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E V Hansen

𝑛 K M Heeger

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𝑎 𝑓

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J Johnston

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𝑔 Y Liu

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𝑝 𝑜 F Mancarella

R Mariam

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A S Zolotarova

𝑜 S Zucchelli

A CUPID Li_2 100 MoO_4 scintillating bolometer tested in the CROSS underground facility

published or not. The documents may come

𝑎𝑞 Dipartimento di Fisica e Astronomia, Alma Mater Studiorum -Università di Bologna, Bologna I-40127, Italy E-mail: cupid.publications@lngs.infn.it, cross.publications@lsc-canfranc.es A : A scintillating bolometer based on a large cubic Li 2 100 MoO 4 crystal (45 mm side) and a

Ge wafer (scintillation detector) has been operated in the CROSS cryogenic facility at the Canfranc underground laboratory in Spain. The dual-readout detector is a prototype of the technology that will be used in the next-generation 0𝜈2𝛽 experiment CUPID. The measurements were performed at 18 and 12 mK temperature in a pulse tube dilution refrigerator. This setup utilizes the same technology as the CUORE cryostat that will host CUPID and so represents an accurate estimation of the expected performance. The Li 2 100 MoO 4 bolometer shows a high energy resolution of 6 keV FWHM at the 2615 keV 𝛾 line. The detection of scintillation light for each event triggered by the Li 2 100 MoO 4 bolometer allowed for a full separation (∼8𝜎) between 𝛾(𝛽) and 𝛼 events above 2 MeV.

The Li 2 100 MoO 4 crystal also shows a high internal radiopurity with 228 Th and 226 Ra activities of less than 3 and 8 𝜇Bq/kg, respectively. Taking also into account the advantage of a more compact and massive detector array, which can be made of cubic-shaped crystals (compared to the cylindrical ones), this test demonstrates the great potential of cubic Li 1 Introduction

Neutrinoless double-beta (0𝜈2𝛽) decay is a unique probe of new physics beyond the Standard Model [START_REF] Vergados | Neutrinoless double beta decay and neutrino mass[END_REF][START_REF] Dolinski | Neutrinoless Double-Beta Decay: Status and Prospects[END_REF] and the observation of this process, suggested about 80 years ago but not yet detected (in contrast to two-neutrino double-beta (2𝜈2𝛽) decay [START_REF] Barabash | Precise Half-Life Values for Two-Neutrino Double-𝛽 Decay[END_REF]), would conclusively demonstrate lepton number violation and the Majorana nature of neutrinos (i.e. a particle that is equal to its own anti-particle).

The bolometric technology, which relies on the use of low-temperature calorimeters acting simultaneously as a 2𝛽 source and a detector, is among the few experimental approaches providing world-leading sensitivity to 0𝜈2𝛽 decay to-date [START_REF] Dolinski | Neutrinoless Double-Beta Decay: Status and Prospects[END_REF]. In addition to high detection efficiency of the "2𝛽 source = detector" technique, bolometers offer high energy resolution, scalability to a large detector mass via arrays of modules, and the possibility to use different and radiopure materials containing the most promising 2𝛽 isotopes (e.g. see [START_REF] Pirro | Advances in Bolometer Technology for Fundamental Physics[END_REF][START_REF] Lumineu | CUPID-0/M collaboration, 100 Mo-enriched Li 2 MoO 4 scintillating bolometers for 0𝜈2𝛽 decay search: from LUMINEU to CUPID-0/Mo projects[END_REF][START_REF] Bellini | Potentialities of the future technical improvements in the search of rare nuclear decays by bolometers[END_REF]). Additionally, recent technological advances have demonstrated the ability to do particle identification [START_REF] Pirro | Advances in Bolometer Technology for Fundamental Physics[END_REF][START_REF] Lumineu | CUPID-0/M collaboration, 100 Mo-enriched Li 2 MoO 4 scintillating bolometers for 0𝜈2𝛽 decay search: from LUMINEU to CUPID-0/Mo projects[END_REF][START_REF] Bellini | Potentialities of the future technical improvements in the search of rare nuclear decays by bolometers[END_REF], allowing for a reduction of backgrounds in the signal region of interest by multiple orders of magnitude.

Bolometric techniques for 0𝜈2𝛽 decay searches have been developed for about 30 years and have resulted in the first tonne-scale bolometric experiment CUORE (Cryogenic Underground Observatory of Rare Events) [START_REF]Improved Limit on Neutrinoless Double-Beta Decay in 130 Te with CUORE[END_REF]. CUORE has been in operation at the Gran Sasso underground laboratory (Italy) since 2017, searching for 0𝜈2𝛽 decay of 130 Te (𝑄-value of the 2𝛽 transition, 𝑄 2𝛽 , is 2528 keV [START_REF] Wang | The AME2016 atomic mass evaluation * (II). Tables, graphs and references[END_REF]). In spite of this extraordinary achievement, the CUORE 0𝜈2𝛽 sensitivity is limited by a background (∼10 -2 counts/yr/kg/keV) coming from alpha decays at surfaces despite the highly radiopure materials used for the detector construction. This is due to the use of pure thermal detectors based on tellurium dioxide crystals (TeO 2 ; 34% of 130 Te in natural tellurium [START_REF] Meija | Isotopic compositions of the elements 2013 (IUPAC Technical Report)[END_REF]) which have the same bolometric response irrespective of the type of the particle interaction [START_REF] Bellini | Response of a TeO 2 bolometer to 𝛼 particles[END_REF].

CUPID (CUORE Upgrade with Particle IDentification

) is a proposed next-generation 0𝜈2𝛽 bolometric experiment [START_REF]CUPID: CUORE (Cryogenic Underground Observatory for Rare Events) Upgrade with Particle IDentification[END_REF], which will reuse the CUORE infrastructure for the operation of a similar-scale isotopically enriched detector with a background ∼10 -4 counts/yr/kg/keV in the region of interest, thus probing 0𝜈2𝛽 decay in so-called "zero-background" conditions. The suppression of the alpha-induced background to a negligible level (i.e. 99.9% of alpha events rejection), while keeping almost 100% of the signal efficiency, is required for particle identification technology. The detector performance is expected to be similar to CUORE and predecessors, with a 5 keV FWHM at 𝑄 2𝛽 as a goal. The activities of 226 Ra, 228 Th, and 232 Th in the enriched bolometers are required to be less than 10 𝜇Bq/kg, making the contribution of the U/Th crystal bulk activity to be below ∼10 -4 counts/yr/kg/keV. The total bulk radioactivity of the crystals should not exceed the mBq/kg level to avoid impacting the detector operation and background with pile-ups [START_REF] Lumineu | CUPID-0/M collaboration, 100 Mo-enriched Li 2 MoO 4 scintillating bolometers for 0𝜈2𝛽 decay search: from LUMINEU to CUPID-0/Mo projects[END_REF][START_REF] Chernyak | Random coincidence of 2𝜈2𝛽 decay events as a background source in bolometric 0𝜈2𝛽 decay experiments[END_REF][START_REF] Chernyak | Rejection of randomly coinciding events in ZnMoO 4 scintillating bolometers[END_REF][START_REF] Chernyak | Rejection of randomly coinciding events in Li 2 100 MoO 4 scintillating bolometers using light detectors based on the Neganov-Luke effect[END_REF].

Four isotopes, 82 Se (𝑄 2𝛽 = 2998 keV [START_REF] Wang | The AME2016 atomic mass evaluation * (II). Tables, graphs and references[END_REF]), 100 Mo (3034 keV [START_REF] Wang | The AME2016 atomic mass evaluation * (II). Tables, graphs and references[END_REF]), 116 Cd (2813 keV [START_REF] Wang | The AME2016 atomic mass evaluation * (II). Tables, graphs and references[END_REF]) and 130 Te, were considered in the CUPID R&D program [START_REF]R&D towards CUPID (CUORE Upgrade with Particle IDentification[END_REF] as isotopes of interest to be embedded in the CUPID detector for the following reasons:

• The 0𝜈2𝛽 decay energy of these isotopes (except for 130 Te) is greater than 2.6 MeV, the end-point of the most energetic intense natural 𝛾-ray radiation;

• Enrichment is available at a large amount and reasonable cost;

• Compounds containing these isotopes can be grown into single crystals usable for cryogenic applications;

• Some of Se-, Mo-, or Cd-containing crystals are also reasonably efficient low-temperature scintillators. The detection of scintillation light using an auxiliary optical bolometer in coincidences with the measurement of particle-induced energy release in the scintillating absorber is a viable tool for particle identification. This technique can also be applied for poorly or non-scintillating crystals, as TeO 2 , to detect Cherenkov radiation allowing particle identification (however, more performing light detectors are demanded to detect a tiny signal).

