Search for neutrinoless double beta decay of 64 Zn and 70 Zn with CUPID-0

CUPID-0 is the ﬁrst pilot experiment of CUPID, a next-generation project searching for neutrinoless double beta decay. In its ﬁrst scientiﬁc run, CUPID-0 operated 26 ZnSe cryogenic calorimeters coupled to light detectors in the underground Laboratori Nazionali del Gran Sasso. In this work, we analyzed a ZnSe exposure of 11.34kgyear to search for the neutrinoless double beta decay of 70 Zn and for the neutrinoless positron-emitting electron capture of 64 Zn. We found no evidence for these decays and set 90% credible interval limits of T 0


Introduction
Double beta decay is among the rarest processes in nature.This transition, where a nucleus changes its atomic number by two units [2], is an ideal benchmark to study atomic physics, nuclear physics as well as physics beyond the Standard Model.Despite the long half-life (10 18 to 10 24 yr), it has been so far observed in 12 nuclei [3].
Several extensions of the Standard Model predict that double beta decay could occur also without neutrino emission, violating the conservation of the total lepton number [4].Such hypothetical transition would result in the creation of two electrons, with important implications in baryogenesis theories [5] and in particle physics, as it would naturally introduce new mass mechanisms.Finally, neutrino-less double beta decay could occur only if neutrinos and anti-neutrinos coincide, in contrast to all the other known fermions [6].Thus, the observation of this transition would allow to determine the nature of this elusive particle.
The detection of neutrino-less double beta decay has been challenging the physicists community for decades.Today, lower limits of its half-life span from 10 24 to 10 26 yr [7,8,9,10,12], and next-generation experiments are pursuing new technologies to reach a sensitivity larger than 10 27 yr.To this purpose, future detectors will have to deploy more than 10 27 emitters (corresponding to a source mass of hundreds of kg) in backgroundfree environments [13].An energy resolution better than ∼ 1% would also be beneficial to keep the background in the region of interest as low as possible.
Among the technologies proposed for double beta decay searches, cryogenic calorimeters stand out for their energy resolution and efficiency [14,15,16].These devices can be sketched as crystals of hundreds of grams cooled at 10 mK and coupled to temperature sensors.Cooling the crystal at cryogenic temperature reduces its thermal capacitance C, so that even small energy deposits ∆E give rise to large temperature variations ∆T = ∆E/C.Such variations can be converted into voltage signals using dedicated temperature sensors.Those chosen by CUPID-0, namely Neutron Transmutation Doped (NTD) Ge thermistors [17], show typical voltage drops of hundreds of µV for a MeV energy deposit in the crystal.Apart from an energy resolution better than 1%, cryogenic calorimeters offer versatility in the choice of the double beta decay emitter, as the crystal can be grown from most of the isotopes of interest.
The most sensitive experiment based on the technique of cryogenic calorimeters is CUORE [18], that is operating a tonne-scale detector (consisting of 988 TeO 2 crystals) with excellent energy resolution and low background [10,11].While CUORE continues its physics programme, the CUPID collaboration (CUORE Upgrade with Particle IDentification [19,20]) has started to design a next-generation experiment to bring the sensitivity of cryogenic detectors above 10 27 yr.The dominant source of background in CUORE are α particles [21].To overcome this problem, CUPID will couple each cryogenic calorimeter to a light detector and exploit the different light yield to disentangle the α background from electrons [22,23].
CUPID-0 completed its first scientific run (June 2017 -December 2018) and was upgraded for a second scientific run, that started in June 2019.In this paper we present a search for the neutrino-less double beta decay of 70 Zn and for the neutrino-less positron-emitting electron capture of 64 Zn.

