe 0νββ decay half-life (T0ν 1/2) sensitivity using two common metrics: exclusion at 90% confidence level (CL) and 3σ-significance discovery potential (defined as the minimum T0ν 1/2required to exclude the null hypothesis with a significance of 99.7% CL). Following Ref. [60] we apply a Figure-of-Merit estimator as a straightforward and easily comparable metric for sensitivity calculations. This approach uses a heuristic counting experiment model to determine the signal expectation S(B) required to pass the statistical test in the given metric, assuming a background count B. This is converted to the half-life sensitivity using: T0ν 1/2= ln 2 NAE MXeS(B),(2) where Eis the sensitive exposure of 136Xe (i.e. the product of the 136Xe mass in the fiducial volume, the measurement time, and the signal detection efficiency), NAis Avogadro’s constant, and MXe is the molar mass of 136Xe. For the exclusion sensitivity S90%CL = 1.64√B, while for the 3σdiscovery potential S3σis constructed using Poisson statistics as detailed in Ref. [60]. Independently of the applied metric, the background Band the sensitive exposure Edepend on the choice of fiducial volume and energy ROI, both of which can be optimised. 19 2300 2350 2400 2450 2500 2550 2600 Energy [keV] 10-6 10-5 10-4 10-3 10-2 Rate [evt/(t × yr × keV)] 0 νββ 0 νββ ROI 137 Xe (LNGS) 137 Xe (Boulby) 137 Xe (Kamioka) 137 Xe (SURF) 137 Xe (SNOLab) 222 Rn 8 Bν 136 Xe ( 2 νββ )Materials before / after vetoes Figure 3. Energy spectra of SS events from signal and relevant backgrounds for 0νββ decay in the inner region of XLZD considering the nominal scenario (see Table 3). The black (gray) line shows the external γ-ray background from detector materials after (before) excluding events with coincident signals in the vetoes; their contribution in the 0νββ ROI (vertical yellow band, defined as Qββ ±1σwith 0.65% energy resolution) is clearly dominated by the 2448 keV γ-ray from the decay of 214Bi in the 238U chain. The irreducible background from 8B solar neutrinos (shown in purple) dominates the internal backgrounds relatively to 137Xe at the various XLZD candidate host sites (shown by the red dotted lines) except at Kamioka and LNGS (where it is at the same level). 222Rn (green line) is subdominant even in the nominal scenario, while the contamination from 2νββ decay (light blue) in the ROI is negligible given the excellent energy resolution achieved by LXe-TPCs. Also shown is a hypothetical 0νββ signal with a half-life of 5×1027 yr (orange line). We find the optimal fiducial volume by gradually adding contiguous detector regions with lowest background index until the sensitivity is maximized. We find optimal natXe masses of 8.2 t (11.0 t) and 13.6 t (17.2 t) for the 3σ-significance discovery potential in the nominal (optimistic) scenario for the 60 t and 80 t configurations, respectively. After this point, Bgrows faster than Eand the sensitivity decreases gradually. The precise optimum volume depends on the underlying sensitivity metric, with 3σdiscovery potential generally leading to larger fiducial masses compared to the 90% CL exclusion sensitivity in all studied detector configurations. The external background is dominant in more than 75% of the active mass, and accordingly the optimised fiducial mass contains less than a quarter of the available target. The choice of the optimal ROI depends on the spectral shape of the background: on a flat background dominated by the internal background sources, S/√Boptimises in a symmetric ±1.4σROI, yielding a 4% relative increase in T0ν 1/2sensitivity compared to a ±1σROI; in a background setting dominated by the external 214Bi γ-ray peak, 20 an asymmetric ROI is more favourable, with the optimal lower bound depending on the energy resolution. For 0.65% energy resolution this increase in sensitivity can be as high as 11% compared to the symmetric ±1σ. For simplicity and the benefit of a straightforward comparison between different scenarios, we keep the energy ROI fixed at ±1σ. A study of the possible sensitivity gains to be realized with more sophisticated analysis methods such as a profile likelihood ratio (PLR) test, which would allow to exploit a larger fraction of the active mass and a wider energy range, is beyond the scope of this work. In the LZ sensitivity study the use of a PLR-based approach resulted in an improvement of 40% to T0ν 1/2compared to a counting analysis in an optimised fiducial volume [11]. 