Efficient alpha background rejection has been demonstrated with detectors containing each of these isotopes [START_REF]R&D towards CUPID (CUORE Upgrade with Particle IDentification[END_REF][START_REF] Poda | Low background techniques in bolometers for double-beta decay search[END_REF][START_REF]CUPID-0 collaboration, Final Result of CUPID-0 Phase-I in the Search for the 82 Se Neutrinoless Double-𝛽 Decay[END_REF][START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF] Helis | Neutrinoless double-beta decay searches with enriched 116 CdWO 4 scintillating bolometers[END_REF]. This paves the way for a future study of 0𝜈2𝛽 across multiple isotopes [START_REF] Giuliani | A multi-isotope 0𝜈2𝛽 bolometric experiment[END_REF] in case a discovery is made. Based on performance and cost, CUPID selected 100 Mo embedded in lithium molybdate (Li 2 MoO 4 ) scintillating crystals [START_REF]CUPID pre-CDR[END_REF].

The technology of 100 Mo-enriched lithium molybdate (Li 2 100 MoO 4 ) scintillating bolometers has been recently developed within the LUMINEU project and it provides [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF] Grigorieva | Li 2 MoO 4 crystals grown by low thermal gradient Czochralski technique[END_REF]:

• A know-how for the mass production of high-quality large radiopure crystals with only few % losses of the enriched material;

• The fabrication of a detector module (which can be easily put into array) with energy resolution comparable to that of TeO 2 bolometers, but with a significantly higher 𝛼 rejection efficiency (e.g. see in [START_REF] Lumineu | CUPID-0/M collaboration, 100 Mo-enriched Li 2 MoO 4 scintillating bolometers for 0𝜈2𝛽 decay search: from LUMINEU to CUPID-0/Mo projects[END_REF]).

Excellent performances of Li 2 100 MoO 4 scintillating bolometers based on cylindrical crystals ( 44×45 mm, ∼0.21 kg, ∼97% enrichment in 100 Mo) have been demonstrated in single-module and 4-crystalarray tests of LUMINEU [START_REF] Lumineu | CUPID-0/M collaboration, 100 Mo-enriched Li 2 MoO 4 scintillating bolometers for 0𝜈2𝛽 decay search: from LUMINEU to CUPID-0/Mo projects[END_REF][START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF] Armengaud | Precise measurement of 2𝜈𝛽𝛽 decay of 100 Mo with the CUPID-Mo detection technology[END_REF] at the Gran Sasso and Modane (LSM; France) underground laboratories. These results have been recently confirmed by the CUPID-Mo experiment [START_REF] Armengaud | The CUPID-Mo experiment for neutrinoless double-beta decay: performance and prospects[END_REF][START_REF]First data from the CUPID-Mo neutrinoless double beta decay experiment[END_REF][START_REF]Performance of the CUPID-Mo double-beta decay bolometric experiment[END_REF] on the scale of a 20-detector array operated at the LSM. Furthermore, the crystal production protocol, adopted by LUMINEU and CUPID-Mo, has been used for the fabrication of 32 Li 2 100 MoO 4 crystals 0.28 kg each (the average enrichment in 100 Mo is 97.7(3)%) for the CROSS (Cryogenic Rare-event Observatory with Surface Sensitivity) 0𝜈2𝛽 experiment [START_REF]The 0𝜈2𝛽-decay CROSS experiment: preliminary results and prospects[END_REF]. CROSS, considered as a part of CUPID R&D, is a project aiming at the development of Li 2 100 MoO 4 and 130 TeO 2 surface-coated bolometers capable of identifying a near surface particle interaction via pulse-shape analysis [START_REF]The 0𝜈2𝛽-decay CROSS experiment: preliminary results and prospects[END_REF]. A key ingredient of the CROSS technology is crystalsurface coating with a superconducting material to modify the signal pulse-shape for an event occurring at its proximity. The CROSS detector performance and radiopurity should be in compliance with CUPID requirements. The feasibility of a highly-efficient identification of near-surface 𝛼 interactions has recently been demonstrated in multiple tests of the CROSS prototypes [START_REF]The 0𝜈2𝛽-decay CROSS experiment: preliminary results and prospects[END_REF][START_REF] Khalife | The CROSS Experiment: Rejecting Surface Events by PSD Induced by Superconducting Films[END_REF][START_REF]The CROSS experiment: rejecting surface events with PSD[END_REF][START_REF]First results of CROSS underground measurements with massive bolometers[END_REF].

A final validation of the technology is planned to be realized as a 0𝜈2𝛽 experiment with at least 32 Li 2 100 MoO 4 bolometers (the addition of the 20 crystals from CUPID-Mo are now also in consideration), hosted in a dedicated cryostat at the Canfranc underground laboratory (Spain). The sensitivity of this medium-scale demonstrator [START_REF]The 0𝜈2𝛽-decay CROSS experiment: preliminary results and prospects[END_REF] is expected to be on the level of the leading 0𝜈2𝛽 experiments, which have masses larger by a factor 10-100.

In contrast to LUMINEU and CUPID-Mo, CROSS is going to use cubic Li 2 100 MoO 4 elements with a 45 mm side. The choice of a cubic shape is driven by the possibility to realize a more compact array structure, which allows to deploy a ∼ 30% higher isotope mass in the available experimental volume, and yields an enhanced efficiency in rejecting background-like events that release energy in neighboring crystals (coincidences). Indeed, a volume (i.e. mass) of a cylindrical crystal with a diameter and height equal to the side of the cubic one is almost 30% less (similar to CUPID-Mo vs. CROSS crystals). It is also evident that the efficiency of coincidences between larger, particularly neighbor, detectors would be increased too. The CROSS development of an array of cubic Li 2 100 MoO 4 bolometers is also an important benchmark for the design of the final CUPID structure, initially considered to be based on cylindrical ( 50 × 50 mm) Li 2 100 MoO 4 scintillating bolometers [START_REF]CUPID pre-CDR[END_REF]. Before using the crystals in the CROSS and CUPID 0𝜈2𝛽 experiments, it is necessary to perform low-temperature test(s) to demonstrate that:

• Bolometric and spectrometric performances of cubic-shaped Li 2 100 MoO 4 scintillating bolometers, operated in modern pulse-tube cryostats with possible vibration disturbances, are similar to those of cylindrical Li 2 100 MoO 4 detectors tested in dry and/or wet dilution refrigerators;

• Scintillation light yield of the cubic-shaped and cylindrical crystals is similar, thus providing a highly efficient particle identification;

• Radioactive contamination of cubic Li 2 100 MoO 4 crystals is compatible to that of cylindrical ones.

With these goals in mind, we realized a first investigation of a scintillating bolometer based on a large-volume (∼90 cm 3 ) cubic-shaped Li 2 100 MoO 4 crystal, described in the present paper. This study is undertaken as part of both the CROSS and CUPID R&D programs.

Detector construction and operation 2.1 Li 100 MoO 4 scintillating bolometer fabrication