The CUPID-0 detector
The CUPID-0 detector is an array of 26 ZnSe cylindrical crystals.Each crystal is surrounded by a plastic reflective foil (3M Vikuiti) and coupled to two light detectors, placed on its top and bottom surfaces.Most of the "standard" light detectors do not work properly at 10 mK.For this reason, CUPID-0 uses small cryogenic calorimeters to convert the impinging photons into thermal signals [39].Both the ZnSe crystals and the light detectors are equipped with a NTD Ge thermistor and with a P-doped Si Joule heater.The heater injects a periodic reference pulse to enable the off-line correction for temperature variations during the data taking [40,41].The detectors are disposed in five towers using a mechanical structure made of high-purity copper and PTFE elements and cooled in an Oxford 3 He/ 4 He dilution refrigerator located in Hall-A of LNGS.The reader can find a detailed description of the CUPID-0 design, construction, commissioning and operation in Ref. [42].
The main goal of the CUPID-0 first scientific run was demonstrating the background suppression capability and understanding the residual background contributions.CUPID-0 successfully reached these objectives, achieving the lowest background for cryogenic experiments (3.5 +1.0 −0.9 ×10 −3 counts/keV/kg/y in the region of interest for 0νDBD of 82 Se at ∼3 MeV) and determining its main sources [43]).
Besides investigating the background suppression attainable with particle identification, CUPID-0 is the first demonstrator based on isotopically enriched crystals.Indeed, 24 of the 26 ZnSe crystals were grown starting from selenium powder 96.3% enriched in 82 Se [44,45].The collaboration decided to enrich in 82 Se as this is a promising emitter for double beta decay searches: it features a Q-value (2997.9±0.3 keV [46]) well above the end-point of the natural β/γ radioactivity and a relatively long half-life for the 2νDBD decay mode: T 2ν 1/2 ( 82 Se) = (8.60±0.03(stat) +0.19 −0.13 (syst))×10 19 yr [47]).The analysis of the data collected in the first scientific run allowed to set the most stringent limits on the half-life for the neutrino-less double beta decay of 82 Se to the ground state of 82 Kr (T 0νββ 1/2 ( 82 Se)>3.5×10 24yr 90% credible interval [48]) and to its 0 + 1 , 2 + 1 and 2 + 2 excited states [49].Moreover, the ZnSe crystals of the CUPID-0 detector contain other two potential emitters for double beta decay: 64 Zn and 70 Zn.In this work we focussed on this isotopes.

Data Production
The data acquired by CUPID-0 in its first scientific run are divided in ten blocks called "DataSet".The first of them was used for the detector commissioning and was not used in the analysis of the 82 Se double beta decay, as the α rejection tools had not yet been optimized.Given that the Q-values of the Zn isotopes lie in a region where the α background is negligible, we decided to include also the commissioning DataSet in the present analysis.Each DataSet begins and ends with four days of calibration runs, performed by exposing the detector to the γ rays emitted by a 232 Th source.We restricted our study to 22 enriched crystals plus a natural one1 , for a total ZnSe active mass of 9.18 kg.The total collected exposure is 11.34 kg×yr.
The signals produced by the ZnSe crystals and light detectors were amplified and filtered with a 120 dB/decade, six-pole anti-aliasing active Bessel filter [50,51,52,53,54,55,56].We used a custom DAQ software package [57] to save on disk the data acquired through a 18 bit analog-to-digital board with sampling frequency of 1 kHz for ZnSe and 2 kHz for the light detectors (which feature faster signals because of their smaller mass).We run a derivative trigger with channel-dependent parameters on each detector to identify pulses and save a 5 (1) seconds window for pulses detected by ZnSe crystals (light detectors).We applied a matched filter algorithm [58,59] to these pulses in order to suppress the most noisy frequencies, improving the evaluation of the signal amplitude.Then, we corrected the amplitudes by temperature drifts exploiting the reference pulses periodically injected by the Si resistors.The corrected-amplitudes were converted into energy using the calibration functions evaluated by attributing the nominal energy to the most intense peaks produced by the 232 Th sources.Finally, we applied an algorithm that allows to improve the energy resolution of the ZnSe crystals by about 10% by removing the correlation between pulses in the ZnSe and in the corresponding light detectors [61].