5. Results and discussion The XLZD 0νββ decay sensitivity projections as a function of exposure time are shown in Figure 4 for both metrics and the two mass configurations being considered. For each of these stages the lower bound of the band corresponds to the nominal scenario and the upper bound to the optimistic scenario. In the 80 t configuration, and if the optimistic scenario is realised, XLZD can exclude 0νββ decay half-lives up to 1.3×1028 yr at 90% CL with 10 years of data. The corresponding 3σdiscovery potential is 5.7×1027 yr. These projections show that XLZD can surpass currently running and planned experiments using 136Xe, such as PandaX-xT [61], KamLAND2-Zen [62], NEXT-HD [63], and nEXO [20], while using a target of natural abundance xenon which brings a much broader science program. The sensitivity is primarily driven by the target mass, with the external γ-ray background rate having the largest impact within each mass. For instance, a γ-ray background at 25% the level of LZ while maintaining the remaining optimistic scenario assumptions decreases the 3σsensitivity by 15.5%; installation at LNGS instead of SURF has an 11% impact; switching the BiPo efficiency, SS/MS discrimination, and energy resolution from the optimistic to the nominal scenario reduces the sensitivity in 6%, 4.3%, and 2.5%, respectively. In fact, a poorer energy resolution of 1% or a pessimistic BiPo efficiency of 99.9% both have impacts of only 12%. It is foreseen that an interim XLZD configuration with 40 t at the same TPC diameter but reduced height will be used for initial technical performance verification and early science [19]. Considering a short run of only 3 years for this interim stage and the reduced self-shielding capability resulting from the shallower aspect ratio, XLZD can nevertheless reach a 3σsensitivity of 1.0×1027 yr (2.5×1027 yr 90% CL exclusion) during this initial run in the optimistic scenario, in line with the DARWIN projections for a detector of similar size [13,57]. The right-side axes of the figures in Figure 4 show the XLZD sensitivity to the effective Majorana neutrino mass, mββ, linked to the 0νββ decay half-life by Eq. (1). The large uncertainty is dominated by the nuclear matrix element (M0ν 136Xe). We adopted 21 14 (60) 9.3 (40) 7 (30) 4.6 (20) mββ sensitivity [meV] 0 2 4 6 8 10 12 Exposure time [yr] 1027 1028 T 0 νββ 1 / 2 exclusion limit (90% CL) [yr] NEXT-HD KamLAND2-Zen XLZD (60 t) XLZD (80 t) nEXO Optimistic Nominal PandaX-xT 21 (90) 14 (60) 9.3 (40) 7 (30) mββ sensitivity [meV] 0 2 4 6 8 10 12 Exposure time [yr] 1027 1028 T 0 νββ 1 / 2 discovery sensitivity (3 σ ) [yr] NEXT-HD KamLAND2-Zen XLZD (60 t) XLZD (80 t) nEXO Optimistic Nominal Figure 4. Sensitivity of XLZD to the 0νββ decay of 136Xe in the two metrics considered in this work: 90% CL exclusion (top) and 3σdiscovery potential (bottom). The projections for the two mass configurations in the two detector performance scenarios considered are shown by the coloured bands, with the nominal scenario setting the lower band limits and the optimistic scenario the upper limits. Also shown are the projections from other planned experiments: KamLAND2-Zen [3,62], NEXT-HD [63], PandaX-xT [61] and nEXO [20]. Note that the nEXO projections were obtained using a profile likelihood ratio test while those for XLZD use the figure-of-merit estimator. The right axis shows the projected sensitivity to the effective Majorana neutrino mass, mββ , considering a maximum (minimum) M0ν 136Xe of 4.77 (1.11) (see text). 22 10-4 10-3 10-2 10-1 m light [eV] 10-3 10-2 10-1 mββ [eV] IO NO XLZD (90% CL) XLZD ( 3 σ ) KamLAND-Zen Figure 5. Sensitivity of XLZD to the effective Majorana neutrino mass as a function of the lightest neutrino mass for the 80 t configuration in the optimistic scenario with 10 years of data. The two metrics considered in this work are shown: 3σdiscovery potential (yellow band) and 90% CL exclusion (green band). The width of the bands is caused by the uncertainty in the nuclear matrix element models (see main text, also for the expected sensitivity using the most recent nuclear matrix elements). The current best experimental limits from KamLAND-Zen, also from 0νββ decay in 136Xe and assuming the same range of NMEs, are shown in grey [5]. The allowed regions (±3σ) for the effective Majorana neutrino mass in the inverted (IO) and normal (NO) neutrino mass ordering scenarios are also shown [64,65]. the parameter values of gA= 1.27, G0νfrom