We construct a dual-readout cryogenic particle detector from a primary scintillating absorber and a light detector. The Li 2 100 MoO 4 absorber consists of a 45×45×45 mm crystal (∼98% enrichment in 100 Mo) of mass 279.42 g. We randomly chose the sample from the batch of 32 identical crystals. The crystals were grown starting from purified 100 Mo powder and using the low-temperaturegradient technique at the Nikolaev Institute of Inorganic Chemistry (Novosibirsk, Russia). The Li 2 100 MoO 4 samples are not perfectly cubic-shaped due to not optimal growing conditions (in particular, the platinum crucible size was not large enough), adapted for the growth of up to 50 mm crystal boules [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF] Grigorieva | Li 2 MoO 4 crystals grown by low thermal gradient Czochralski technique[END_REF][START_REF] Armengaud | The CUPID-Mo experiment for neutrinoless double-beta decay: performance and prospects[END_REF]. A Neutron Transmutation Doped (NTD) Ge thermistor [START_REF] Haller | Advanced far-infrared detectors[END_REF] with a size of 3×3×1 mm and a P-doped Si chip [START_REF] Andreotti | Production, characterization and selection of the heating elements for the response stabilization of the CUORE bolometers[END_REF] were epoxy-glued on the crystal top. The dependency of the NTD Ge resistance on temperature can be approximated as 𝑅(𝑇) = 𝑅 0 • 𝑒 (𝑇 0 /𝑇 ) 0.5 with the parameters 𝑇 0 ∼ 3.8 K and 𝑅 0 ∼ 1.5 Ω. The Si chip is used as a resistive element to periodically inject constant energy pulses used for off-line stabilization of the bolometric response [START_REF] Alessandrello | Methods for response stabilization in bolometers for rare decays[END_REF]. The crystal holder is made from copper to host cubic crystals of up to 5 cm side and optical bolometers at their top and/or bottom [START_REF] Novati | Sensitivity enhancement of the CUORE experiment via the development of Cherenkov hybrid TeO 2 bolometers[END_REF][START_REF] Bergé | Complete event-by-event 𝛼/𝛾(𝛽) separation in a full-size TeO 2 CUORE bolometer by Neganov-Luke-magnified light detection[END_REF][START_REF]The CROSS experiment: search for 0𝜈2𝛽 decay with surface sensitive bolometers[END_REF]. As for the light detector (LD) we use a SiO-coated Ge wafer of 44 mm diameter and 0.175 mm thickness, instrumented with a 3×1×1 mm NTD. The LD was mounted in the copper holder near the Li 2 100 MoO 4 detector (LMO). The crystal is fixed inside the copper holder by PTFE (polytetrafluoroethylene) pieces, as seen in Fig. 1. The PTFE supports act also as thermal contacts to the heat sink of the cryostat.

There are edge chamfers on the crystals, see Fig. 1.

The Cu holder of the detector is coated with Au to avoid oxidation, while the internal part of the holder is also coated with Ag to improve light reflection. The Li 2 100 MoO 4 crystal inside the Cu housing is surrounded with a Vikuiti™ reflecting film, which is the same used in LUMINEU and CUPID-Mo. The NTD Ge is wire-bonded with Au wires, while the heater is bonded with Al wires. A 238 U/ 234 U source is placed on the holder's top cap. The source was obtained by depositing an uranium-containing liquid drop on a thin copper substrate that was then dried by evaporation. Part of the alpha particles (as well as nuclear recoils) emitted are degraded in energy. The LD is fabricated in the same way using a dedicated Cu holder, three PTFE elements, and an NTD Ge sensor glued. A 55 Fe X-ray source is placed close to the LD to irradiate the Ge surface opposite to the Li 2 100 MoO 4 absorber.

Low-temperature underground measurements

We tested the detector in the CROSS Cryogenic Underground (C2U) facility [START_REF]The new CROSS Cryogenic Underground (C2U) facility: an overview[END_REF], in operation at the Canfranc laboratory (Spain) since April 2019. The cryostat is placed inside a Faraday cage with acoustic isolation, formerly used by the ROSEBUD dark matter experiment [START_REF] Cebrián | Bolometric WIMP search at Canfranc with different absorbers[END_REF]. The set-up operates a pulse-tube (Cryomech PT415) based dilution refrigerator, developed by CryoConcept (France), which is also assisted by Ultra Quiet Technology™ (UQT) to mitigate vibrations [START_REF] Olivieri | Vibrations on pulse tube based Dry Dilution Refrigerators for low noise measurements[END_REF]. During the cryostat commissioning, it was found the UQT to efficiently reduce vibrations in the vertical direction, but not as much horizontally [START_REF]The new CROSS Cryogenic Underground (C2U) facility: an overview[END_REF] resulting in a noise excess affecting the bolometric performance [START_REF] Helis | Neutrinoless double-beta decay searches with enriched 116 CdWO 4 scintillating bolometers[END_REF]. Thus, the hybrid bolometer was spring-suspended from the detector plate. In order to reduce the environmental background, the cryostat is surrounded externally by a 25 cm thick low-radioactivity lead shield. Moreover, the detector volume inside the cryostat is shielded from the dilution unit and cryostat upper parts with a 13 cm thick disk made of sandwiched lead and copper (120 kg total mass). The shielding of the set-up has not been completed yet, in particular an anti-radon Plexiglas box (to be flushed with a deradonized air) and a muon veto will be installed soon.

The signal readout is based on a low-noise room-temperature DC front-end electronics [START_REF] Arnaboldi | The programmable front-end system for CUORICINO, an array of large-mass bolometers[END_REF] tracing back to the Cuoricino experiment. The data acquisition (DAQ) is a new design candidate for CUPID [START_REF] Carniti | High-Resolution Digitization System for the CROSS Experiment[END_REF] and consists of two 12-channel boards with a programmable 6-pole Bessel-Thomson anti-aliasing filter and integrated 24-bit ADC. A cut-off frequency of the low-pass filter can be set from 24 Hz up to 2.5 kHz. With the 24 bit ADC resolution, the input noise is not limited by the ADC even with the lowest gain value set at a programmable-gain amplifier (PGA). An additional advantage of such ADC resolution is that the PGA stage can be made much simpler or removed, with less power consumption, cost, and space. The sampling rate up to 25 kS/s can be set (250 kS/s with half of channels). The ADC-digitized continuous data are readout by an external FPGA (fieldprogrammable gate array) module and then transferred to a personal computer via Ethernet. The DAQ control is done with the help of a MATLAB-based graphical user interface program. The monitoring on-line of the data quality is realized as a LabVIEW application.

We collected data from the end of December 2019 until the beginning of April 2020. The measurements were performed at temperatures 18 and 12 mK. We periodically calibrated the LMO by inserting a thoriated tungsten wire inside the lead shield. We chose the working points for both operational temperatures to be a few nA current on the NTD sensor resulting in a few MΩ resistance. The data are sampled continuously at a 2 kS/s sampling rate, and the full data stream is 100 MoO 4 cubic-shaped scintillator. We report the detectors rise and decay times, the signal amplitude per unit of deposited energy, the energy resolution (FWHM) of the baseline after the optimum filter, at 5.9 keV X-ray of 55 Mn (LD), and at 2615 keV 𝛾 quanta of 208 Tl (LMO). We skip the computation of FWHM at 2615 keV for the 18 mK dataset due to poor statistics of the 𝛾 peak. Particle identification parameters (defined in Sec. 3.2) as light yield for 𝛾(𝛽)s 𝐿𝑌 𝛾 (𝛽) and a quenching factor for 𝛼 particles 𝑄𝐹 𝛼 , as well as the discrimination power between 𝛼 and 𝛾(𝛽) distributions 𝐷𝑃 𝛼/𝛾 (𝛽) for events selected in the 2.0-5.1 MeV energy range are also quoted. written to disk for offline analysis. The Bessel-Thomson cut-off frequency was set at 300 Hz, as a compromise between the bandwidth of the LMO (slow) and LD (relatively fast). We used around-3-week-long stable periods of data for the analysis at each regulated temperature, not affected by external events (e.g. power cuts). We select 314 h of physics data at each temperature and 65 and 220 h of the 232 Th calibration data at 18 and 12 mK, respectively.

The acquired data are triggered offline to tag discrete energy depositions. The triggered pulses are then processed by the optimum filter technique [START_REF] Gatti | Processing the signals from solid-state detectors in elementary-particle physics[END_REF] to evaluate the signal amplitude (i.e. energy) and several pulse-shape parameters. In the reconstruction of the coincidences between the LMO and LD, we account for the LD faster response and correct for its constant time shift with respect to the LMO signal, similarly to the method described in [START_REF] Piperno | Optimizing the energy threshold of light detectors coupled to luminescent bolometers[END_REF].

Results

Detector performance

The performance parameters achieved by the LMO and LD in the 18 and 12 mK tests are listed in Table 1. The rise and decay time constants, defined respectively as time intervals of the (10-90)% rising edge and (90-30)% trailing edge relative to the signal maximum, of the LMO are ∼0.02 and ∼0.15 s, respectively. We expect the LD response to be faster by an order of magnitude because of the smaller heat capacity of both the Ge absorber and the NTD thermistor. The time constants obtained are in agreement with the results of previous investigations of similar size LMOs and LDs [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF] Armengaud | Precise measurement of 2𝜈𝛽𝛽 decay of 100 Mo with the CUPID-Mo detection technology[END_REF]. It is worth noting that the time response of the bolometric detectors depend on the operation temperature and the sensor polarization (see, e.g., [START_REF] Beeman | Characterization of bolometric Light Detectors for rare event searches[END_REF]). However, optimization of the detector time response was out of the scope of the present study. The LD signal amplitude per unit of deposited energy is 1.2 𝜇V/keV at 18 mK and 1.4 𝜇V/keV at 12 mK. The LMO signal amplitude is of course inferior, 17 nV/keV at 18 mK and doubles at 12 mK. Since the working points were not optimized to get the highest sensitivity, these results are good but not extraordinary among similar devices [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF] Armengaud | Precise measurement of 2𝜈𝛽𝛽 decay of 100 Mo with the CUPID-Mo detection technology[END_REF].