In the last step of the data production, we searched for time-coincidences among events simultaneously trig-gered in more than one ZnSe crystal.This information is crucial to suppress the background for the searched signatures.To optimize the time-window in which two or more events are defined as coincident, we exposed the detector to an intense γ source producing a sample of "real" coincident events.This study allowed to set the optimal time-window to ±20 ms.
More details about data production techniques and algorithms can be found in Ref. [60].Due to its poor natural isotopic abundance of (0.68±0.02)%2 , the exposure collected for 70 Zn amounts to (0.034±0.001) kg×yr.
The probability for the two electrons emitted in ββ decays to be fully contained in the ZnSe crystal where they are produced was evaluated through a GEANT-4 based simulation, resulting (95.67±0.46)%.We searched for this process in the spectrum of events triggered in a single ZnSe crystal ("single events"), in order to suppress the background.
We selected particle-like events by applying basic cuts to the shape of the pulses recorded by ZnSe crystals.In Figure 1 we show the energy spectrum of the single events passing these selection criteria.  6Zn in Signature C (Section 5).We highlight that Signature C is partly overlapped to the peak of 65 Zn.
The shape cuts, that allow to reject spikes due to the electronics or pile-up events, were optimised on a physical peak very close to the region of interest [60].For this analysis we relied on the 1115 keV peak of 65 Zn, an isotope produced via cosmogenic activation of Zn, with a relatively long half life of 244 days.Half of the events belonging to the 65 Zn peak were used to choose the values of the cuts optimising the signal-to-background ratio, while the remaining events were used to compute the efficiency of data selection.The trigger efficiency and the efficiency of energy reconstruction (both ∼100%) were evaluated using the reference pulses injected with the Si heater, following the procedure outlined in Ref. [60].Combining these values with the data selection efficiency computed on the 65 Zn peak, we obtained a total efficiency of (95.1±0.8)%.The computed efficiency was confirmed also at the energy of the 40 K line at ∼1. 46 MeV and of the 208 Tl line at ∼2.6 MeV.
We highlight that, in contrast to the analysis of 82 Se 0νββ, we did not exploit the α rejection capability offered by scintillating bolometers, neither the aggressive time-veto described in Ref. [60].These analysis tools would not have been helpful, as the Q-value of 70 Zn lies in a region in which the background is largely dominated by electrons produced in the 2νββ decay of 82 Se.
To compute the energy resolution at the Q-value of 70 Zn, we followed the approach described in Ref. [60], in which we first derived the response function to monochromatic energy deposits, and then used this model to fit the most prominent peaks in the calibration and background spectra.In cryogenic calorimeters a gaussian function is usually not able to fully describe the response to a monochromatic energy deposit [63,64].In CUPID-0 in particular, the simplest model giving a satisfactory description of a peak consisted in the combination of two gaussian functions.Using this model, we studied the width of the peaks as a function of the energy for each DataSet.The dependency of the energy resolution on the energy was described using a linear function.We obtained consistent values across the ten DataSets, excluding possible time-variations of the resolution during the CUPID-0 data-taking.The energy resolution extrapolated at the Q-value of the decay, averaged on the ten DataSets, resulted (4.45 ± 0.02) keV RMS.
Finally, we searched for the 70 Zn 0νββ decay signal by performing a simultaneous unbinned extended maximum likelihood (UEML) fit in a 100 keV large analysis window centered around the Q-value.The signal was modelled using the bi-Gaussian line shape with a mean value fixed at the position of the 70 Zn Q-value.The energy resolution was fixed to the value obtained at the Q-value, and the signal decay rate Γ 0νββ was treated as a free parameter independent from the DataSet.We summed to this function an exponentially decreasing, DataSet-independent background, whose index was again treated as free parameter of the fit.
