Result on the Neutrinoless Double Beta Decay Search of 82 Se with the CUPID-0 Experiment

: CUPID-0 is the ﬁrst large array of scintillating Zn 82 Se cryogenic calorimeters (bolometers) implementing particle identiﬁcation for the search of the neutrinoless double beta decay (0 νββ ). The detector consists of 24 enriched Zn 82 Se bolometers for a total 82 Se mass of 5.28 kg and it has been taking data in the underground LNGS (Italy) since March 2017. In this article we show how the dual read-out provides a powerful tool for the α particles rejection. The simultaneous use of the heat and light information allows us to reduce the background down to (3.2 + 1.3 − 1.1 ) × 10 − 3 counts/(keV kg year), an unprecedented level for cryogenic calorimeters. In a total exposure of 5.46 kg year Zn 82 Se we set the most stringent limit on the 0 νββ decay 82 Se half-life T 0 ν 1/2 > 4.0 × 10 24 year at 90% C.I.


Introduction
The neutrinoless double beta deca 0νββ [1] is a transition, in which a nucleus (A, Z) decays into its isobar (A, Z + 2) with the simultaneous emission of two electrons. Both the parent and the daughter nucleus must be more bound than the intermediate one (A, Z + 1) in order to avoid the occurrence of the sequence of two single beta decays. Such a condition, due to the pairing term, is fulfilled in nature for 35 even-even nuclei [2]. This process violates the lepton number by two units; it's not allowed by the Standard Model of interactions but it's envisaged in many of its extensions in which neutrinos are their own antiparticles [2]. Its discovery would establish unambiguously the nature of neutrinos as Majorana fermions [3]. In the standard paradigma [2,4] the decay is mediated only by the exchange of three virtual light neutrinos between two charged weak interaction vertices. The chirality mismatch imposed by the V-A structure of the ElectroWeak theory leads to an amplitude proportional to a linear combination of the three neutrino masses. Their squared mass differences are known from neutrino oscillation experiments ∆m 2 12 [4][5][6] and their sum is constrained to be less than 0.66 eV at 95% C.L. from cosmological observations but the absolute scale is still unknown [4][5][6]. Three possible orderings are therefore conceivable: normal hierarchy (NH), in which m ν1 <m ν2 <m ν3 , inverted hierarchy (IH) where m ν3 <m ν1 <m ν2 , and the quasi-degenerate hierarchy (QD), for which masses differences are tiny compared to their absolute values.
At present, no 0νββ evidence has been found and actual limits on the decay half-life, in the range of (10 24 -10 26 ) years [5][6][7][8][9][10][11][12][13], are probing the QD region. The main signature of the 0νββ decay is a peak in the sum energy spectrum of the electrons at the Q-value of the reaction which must be resolved over a continuous background [5]. In order to completely explore the IH region (τ ≈10 27−28 years), new technologies must be developed, able to reduce the specific background close to zero at the ton × year exposure scale in combination with a sensitive mass of hundreds of kg of isotope and a FWHM energy resolution better than 0.5% [5,14].
Cryogenic calorimeters (usually called bolometers) play an important role in this field of research [15,16] and in this contribution we review the most recent results obtained by the CUPID-0 experiment.