The LD is calibrated with the 5.9 and 6.5 keV X-rays emitted by the 55 Fe source. The energy spectrum of the 55 Fe source gathered over 913 h of physics and thorium calibration runs is shown in Fig. 2. The almost fully resolved Mn K 𝛼 /K 𝛽 doublet is visible thanks to the high LD energy resolution: ≈0.3 keV FWHM at 5.9 keV. The baseline noise is 0.2-0.3 keV FWHM, demonstrating a reasonably low threshold. It is worth noting that such devices do not always show a high energy resolution even if characterized by ten(s) eV RMS noise , due to the position-dependent response

In particular, to get the fastest response in view of the rejection of random coincidence events induced background in the 100 Mo 0𝜈2𝛽 region of interest [START_REF] Chernyak | Random coincidence of 2𝜈2𝛽 decay events as a background source in bolometric 0𝜈2𝛽 decay experiments[END_REF][START_REF] Chernyak | Rejection of randomly coinciding events in ZnMoO 4 scintillating bolometers[END_REF][START_REF] Chernyak | Rejection of randomly coinciding events in Li 2 100 MoO 4 scintillating bolometers using light detectors based on the Neganov-Luke effect[END_REF].

For example, the Mn doublet resolution of 0.3-0.5 keV FWHM was measured with LDs made of 30-45 𝜇m thick Ge wafers [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF], while the 0.08 keV FWHM resolution was achieved by a 33 g Ge bolometer ( 20×20 mm) characterized by a similar noise level [START_REF]Searching for low-mass dark matter particles with a massive Ge bolometer operated above ground[END_REF]. of thin bolometers. We measured the LMO energy scale and resolution with the most intense gamma peaks in the thorium spectrum, illustrated in Fig. 3 (top panel). Because of the incomplete shielding, the physics data (Fig. 3, bottom panel) also exhibit several 𝛾 peaks from residual environmental radioactivity (daughters of 226 Ra and 228 Th sub-chains). The 238 U/ 234 U alpha source also emits 𝛽 particles from 234𝑚 Pa decays (𝑄 𝛽 = 2.27 MeV [START_REF] Audi | The NUBASE2016 evaluation of nuclear properties[END_REF]), which, together with the 100 Mo 2𝜈2𝛽 decays [START_REF] Armengaud | Precise measurement of 2𝜈𝛽𝛽 decay of 100 Mo with the CUPID-Mo detection technology[END_REF], are responsible for the most part of the continuum background above 0.5 MeV, seen in Fig. 3 (bottom panel).

The energy dependence of the LMO energy resolution is presented in Fig. 4. The results extracted from physics data are limited by the poor statistics. The detector demonstrates a good energy resolution in a wide energy interval exhibiting a peak width slightly increasing with energy, in agreement with early findings [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF]First data from the CUPID-Mo neutrinoless double beta decay experiment[END_REF]. In particular, we achieved a 6 keV energy resolution (FWHM) for 𝛾-ray quanta of 208 Tl with energy 2615 keV, and a 2.5 keV FWHM baseline noise.

The resolution at the 𝑄 2𝛽 of 100 Mo is expected to be very similar (Fig. 4). These results are in agreement with prior measurements for cylindrical LMOs [START_REF] Lumineu | CUPID-0/M collaboration, 100 Mo-enriched Li 2 MoO 4 scintillating bolometers for 0𝜈2𝛽 decay search: from LUMINEU to CUPID-0/Mo projects[END_REF][START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF] Armengaud | The CUPID-Mo experiment for neutrinoless double-beta decay: performance and prospects[END_REF], confirming an excellent bolometric performance independent of the crystal shape. It is also evident that a low baseline noise is crucial in obtaining a high energy resolution with a Li 2 100 MoO 4 bolometer. It is worth noting, the lowest noise achieved with the LMO is a factor 2-4 worse than the best reported values for large-volume lithium molybdate bolometers [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF] Armengaud | The CUPID-Mo experiment for neutrinoless double-beta decay: performance and prospects[END_REF]. Thus, taking into account sub-optimal noise level of the present study, there is still room for improvement.

Particle identification capability

Coincidences between the LMO and LD have been used to probe the scintillation based particle identification (PID). For each event triggered by the LMO we calculated a PID parameter, the socalled light yield (𝐿𝑌 ), defined as the ratio of the LD to LMO measured energy. The 𝐿𝑌 dependence on particle energy is shown in Fig. 5, where the population of 𝛾(𝛽) events is clearly separated from 𝛼's. Such a powerful separation is achieved thanks to the quenching of the scintillation light for 𝛼 particles with respect to 𝛾(𝛽)'s of the same energy and low noise of the LD. Different ionization properties lead also to a different amplitude measured by the LMO. Figure 5 shows a ∼7% increase of an 𝛼 event energy with respect to the gamma energy scale, in agreement with previous studies of LMO bolometers [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF] Armengaud | The CUPID-Mo experiment for neutrinoless double-beta decay: performance and prospects[END_REF]. This difference, called thermal quenching, hints at a possibility of PID by pulse-shape analysis of the heat channel itself [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF], but it is by far less reproducible due to a strong dependence on the noise conditions .

Since the present detector does not have the CROSS technology of the surface coating for PID purpose, we skip an analysis of pulse-shape discrimination of 𝛼 events. In order to investigate a 𝐿𝑌 -based 𝛼/𝛾(𝛽) separation close to the 100 Mo 0𝜈2𝛽 region of interest (ROI), we selected events within the 2.0-5.1 MeV energy range and a 𝐿𝑌 interval of 0.4-1.0 keV/MeV for 𝛾(𝛽)'s and 0-0.25 keV/MeV for 𝛼's; both are shown in Fig. 6. A Gaussian fit to each distribution provides a 𝐿𝑌 mean value (𝜇) and standard deviation (𝜎), which we used to calculate the so-called discrimination power defined as 𝐷𝑃 𝛼/𝛾 (𝛽) = 𝜇 𝛾 (𝛽) -𝜇 𝛼 / √ 𝜎 2 𝛾 (𝛽) + 𝜎 2 𝛼 . The 𝐷𝑃 𝛼/𝛾 (𝛽) based on the present data is around 8 (Table 1), meaning about 8𝜎 𝛼 of alpha event rejection while keeping almost 100% of 𝛾(𝛽)'s. This rejection power fully satisfies the CUPID goal of identifying 99.9% of alpha particles (corresponding to 𝐷𝑃 𝛼/𝛾 (𝛽) ∼ 3.1).

The LMO light yield for 𝛾(𝛽) events (𝐿𝑌 𝛾 (𝛽) ) was found to be 0.64 keV/MeV, similar to one measured with cylindrical shaped LMOs of 44×45 mm size [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF] Armengaud | The CUPID-Mo experiment for neutrinoless double-beta decay: performance and prospects[END_REF][START_REF]Performance of the CUPID-Mo double-beta decay bolometric experiment[END_REF]. However, in the present study the light collection efficiency was affected by the smaller area of the LD (15 cm 2 ) with respect to the LMO surface facing it (20 cm 2 ) and by the entrance window of the Cu holder ( 45 mm). Thus, considering only the direct light, the 𝐿𝑌 𝛾 (𝛽) is expected to be ∼ 0.85 keV/MeV, once a 45 mm side square LD is coupled to the LMO. In case of the use of two LDs, the 𝐿𝑌 should be roughly doubled, as demonstrated by CUPID-Mo [START_REF] Armengaud | The CUPID-Mo experiment for neutrinoless double-beta decay: performance and prospects[END_REF][START_REF]Performance of the CUPID-Mo double-beta decay bolometric experiment[END_REF]. The quenching factor (𝑄𝐹 𝛼 ) for 𝛼 particles of 210 Po observed in the data (see the next section) is 0.2 , in agreement with the previous data [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF] Armengaud | The CUPID-Mo experiment for neutrinoless double-beta decay: performance and prospects[END_REF][START_REF]Performance of the CUPID-Mo double-beta decay bolometric experiment[END_REF].