Ref. [50] and a M0ν 136Xe ∈[1.11,4.77] range which covers the predictions from the most commonly used phenomenological models for direct comparison with other experiments [66–78]. In particular, the minimum value assumes the deformed-QRPA [66] model and the maximum the NREDF [78] model. Figure 5 shows the allowed ⟨mββ⟩parameter space as a function of the lightest neutrino mass for the inverted and the normal neutrino mass ordering scenarios, along with the XLZD 90% CL and 3σ⟨mββ⟩sensitivities for the 80 t configuration in the optimistic scenario after 10 years of data, represented by the yellow (4.8–20.5 meV) and green band (7.3–31.3 meV), respectively. XLZD will exclude the inverted neutrino mass ordering— except for the deformed-QRPA model—and probe a significant fraction of the normal ordering scenario. Similarly, if the neutrino masses follow the inverted ordering, XLZD will confirm that hypothesis at the 3σlevel for most of the considered NMEs. Recent developments in nuclear models include a quenching effect in gA(required for agreement with experimental data) [79] and the addition of a previously neglected 23 10-10 10-9 10-8 10-7 Muon flux [evt/(cm 2 × s)] 1028 T 0 νββ 1 / 2 exclusion limit (90% CL) [yr] Kamioka (2700 m.w.e) LNGS (3800 m.w.e) Boulby (3330 m.w.e) SURF (4200 m.w.e) SNOLAB (5890 m.w.e) Optimistic Nominal XLZD (60 t) XLZD (80 t) Figure 6. Projected 90% confidence level (CL) exclusion limits of XLZD to the 0νββ decay of 136Xe as a function of muon flux (which drives the 137Xe background) after 10 years of data. The coloured bands show the projections for the two mass configurations, bounded by the nominal (lower limit) and optimistic (upper limit) scenarios (see Table 3). The vertical dashed lines indicate the fluxes corresponding to each of the possible hosting laboratories, along with their corresponding water equivalent depth. short-range term [80, 81]. Considering recent NME models which include these two modifications, the 90% CL lower limits on ⟨mββ⟩of XLZD with 10 years of data in the 80 t configuration and in the optimistic scenario are 7.4–23.5 meV, 4.2–10.2 meV, and 12.1–21.3 meV for the shell model [82–84], QRPA [83,84], and ab-initio calculation [85], respectively. The corresponding 3σdiscovery potential ranges are 11.2–35.5 meV, 6.3– 15.4 meV, and 18.3–32.2 meV, respectively. We also studied the effect of the 137Xe production rate on the sensitivity, as this background will depend on the choice of underground laboratory. The results for the exclusion sensitivity are shown in Figure 6. The bands for each mass stage represent the range between the detector performance scenarios, dominated by the external γ-ray background. Installation at SNOLAB, with a significantly lower muon rate compared to SURF (optimistic scenario), has only a modest effect in the sensitivity (which increases to 1.4×1028 yr for the 80 t mass configuration). It is clear that when the cosmogenic 137Xe rate is sub-dominant (SNOLAB, SURF, Boulby) or at the same level (LNGS) as the 8B background, the impact on the sensitivity is much smaller than that of varying the external γ-ray rate between the two scenarios considered. This is not the case for the Kamioka site, in which case the effect on the projected sensitivity is significant. XLZD will nominally use natural abundance xenon for its target, but scenarios with different 136Xe concentration may be warranted at a later stage to investigate a putative signal (in XLZD or in another experiment). Figure 7 shows the effect of 24 0 5 10 15 20 25 136 Xe abundance [%] 1027 1028 T 0 νββ 1 / 2 discovery sensitivity (3 σ ) [yr] NEXT-HD nEXO Natural Xe Optimistic Nominal XLZD (60 t) XLZD (80 t) Figure 7. Dependence of the 0νββ 3σdiscovery potential of XLZD with the abundance of 136Xe in the target with 10 years of data. The coloured bands show the projections for the two mass configurations, and are limited by the nominal (lower limit) and optimistic (upper limit) scenarios (see Table 3). Also shown are the projections from NEXT-HD [63] and nEXO [20]. varying the 136Xe concentration on the 3σdiscovery potential for the two mass stages and two detector performance scenarios considered. 