The Detector
A bolometer [17,18] is a single crystal calorimeter operating at ∼10 mK in which the temperature increase, following an energy release inside the crystal itself, is picked-up by a highly sensitive thermometer. This technology allows us to embed the 0νββ source in the detector itself and it exhibits excellent energy resolution and very high detection efficiency. One-Ton scale detectors composed of a thousand bolometers could be successfully operated as demonstrated by the CUORE experiment [11,19]. The CUORE sensitivity is limited by the residual background generated by energy-degraded α particles emitted by surface contaminations of the detector material. To suppress α particles the CUPID-0 experiment makes use of scintillating bolometers [20][21][22] in which a small fraction of the released energy is converted into scintillating light. The light escapes the crystal and it is absorbed by a thin bolometer working as light detector. The dual read-out allows us to identify the particle type because α particles have a different light yield and scintillation time-development compared to iso-energetic electrons [23][24][25][26][27].
The CUPID-0 detector is an array of Zn 82 Se bolometers, enriched in 82 Se at ∼95% [28][29][30]. The isotope under study for the 0νββ decay is 82 Se with a Q ββ = 2997.9 ± 0.3 keV [31], well above the energy of the most intense natural high-energy 208 Tlγ line at 2615 keV. The 2νββ decay of 82 Se, allowed by the Standard Model, has a life time τ 1/2 = (9.39 ± 0.17(stat) ± 0.58(syst))×10 19 year [32] longer enough to reduce to a negligible level the background induced by the pile-up of two 2νββ events in the region of interest. The array consists of 24 Zn 82 Se crystals for a total mass of 9.65 kg, corresponding to 5.13 kg of 82 Se and two natural ZnSe crystals (40 g of 82 Se mass) not used in the analysis. The number of 82 Se nuclei under investigation is (3.41 ± 0.03) × 10 25 excluding two crystals featuring poor performances. Each Zn 82 Se is held in a copper frame by means of small PTFE supports and surrounded by a 3 M Vikuiti plastic reflector to enhance the light collection. The light detector (LD) is a 170-µm-thick Ge disk [33] working as a bolometer. One side of the LD is coated with a SiO 60-nm-thick layer to enhance light absorption [34].
Both the LD and Zn 82 are equipped with an NTD -Ge thermistor sensor [35], acting as temperaturevoltage transducer, and a Si Joule heater [36], which periodically injects a fixed amount of energy to equalise the bolometer gain [37,38].
The signal, amplified and filtered by a six-pole anti-aliasing active Bessel [39][40][41][42][43][44], is recorded by an 18 bit ADC board operating at 1(2) kSPS for the Zn 82 Se (LD). The detector is anchored to the mixing chamber of an Oxford 1000 3 He/ 4 He dilution refrigerator [45] operating at a temperature of about 10 mK and located in Hall A of the Laboratori Nazionali del Gran Sasso (average depth ∼3650 m water equivalent [46]).
The CUPID-0 detector cool down began in January 2017 and, after a period of commissioning it reached stable data taking beginning in May 2017. Here we report the analysis obtained with an a Zn 82 Se exposure of 5.46 kg year. The results of the first 3.44 kg year data have been published in Ref. [47].

Data Analysis and Results
We acquire the complete data stream for both the Zn 82 Se and the light detector. For the ZnSe, we implement a derivative software trigger while pulses produced by the Joule heater are flagged by the data acquisition system. The waveform is analysed 4 s after the trigger and 1 s before (baseline).
We use the optimum filter algorithm [48,49] to infer the pulse amplitude and the shape parameters. The amplitude is corrected for any shift in thermal gain using the reference pulse injected by the heater every 400 s [37] and the baseline to estimate the detector temperature. We find the amplitude-energy conversion using the most intense γ lines produced by a 232 Th source [47,50].
We discard events on the Zn 82 Se inconsistent with the filter signal template and events on different bolometers if they occur within 20 ms since they are most likely induced by multiple Compton γ's.
The LD signal amplitude and shape is estimated applying the optimum filter at a fixed time delay compared to the Zn 82 Se heat signal as detailed in Ref. [51]. We build a light shape parameter [27] and we optimize the selection in order to have a unitary efficiency while rejecting the α background and shown in Figure 1. Finally we suppress the background induced by the internal 208 Tlβ/β + γ decay to 212 Pb (τ 1/2 = 3.01 min) tagging the 212 Bi ( 208 Tl mother ) which α decays with a Q α = 6207 keV. If the contamination is close to the surface and the α escapes the crystal, only part of the energy of the parent decay is collected. We therefore require the α particle to be in the energy range 2.0-6.5 MeV.
The resulting background index in the region of interest 2800-3200 keV, after the whole selection, results to be BI = (3. The total efficiency on the signal 0νββ candidate is (75 ± 2)%. It comprises the selection efficiency, evaluated on the most prominent peak in the physics spectrum [52], the 65 Zn and the 0νββ containment efficiency estimated via GEANT4 simulation. No signal events were found and we set a 90% credibile interval Bayesian lower limit on the 82 Se half life T 0ν 1/2 > 4.0 × 10 24 year. Details of the analysis and the procedure used to compute the upper limit can be found in Ref. [47,50].

Conclusions
CUPID-0 demonstrates that a large array of enriched scintillating bolometers can be successfully operated. The simultaneous readout of the heat and light signals allows us to reject the α induced background and reach the lowest background level ever achieved with bolometric experiments: (3.2 +1.3 −1.1 ) × 10 −3 counts/(keV kg year). This represents a key milestone for the next generation of tonne-scale experiments. In a total exposure of 5.46 kg year Zn 82 Se we set the most stringent limit on the neutrinoless double beta decay 82 Se half-life T 0ν 1/2 > 4.0 × 10 24 year at 90% C.I. The data taking is on going and new results will be released in Spring 2019.