Li 2 100 MoO 4 crystal radiopurity

A highly-efficient PID together with a good energy resolution of the LMO operated over four weeks of background measurements allow us to quantify the Li 2 100 MoO 4 radiopurity with a high sensitivity. The spectrum of alpha events selected from the physics data (and recalibrated to 𝛼 energy) is presented in Fig. 7; the energy interval covers most 𝑄 𝛼 -values of radionuclides from the U/Th chains. As it is seen in Fig. 7, the use of the 238 U/ 234 U smeared 𝛼 source prevents estimation of the alpha activity of 232 bolometers. Also, the total rate of 210 Po events (∼0.06 mHz) is rather low to be a notable source of pile-ups, which are of certain concern for slow response thermal detectors [START_REF] Poda | Low background techniques in bolometers for double-beta decay search[END_REF].

The spectrum shows no other structures, so we can only set limits on other radionuclide contaminations. In order to be conservative, we considered all events within 25 keV of each expected peak location. The background (1 count per 50 keV) was estimated in the 5.65-5.75 and Such a parameter is typically quoted without the correction from the thermal quenching and we follow that convention here. 5.85-5.95 MeV energy intervals, containing no 𝑄 𝛼 -value of U/Th radionuclides. The data exhibit no events of 228 Th (𝑄 𝛼 = 5520 keV [START_REF] Wang | The AME2016 atomic mass evaluation * (II). Tables, graphs and references[END_REF]) and two counts of 222 Rn (𝑄 𝛼 = 5590 keV [START_REF] Wang | The AME2016 atomic mass evaluation * (II). Tables, graphs and references[END_REF]; a daughter of 226 Ra), thus we place 90 confidence level (C.L.) upper limits of 1.6 and 4.9 counts, respectively [START_REF] Feldman | Unified approach to the classical statistical analysis of small signals[END_REF]. A selection efficiency of 95.7% was estimated using alpha events of the 238 U/ 234 U smeared 𝛼 source, distributed in the 3.5-4.8 MeV energy interval. Therefore, the activity of 228 Th and 226 Ra in the Li 2 100 MoO 4 crystal bulk is below 3 and 8 𝜇Bq/kg at 90% C.L., respectively. Taking into account the reasonably short half-lives of 228 Ra (5.75 yr [START_REF] Audi | The NUBASE2016 evaluation of nuclear properties[END_REF]) and 228 Th (1.91 yr [START_REF] Audi | The NUBASE2016 evaluation of nuclear properties[END_REF]), the limit on the 228 Th activity can also represent the 232 Th contamination in the crystals, as e.g. seen in [START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF][START_REF]First data from the CUPID-Mo neutrinoless double beta decay experiment[END_REF][START_REF]Performance of the CUPID-Mo double-beta decay bolometric experiment[END_REF].

The limits on the 228 Th and 226 Ra activity in the studied Li 2 100 MoO 4 crystal are on the same level as reported by LUMINEU [START_REF] Lumineu | CUPID-0/M collaboration, 100 Mo-enriched Li 2 MoO 4 scintillating bolometers for 0𝜈2𝛽 decay search: from LUMINEU to CUPID-0/Mo projects[END_REF][START_REF] Armengaud | Development of 100 Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search[END_REF], which were obtained by the analysis of a comparable exposure. A significantly larger exposure of the CUPID-Mo experiment [START_REF] Armengaud | The CUPID-Mo experiment for neutrinoless double-beta decay: performance and prospects[END_REF][START_REF]First data from the CUPID-Mo neutrinoless double beta decay experiment[END_REF][START_REF]Performance of the CUPID-Mo double-beta decay bolometric experiment[END_REF] shows that the level of remaining contaminants in Li 2 100 MoO 4 scintillators can be even an order of magnitude lower. As the protocol of the CROSS crystal production was the one adopted by LUMINEU and CUPID-Mo, it seems natural to assume the radiopurity of the CROSS crystals to be similar to that of CUPID-Mo ones. It is worth noting that the 228 Th ( 232 Th) and 226 Ra contamination on the level of 10 𝜇Bq/kg is compatible with a background contribution below 10 -4 counts/yr/kg/keV to the 100 Mo 0𝜈2𝛽 ROI, and it is fully acceptable not only for the medium-scale CROSS experiment (with ∼10 kg detector mass), but also for the tonne-scale extension of CUPID.

Conclusions

We report that performance and radiopurity of a scintillating bolometer based on a large cubicshaped Li 2 100 MoO 4 crystal -randomly taken from 32 identical crystals (with a 45 mm side and a mass of 0.28 kg each) of the CROSS 0𝜈2𝛽 project-are similar to those of cylindrical 0.2 kg Li 2 100 MoO 4 bolometers, used in LUMINEU and CUPID-Mo 2𝛽 experiments. In particular, the Li 2 100 MoO 4 detector energy resolution at 2615 keV 𝛾 quanta (as well as its approximation to 3034 keV, the 100 Mo 2𝛽 decay energy) is 6 keV FWHM. A scintillation light yield of the cubicshaped crystal, 0.64 keV/MeV for 𝛾(𝛽)'s, is compatible to that of cylindrical crystals. However, the measured light yield is affected by about 30% lower detection surface of the optical bolometer with respect to the nearby Li 2 100 MoO 4 crystal face. In spite of sub-optimal light collection, a full separation (∼8𝜎) between 𝛼 and 𝛾(𝛽) events above 2 MeV has been achieved. A high radiopurity of the cubic-shaped Li 2 100 MoO 4 crystal was also demonstrated by the present study, where only 210 Po is detected with the activity of 80 [START_REF] Chernyak | Random coincidence of 2𝜈2𝛽 decay events as a background source in bolometric 0𝜈2𝛽 decay experiments[END_REF] 𝜇Bq/kg, while the content of 228 Th and 226 Ra (the most harmful radionuclides from U/Th families for 0𝜈2𝛽 searches) is estimated to be less than 3 and 8 𝜇Bq/kg, respectively.

The performed investigation additionally proves the excellent prospects of Li 2 100 MoO 4 scintillating bolometers for high-sensitivity 0𝜈2𝛽 decay searches. The cubic shape of large-volume (∼90 cm 3 ) Li 2 100 MoO 4 crystals allows a more compact detector array structure and thus the deployment of a larger isotope mass in the experimental volume, as well as an increased efficiency of multi-site event detection. In view of these results, large-mass (∼0.3 kg) radiopure cubic-shaped Li 2 100 MoO 4 crystals operated as bolometers satisfy the demands of the CROSS and CUPID projects.

Figure 1 .

 1 Figure 1. A photograph of the partially assembled Li 2 100 MoO 4 scintillating bolometer; the construction elements (see text) are labeled. A 45 mm hole at the bottom of the holder, visible in transparency, acts as an entrance window for the Li 2 100 MoO 4 scintillation light to be registered by a bolometric Ge light detector.

Figure 2 .

 2 Figure 2. The energy spectrum of the 55 Fe X-ray source measured by a 1.4 g Ge bolometric light detector over 913 h (12 and 18 mK data) in the CROSS pulse tube based cryogenic facility at the Canfranc underground laboratory (Spain). A fit to the data by a model assuming a double-Gaussian function and a flat background component is shown by solid (red) line. The energy resolution (FWHM) is quoted for the 5.9 keV X-ray peak of Mn K 𝛼 .

Figure 3 .

 3 Figure3. The energy spectra of 𝛾(𝛽) events accumulated by the LMO over the calibration (285 h; top panel) and physics data (628 h; bottom panel) measurements in the C2U facility at the Canfranc underground laboratory. The most prominent 𝛾 peaks are labeled. The contribution of 𝛼 events to the physics data has been removed with the scintillation light based particle identification (see text). The inset shows the 𝛾 peak with energy of 2615 keV in the calibration data together with a fit and the calculated energy resolution (FWHM).

Figure 4 .

 4 Figure 4. Energy dependence of the 279 g Li 2 100 MoO 4 bolometer energy resolution (FWHM) measured in the calibration (filled circles; 12 mK) and physics (open circles; 18 and 12 mK) runs. The fitting curve is shown by the dashed line, while the solid line indicates the 100 Mo 𝑄 2𝛽 .

Figure 5 .