137Xe production was estimated for LNGS [86] (nominal performance) for the various enrichment scenarios and scaled for SURF (optimistic) using the production ratio for natural xenon in these two laboratories (Table 2). If XLZD or nEXO were to report an observation which is in tension with their background model but falling short of a discovery, XLZD will be able to confirm it at the 3σlevel in 10 years with less than 20% enrichment in the 80 t stage, or even in the 60 t stage with 25% enrichment. Conversely, a signal observation in XLZD can also be tested by running the experiment with some depletion level, which would not impact the background expectation significantly while reducing the signal rate—a strategy already being explored by NEXT [87]. 6. Conclusions The XLZD collaboration is designing an experiment based on two-phase xenon TPC technology capable of completely probing the spin-independent WIMP-nucleon scattering parameter space down to the neutrino fog. With a target mass of up to 80 t and an extremely low background this experiment will be able to study other wellmotivated physics channels. In this work we presented the initial sensitivity projections of XLZD in the search for 0νββ decay in 136Xe, a process which can be used to search for new physics, probe the Majorana nature of the neutrino, and determine the neutrino mass ordering. 25 The large target volume is very effective at shielding the inner region of the detector from external high-energy γ-rays that would otherwise dominate the background in this search, while providing several tons of the source isotope even at natural abundance. Moreover, the excellent energy resolution (σE= 0.67%) already demonstrated in detectors based on dual-phase xenon TPCs can be used to minimize the width of the ROI, thus decreasing leakage of the 136Xe 2νββ continuum and from the nearby γ-ray lines from 214Bi and 208Tl. Importantly, the γ-ray background can be further reduced by the capability to identify multiple scatter interactions down to 3 mm separation in the vertical direction and with a very low energy threshold per vertex. Finally, an instrumented xenon skin and an outer detector surrounding the TPC provide an additional reduction of this background by vetoing coincident signals, which is particularly effective in mitigating against the 2615 keV line from 208Tl. The use of a natural abundance xenon target has the advantage of limiting the cosmogenic production of the 137Xe background, as 136Xe has the lowest neutron capture cross section amongst all naturally-occurring xenon isotopes. This background remains sub-dominant if the experiment is installed at SNOLAB, SURF, Boulby or LNGS. With a thorough material screening and selection campaign and an online radon reduction system capable of reducing 222Rn to the 0.1µBq/kg level, XLZD will reach a 90% CL half-life exclusion sensitivity of 1.3×1028 yr with 10 years of data in the 80 t configuration, fully excluding the inverted neutrino mass ordering scenario for all but one of the most commonly used NMEs. With a 3σdiscovery sensitivity of 5.7×1027 yr it will also probe the inverted ordering scenario for a signal for most of these NME models. These sensitivities will be further improved by the use of a PLR-based statistical analysis in a larger volume and using a wider energy range, realistically allowing the full exclusion of the inverted ordering at 90% CL. Conversely, recent NME calculations suggest somewhat reduced sensitivities for all 0νββ decay experiments [3, 82–85]. A second stage can be envisioned using xenon with some level of 136Xe enrichment to increase its sensitivity, allowing for probing at the 3σlevel a possible hint of a signal during the first XLZD stage at the T1/2= 1.3×1028 yr level. Conversion from measured half-lives to the physically relevant effective Majorana neutrino mass requires knowledge of the NME for the relevant isotope, which can vary by factors of a few between nuclear models resulting in large uncertainties in ⟨mββ⟩. XLZD will be able to measure or significantly improve the current best limits on the half-life of the 136Xe 2νββ decay to the first excited 0+state of 136Ba [88,89]. This yet unobserved SM-allowed decay can thus be used to benchmark the predictions of the various nuclear models and help to reduce theoretical uncertainties [90]. Complementarity between experiments using different isotopes (e.g. SNO+ [91], LEGEND [92], CUPID [93], AMoRE [94], SuperNEMO [95]) is crucial to reduce NME uncertainties when probing the neutrino mass hierarchy space and to claim a possible discovery. Furthermore, multiple measurements in different isotopes will be required to characterise the physical mechanism mediating this decay.