 5 Figure5. Light yield as a function of energy deposited in the LMO and measured in a 125 h long 232 Th calibration at 12 mK. The energy scale is calibrated with 𝛾 quanta. The population of 𝛾(𝛽) events is clearly separated from the 𝛼 events, mainly originated by the 238 U/ 234 U smeared 𝛼 source. The 𝛼 events shown in red were selected above 1 MeV with a 𝐿𝑌 cut below 0.25 keV/MeV.

Figure 6 .

 6 Figure 6. The light yield distributions for 𝛼 and 𝛾(𝛽) particles, selected in the 2.0-5.1 MeV energy interval.The former distribution is rescaled by a factor 0.1 to improve the visibility of the later one. A Gaussian fit to each distribution is shown by a solid line. The discrimination power between the two populations is ∼8.

Figure 7 .

 7 Figure 7. A part of the 𝛼 energy spectrum accumulated by the LMO operated over 628 h in the CROSS underground cryostat in Canfranc. The energy interval covers the 𝑄 𝛼 -values of the most 𝛼-active radionuclides from U/Th decay chains. In addition to a dominant contribution from the used 238 U/ 234 U source, the spectrum exhibits only two populations of 210 Po originated by external (surface of nearby materials) or internal (crystal bulk) contaminations of the detector.

  2 100 MoO 4 scintillating bolometers for high-sensitivity searches for the 100 Mo 0𝜈2𝛽 decay in CROSS and CUPID projects.

	Contents
	1 Introduction	1
	2 Detector construction and operation	4
	2.1 Li 2	100 MoO 4 scintillating bolometer fabrication	4
	2.2 Low-temperature underground measurements	5
	3 Results		6
	3.1 Detector performance	6
	3.2 Particle identification capability	9
	3.3 Li 2	100 MoO 4 crystal radiopurity	11
	4 Conclusions	13

K

: Double-beta decay, Cryogenic detector, Bolometer, Crystal scintillator, Lithium molybdate, Particle identification, Radiopurity

Table 1 .

 1 Performance of a scintillating bolometer based on the 44 mm Ge light detector coupled to the 45 mm side Li 2

  Th, 238 U and some of the daughters with 𝑄 𝛼 ≤ 4.8 MeV. However, we can investigate a possible contamination by 226 Ra and 228 Th, which are the most harmful contaminants for 0𝜈2𝛽 searches. The energy region above 4.8 MeV contains only two peak-like structures both ascribed to 210 Po 𝛼 events, and originated by the 210 Pb contamination [47]. A clear peak at 5.4 MeV is induced by the 210 Po decays in the Li 2 100 MoO 4 crystal bulk with the activity of 80(12) 𝜇Bq/kg. A 210 Po ( 210 Pb) bulk contamination on the level of ten(s)-hundred(s) 𝜇Bq/kg is typical for Li 2 100 MoO 4 crystals [5, 18, 24, 26]. A broad distribution peaked at 5.3 MeV is caused by the 210 Po decay on the surface of materials facing the LMO (a 0.1 MeV energy is taken away by the 206 Pb nuclear recoil). The decays of 210 Po at surfaces of the detector materials can populate the 100 Mo 0𝜈2𝛽 ROI as energy-degraded alpha events, but they can be easily rejected thanks to the efficient PID of Li 2 100 MoO 4 scintillating

Acknowledgments

The CROSS and CUPID Collaborations thank the directors and staff of the Laboratorio Subterráneo de Canfranc and the technical staff of our laboratories. This work was supported by the Istituto Nazionale di Fisica Nucleare (INFN); by the European Research Council (ERC) under the European Union Horizon 2020 program (H2020/2014-2020) with the ERC Advanced Grant no. 742345 (ERC-2016-ADG, project CROSS) and the Marie Sklodowska-Curie Grant Agreement No. 754496; by the Italian Ministry of University and Research (MIUR) through the grant Progetti di ricerca di Rilevante Interesse Nazionale (PRIN 2017, grant no. 2017FJZMCJ); by the US National Science Foundation under Grant Nos. NSF-PHY-1614611 and NSF-PHY-1401832; by the P2IO LabEx (ANR-10-LABX-0038) managed by the Agence Nationale de la Recherche (France). This material is also based upon work supported by the US Department of Energy (DOE) Office of Science under Contract Nos. DE-AC02-05CH11231 and DE-AC02-06CH11357; and by the DOE Office of Science, Office of Nuclear Physics under Contract Nos. DE-FG02-08ER41551, DE-SC0011091, DE-SC0012654, DE-SC0019316, DE-SC0019368, and DE-SC0020423. This work was also supported by the Russian Science Foundation under grant No. 18-12-00003 and the National Research Foundation of Ukraine under Grant No. 2020.02/0011.


A Armatol

E Armengaud

W Armstrong

C Augier

F T Avignone

O Azzolini

A Barabash

G Bari

A Barresi

D Baudin

F Bellini

G Benato

M Beretta

L Bergé

M Biassoni

J Billard

V Boldrini

A Branca

C Brofferio

C Bucci

J Camilleri

S Capelli

L Cappelli

L Cardani

P Carniti

N Casali

A Cazes

E Celi

C Chang

M Chapellier

A Charrier

D Chiesa

M Clemenza

I Colantoni

F Collamati

S Copello

F Cova

O Cremonesi

R J Creswick

A Cruciani

A D'addabbo

G D'imperio

I Dafinei

F A Danevich

M De Combarieu

M De Jesus

P De Marcillac

S Dell'oro

S Di Domizio

V Dompè

A Drobizhev

L Dumoulin

G Fantini

M Fasoli

M Faverzani

E Ferri

F Ferri

F Ferroni

E Figueroa-Feliciano

J Formaggio

A Franceschi

C Fu

S Fu

B K Fujikawa

J Gascon

A Giachero

L Gironi

A Giuliani

P Gorla

C Gotti

P Gras

M Gros

T D Gutierrez

K Han

E V Hnasen

K M Heeger

D L Helis

H Z Huang

R G Huang

L Imbert

J Johnston

A Juillard

G Karapetrov

G Keppel

H Khalife

V V Kobychev

Yu G Kolomensky

S Konovalov

Y Liu

P Loaiza

L Ma

M Madhukuttan

F Mancarella

R Mariam

L Marini

S Marnieros

M Martinez

R H Maruyama

B Mauri

D Mayer

Y Mei

S Milana

D Misiak

T Napolitano

M Nastasi

X F Navick

J Nikkel

R Nipoti

S Nisi

C Nones

E B Norman

V Novosad

I Nutini

T O'donnell

E Olivieri

C Oriol

J L Ouellet

S Pagan

C Pagliarone

L Pagnanini

P Pari

L Pattavina

B Paul

M Pavan

H Peng

G Pessina

V Pettinacci

C Pira

S Pirro

D V Poda

T Polakovic

O G Polischuk

S Pozzi

E Previtali

A Puiu

A Ressa

R Rizzoli

C Rosenfeld

C Rusconi

V Sanglard

J Scarpaci

B Schmidt

V Sharma

V Shlegel

V Singh

M Sisti

D Speller

P T Surukuchi

L Taffarello

O Tellier

C Tomei

V I Tretyak

A Tsymbaliuk

A Vedda

M Velazquez

K J Vetter

S L Wagaarachchi

G Wang

L Wang

B Welliver

J Wilson

K Wilson

L A Winslow

M Xue

L Yan

J Yang

V Yefremenko

V Yumatov

M M Zarytskyy

J Zhang

A Zolotarova

S Zucchelli

A novel technique for the study of pile-up events in cryogenic bolometers

Precise characterization of detector time resolution is of crucial importance for next-generation cryogenic-bolometer experiments searching for neutrinoless double-beta decay, such as CUPID, in order to reject background due to pile-up of two-neutrino double-beta decay events. In this paper, we describe a technique developed to study the pile-up rejection capability of cryogenic bolometers. Our approach, which consists of producing controlled pile-up events with a programmable waveform generator, has the benefit that we can reliably and reproducibly control the time separation and relative energy of the individual components of the generated pile-up events. The resulting data allow us to optimize and benchmark analysis strategies to discriminate between individual and pileup pulses. We describe a test of this technique performed with a small array of detectors at the Laboratori Nazionali del Gran Sasso, in Italy; we obtain a 90% rejection efficiency against pulsergenerated pile-up events with rise time of ∼ 15 ms down to time separation between the individual events of 2 ms.

I. INTRODUCTION

Two-neutrino double-beta decay (2νββ), despite being a rare process, constitutes a dominant fraction of intrinsic radioactivity in low-background neutrinoless doublebeta decay (0νββ) [1] detectors. Excellent detector energy resolution is essential to distinguish between 2νββ decays and 0νββ decay candidates. However, for nextgeneration 0νββ searches, aiming at unprecedented low backgrounds, random pile-up of 2νββ events can constitute a non-negligible continuum background in the region of interest (ROI) around the 0νββ transition Q-value [2].

Cryogenic bolometers meet the requirements of excellent energy resolution, low background and large mass needed for a high-sensitivity 0νββ decay search. These detectors have set some of the most stringent limits on the 0νββ decay half-life in multiple isotopes, in particular 82 Se [3], 100 Mo [START_REF] Armengaud | A new limit for neutrinoless double-beta decay of 100 Mo from the CUPID-Mo experiment[END_REF] and 130 Te [5,6]. The CUORE Upgrade with Particle IDentification (CUPID), a proposed upgrade of the CUORE experiment, will search for 0νββ decay of 100 Mo, aiming at a half-life sensitivity greater than 10 27 yr [7]. CUPID will consist of a large array of 100 Moenriched Li 2 MoO 4 (LMO) scintillating bolometers instrumented with cryogenic light detectors (LDs). The experiment will exploit the experience acquired by running CUORE, the first tonne-scale cryogenic bolometer array, and will take advantage of its low-background cryogenic infrastructure [8]; CUPID will combine this with the effective background reduction strategies demonstrated by the CUPID-0 [9] and CUPID-Mo [10] detectors to realize a one-tonne array with a background index of the order of 10 -4 counts keV -1 kg -1 yr -1 in the ROI.

In order to meet this goal, it is important to assess and mitigate each individual background component in the final technical design. Given the short decay halflife of 100 Mo, 7.1 × 10 18 yr [11], the 2νββ pile-up is expected to constitute a non-negligible fraction of the overall CUPID background budget. An estimate for a single CUPID-like crystal (300 g of LMO with 100% enrichment of 100 Mo) assuming a 1-ms resolving time for the heat detector puts the expected background rate from pile-up of about 3.5 × 10 -4 counts keV -1 kg -1 yr -1 [7]. Characterization of the pile-up induced background requires a thorough understanding of the resolving time CUPIDlike bolometers can achieve.

CUPID will use neutron transmutation doped (NTD) thermistors [START_REF] Haller | Neutron Transmutation Doping of Semiconductor Materials[END_REF] as temperature (phonon) sensors. NTDbased macro-calorimeters have a relatively slow time response; for crystals of a few hundreds grams, the typical rise time of a thermal pulse is of the order of few tens of ms and the pulse decay is typically in the range of (0.1-1) s. In an ideal detector, the rise time is generally a function of the temperature-dependent NTD working resistance, while the decay time is proportional to the ratio of the absorber crystal heat capacity and the conductance to the thermal sink. Given the relatively slow response to an energy deposition, multiple particle interactions close in time will produce overlapping thermal pulses, resulting in a cumulative pulse, whose rising edge will be affected by the pile-up of the underlying events. Therefore, characterizing the rising edge of thermal pulses is crucial to discrimination of pile-up events.

In this work, we describe a new technique we developed to study the time resolution of CUPID-like detectors, and produce a controlled sample of pile-up events to determine the pile-up rejection efficiency of a pulse shape analysis. We tested this technique in a dedicated measurement carried out at the Laboratori Nazionali del Gran Sasso (LNGS), in Italy.

II. MEASUREMENT

An array of LMO crystals was deployed to study the performance of CUPID-like detectors, with crystals of similar dimension and shape to those that are intended to be used in the actual experiment [START_REF] Armatol | [END_REF]. This deployment is one of a series of bolometric tests planned to optimize the final technical design for CUPID. The array was operated at the Hall C cryogenic facility at LNGS between the summer of 2019 and the spring of 2020. The final runs of this measurement were devoted to generating a controlled sample of pile-up events to study the pile-up rejection efficiency.

The array consisted of 8 LMO cubic crystals (45×45× 45 mm 3 ) arranged in two 4-crystal floors. The crystals on the bottom floor were covered on the side with a reflecting aluminum foil, while those on the top floor were not. A total of 12 Ge disks (diameter 44-mm, thickness 0.175 mm) acting as LDs were placed below, in between, and above the crystal-floors, so that each LMO crystal faced two LDs. Each LMO crystal and LD was instrumented with a NTD sensor for the signal readout. For the pile-up study we focused on three LMO detectors which were instrumented with a functioning silicon heater, since pulsing the heater is crucial to generating the controlled sample of pile-up events.

The detector was operated at about 18 mK and the measured NTD working resistances were in the range of (10 -50) MΩ. The observed rise time values for thermal pulses in the LMO crystals were approximately 15 ms.

Detector signals were conditioned by custom front-end electronics boards, which include a programmable amplifier and anti-aliasing (Bessel-Thomson) filter [START_REF] Arnaboldi | [END_REF]. The filter cut-off frequency was set to 63 Hz, slightly higher than the expected signal bandwidth, to reduce the high frequency noise while not affecting the signal shape. The boards also provided independent programmable biases for the NTDs. The detector waveforms were acquired continuously with a sampling frequency of 2 kHz. The data stream was then triggered by means of an online derivative trigger [15]. Each triggered pulse (i. e. an event) consists of a 5-s window opened around the trigger sample, which by construction is fixed to 1 s from the start of the time window (pre-trigger).

The runs dedicated to the study of pile-up background aimed at producing a controlled set of pile-up events on which to benchmark the rejection efficiency of our analysis algorithms. To do this, we continuously injected signal-like pulses in the detector, scanning a range of values for both the pulse amplitudes and the time separation between consecutive pulses. The pulses were induced by injecting a calibrated amount of energy (via Joule heat-ing) into the crystals heaters using a programmable waveform generator (Tektronix AFG1062).

This technique is commonly used for the thermal gain stabilization of bolometers [16,17]. Our experience has shown that the heater can be used to correct the (temperature-dependent) detector gain against small temperature drifts because the pulse amplitude to temperature ratio behaves in the same way for heater pulses and particle pulses. However, in this work, for the first time we tried to emulate the shape of physics pulses with heater pulses, paying special attention to the rising edge. The underlying idea, now tested with a commercial module, is to include this feature in our pulser, thus being constantly able to monitor the pile-up discrimination of our detectors. The pulse shape of physics pulses and heater-induced pulses can be different due to the mechanisms of phonon generation and propagation. A possible reason is that the heater should mainly inject acoustic phonons into the crystal, while particle interactions would produce optical phonons directly inside the absorber, which immediately begin to degrade [18]. The shape and amplitude of heater pulses is also affected by the heater-wire conductance, which appears as an additional component of the detector.

Using the heater allows the detector to be thermally excited with precise control of the time separation and energy of the underlying excitation pulses. Given the goals of the study, this approach is more effective than using an intense radioactive source which has several disadvantages, including that the activity has to be tuned to a suitable rate and the arrival time and energy of particles exciting the detector cannot be controlled on the event-by-event level.

The waveform generator was configured to deliver a particular class of pulses for a fixed amount of time. For each configuration, we set the number of pulses to be injected, the pulse amplitudes and the time interval between successive pulses. The shape of the input waveform was chosen so that the rising edge of the heater-induced pulses matched as closely as possible the rising edge observed for particle-induced pulses. Figure 1 shows the rising edge observed for thermal pulses from particle events and heater events excited with rectangular, exponential and sawtooth waveforms. We found that the thermal pulses excited by sawtooth waveforms (right triangle with vertical rise and slow negative ramp) best reproduced the rising edge observed in particle induced pulses.

To generate reference individual pulses, the proxy for a well isolated particle events, we set the waveform-tooth width and amplitude to 50 ms and 170 mV, respectively, which produced pulses in the detectors with equivalent particle energies of (1.5 -2.5) MeV on the different channels. The time interval between two successive individual waveforms was set to 15 s, so that the detectors had returned to baseline before the start of a new pulse. For the pile-up sample, we generated pairs of excitations with the second beginning before the detector had recovered from the first excitation in the pair. We set the waveform- 2. Examples of heater-induced pile-up pulses excited by two sawtooth waveforms with amplitude ratio α = 1.4 close in time. It can be seen that the time separations between the two pulses (the begin of the rise is taken as a reference) reflects that of the original waveforms (∆t). A time-isolated reference pulse is shown for comparison.

tooth width to 50 ms for both excitations, fixed one amplitude to 170 mV and varied the other from 40 mV to 240 mV in steps of 50 mV. We denote the ratio of the two amplitudes in the pair by α, and so this parameter varied between 0.24 and 1.4. We explored values of the time separation (∆t) between the pulse pairs in the pileup sample ranging from 40 ms down to 1 ms (the Nyquist limit for the ADC sampling frequency). Figure 2 shows some of the observed thermal pulses; it can be seen that the distortion of the rising edge of pile-up pulses follows the time separation between the excitation pulses.

III. DATA ANALYSIS

The data analysis follows two main steps, a low-level processing and then a high-level analysis, i. e. the actual pile-up study. The low-level processing involves applying FIG. 3. Time distribution of the events in one of the pile-up runs. Each interval corresponds to a different α/∆t configuration. In this sequence, α is fixed to 0.24 while ∆t goes from 1 ms to 11 ms (from left to right). The gray dots represent the events selected as heater pulses, the red dots the discarded ones; we keep only clean events with a single trigger fired in the 5-s window.

a software filter to optimize the signal-to-noise ratio and calculating a set of summary variables for each event such as pulse rise time, decay time and energy. These steps are analogous to the standard CUORE workflow [19], which has also been adopted as the starting point for the main analysis of the LMO detectors [START_REF] Armatol | [END_REF]. These analysis tools are well established and have been applied over the years on multiple detectors [20,21]. The software filter uses the Optimum Filter (OF) technique [22], which reduces the impact of noise on the reconstructed pulse amplitude and pulse shape parameters. In order to define the OF transfer function, we use the average of the time-isolated reference pulses as the signal response of the system, while we build the noise power spectrum from signal-less event windows acquired in the reference run.

The first step of the high-level analysis is to associate each event with the corresponding waveform generator configuration. This is done based on the event timestamp since, as shown in Fig. 3, each waveform generator configuration corresponds to a specific time window.

We keep only clean events with a single trigger fired in the 5-s window. As pulser events dominate the event rate -the random coincidence of pulser events and events due to natural radioactivity proved to be negligible during the measurement -we apply a ±5 keV-cut around the median energy of the pulses for each configuration to suppress non-pulser events.

Once the events are selected for each configuration, we study how each of the pulse shape variables calculated in the low-level analysis are distributed for these events. We fit each distribution, one per channel, with a Gaussian function and take the resulting mean M x,i and standard deviation σ x,i , where x indexes the pulse shape variable studied (rise time, decay time, etc.) and i indexes the waveform generator configuration or time interval. To quantify the utility of a variable to discriminate between individual isolated pulses and pile-up pulses, we define the discrimination power as the distance between the two corresponding distributions, namely

D ≡ |M x,i -M x,R | σ 2 x,i + σ 2 x,R , (1)
where R labels the (channel-dependent) reference quantities for individual isolated heater pulses. The pulse rise time and decay time are natural choices for the variables on which to discriminate since we expect the shape of the pulse to be different in case of isolated and pile-up pulses. However, we use a related combined variable based on the so-called Test Value Left (TVL) and Test Value Right (TVR). These are χ 2 -like parameters which quantify how well the shape of each filtered pulse matches the shape of the filtered average reference pulse on the left (i. e. rise) and right (i. e. decay) side of the pulse maximum. We find that the combination TVL 2 + TVR 2 leads to an effective separation (D > 3) already at values of ∆t of the order of a ms. Recalling Fig. 1, we note that this analysis is comparing heater-induced pileup pulses to heater-induced isolated pulses and although we constructed the pulses to have similar rise times to particle induced pulses, the decay times are dissimilar. However, we expect the TVR variable will continue to provide some benefit when comparing isolated particle pulses to pile-up particle pulses as the decay time profile of a pile-up pulse is expected to be distorted compared to an isolated pulse. This will be tested in future studies.

In addition to TVL 2 + TVR 2 , we consider another variable, the time separation between the start of the pulse window and the moment in which the filtered pulse reaches its maximum, which we call delay. The delay is sensitive to the noise and proved to be a good discriminator for some configurations of α and ∆t (Fig. 4). Its complementarity to TVL 2 + TVR 2 is due to the way we implement the OF. In order to calculate TVL and TVR, the maximum of the filtered pulse is aligned to that of the average pulse; the quality of the alignment depends on the residual noise of the filtered pulse. The more precisely the maxima are superimposed, the more the test values will be sensitive to the pulse distortions due to pile-up. On the other hand, if the alignment is not optimal, the TVL 2 + TVR 2 might be misled by an overall matching of the pulses, but the delay variable would hint towards a different pulse shape due to possible pile-up.

We analyze all the pulser events in the pile-up runs and define a rejection efficiency, ε rej , as the fraction of events that lie outside the (M x,R ± 3σ x,R ) range for at least one of the two considered variables, TVL 2 + TVR 2 and delay. This interval is chosen so that the cut applied to the time-isolated reference pulses would select essentially all the events. For each α we fit the distribution of ε rej as a function of ∆t with an error function constrained to pass through the origin and extract the ∆t threshold corresponding to ε rej = 90% (Fig. 5).

The combined results of this analysis are summarized in Fig. 6, which shows the ∆t thresholds obtained for each α for each detector. The two outliers (correspond- ing to α = 1.12 for Channel 04 and α = 1.41 for Channel 03) are thought to be due to the sub-optimal detector operating conditions which we experienced while collecting the corresponding data. These points will be further investigated in future measurements.

IV. SUMMARY AND OUTLOOK

We developed a new technique to investigate the ability of cryogenic bolometers to reject pile-up events. Using a controlled sample of pile-up signal events generated by injecting known excitations from a programmable waveform generator into the crystal heaters we identified a set FIG. 6. ∆t thresholds corresponding to εrej = 90% for each configuration of α obtained for the three channels. The two outliers at α = 1.12 for Channel 04 and α = 1.41 for Channel 03 are likely due to sub-optimal detector conditions while collecting data for ∆t = 1 ms.

of pulse shape parameters that allow for effective discrimination between individual and pile-up pulses, obtaining a 90% rejection-efficiency for ∆t down to 2 ms for pulses with rise time of about 15 ms. This work is part of a campaign of measurements planned to optimize the technical design of the CUPID detector and develop the analysis chain. In future measurements related to pile-up studies we plan to improve noise conditions and cryogenic stability, explore higher sampling frequencies to probe ∆t < 1 ms and optimize the input excitation functions to better reproduce both the rising and falling edge of physics pulses. These data will be used to benchmark detector response simulations in development to assess the impact of pile-up on CUPID.

FIG. 4 . 1 FIG. 5 .

 415 FIG. 4. Comparison between the discrimination power (D) obtained with the TVL 2 + TVR 2 and delay variables for the configuration α = 0.24 of Channel 03. The value D = 3 for both variables is indicated with a dashed line. The configuration with ∆t = 5 ms has been tested in two different runs; the different values of discrimination power are likely due to the different detector noise (see the discussion in the text).

ACKNOWLEDGMENTS

The CUPID Collaboration thanks the directors and staff of the Laboratori Nazionali del Gran Sasso and the technical staff of our laboratories. This work was supported by the Istituto Nazionale di Fisica Nucleare (INFN); by the European Research Council (ERC) under the European Union Horizon 2020 program (H2020/2014-2020) with the ERC Advanced Grant No. 742345 (ERC-2016-ADG, project CROSS) and the Marie Sklodowska-Curie Grant Agreement No. 754496; by the Italian Ministry of University and Research (MIUR) through the grant Progetti di ricerca di Rilevante Interesse Nazionale (PRIN 2017, grant No. 2017FJZMCJ); by the US National Science Foundation under Grant Nos. NSF-PHY-1401832, NSF-PHY-1614611, and NSF-PHY-1913374. This material is also based upon work supported by the US Department of Energy (DOE) Office of Science under Contract Nos. DE-AC02-05CH11231 and DE-AC02-06CH11357; and by the DOE Office of Science, Office of Nuclear Physics under Contract Nos. DE-FG02-08ER41551, DE-SC0011091, DE-SC0012654, DE-SC0019316, DE-SC0019368, and DE-SC0020423. This work was also supported by the Russian Science Foundation under grant No. 18-12-00003 and the National Research Foundation of Ukraine under Grant No. 2020.02/0011. This research used resources of the National Energy Research Scientific Computing Center (NERSC). This work makes use of both the DIANA data analysis and APOLLO data acquisition software packages, which were developed by the CUORICINO, CUORE, LUCIFER and CUPID-0 Collaborations.