In this study, we considered also effects due to a possible residual mis-calibration evaluated by fitting the position of the 65 Zn with the same bi-gaussian model.The mean position of the 65 Zn peak was shifted by (−1.08 ± 0.15) keV with respect to its nominal value, in full agreement with the study performed in a much wider energy range exploiting the peaks produced during a 56 Co calibration [60].This position shift was treated as a systematic source of uncertainty, independent from the DataSet.On the contrary, the energy resolution, efficiency and exposure were parameters specifically fixed for each DataSet.We weighted the likelihood with a Gaussian probability density function (p.d.f.) for each influence parameter, by fixing the mean and width of the p.d.f.respectively to the best-estimated values and uncertainties of each parameter.
We integrated the likelihood using a uniform nonnegative prior for Γ 0νββ and marginalizing over the background index nuisance parameter (Figure 2).We found no evidence for the searched process in an exposure of 2.95×10 23 emitters×yr and set a 90% credible interval Bayesian lower limit on the half-life of T 0νββ 1/2 ( 70 Zn)>1.6×10 21yr, surpassing by two orders of magnitude the previous limits [1]. 5 Analysis of the 64 Zn 0νβ + EC decay 64 Zn features a Q-value of (1094.9±0.8)keV [62] and a natural isotopic abundance of (47.5±0.1)% 3 .This isotope can decay via electron capture -β + : 64 Zn + e → 64 Ni + E de−excitation + β + where e is the captured electron, and E de−excitation the X-rays or Auger electrons emitted after the capture.Computing the containment efficiency for these de-excitation products would require a full simulation of the atomic recombination following the 0νβ + EC decay [65].A simpler solution is to assume every decay is followed by the emission of just one X-ray of exactly 8 keV and to apply a volume cut corresponding to the most external layer of 27 µm thickness of each crystal.This yield a 0.2% systematic effect on the half-life of 64 Zn.
The positron emitted during the decay carries away an energy equal to (Q-value -2m e ∼73 keV).It then annihilates into two 511 keV γ's, which can escape from the crystal giving rise to a rather complex signature.While the 73 keV release will be always deposited in the crystal where the decay occurs, the two photons can be fully (or partly) contained in the same crystal, or they can deposit their full (partial) energy in other crystals, or totally escape detection.The scheme of the possible signatures involving one or two ZnSe crystals is summarized in Table 1.Higher multiplicity events were not included in the analysis due to their low efficiency.
Table 1 Possible signatures of the 64 Zn electron captureβ + decay.In the column "Signature", β + is the positron energy, while γ 1 and γ 2 are the two 511 keV photons emitted by the positron annihilation.E I is the energy deposit in the scenario in which a single crystal is involved, while E I +E II indicates that two crystals were hit by the decay products of 64 Zn.

Signature
E Since the analysis threshold is set at 200 keV, we excluded from the analysis Signature A, that features a single energy deposit of 72.9 keV.We also discarded signature B, which would result in a peak at 583.9 keV.At this energy, indeed, we expect a peaking background 3 from inductively coupled plasma mass spectroscopy due to the 583.2 keV γ of 208 Tl, a contaminant of the CUPID-0 setup.As a consequence, we restricted our analysis to the signatures C, D and E. Fig. 3 Orange: spectrum of the sum of the energies simultaneously released in two crystals.Blue: the same spectrum requiring that one of the two energies was equal to 511 keV ±2σ.The vertical bars indicate the total energy of the Signatures D (dotted) and E (dashed).We highlight that Signature D is partly overlapped to the peak of 65 Zn.
Signature C would result in a monochromatic peak in the spectrum of a single events (Figure 1).For this case, we followed the same procedure outlined in section 4 and derived the parameters of the fit at the energy of interest (Table 2).
In Signature D, the total absorbed energy is the same as Signature C, but in this case two crystals are involved in the detection.We thus produced a spectrum by summing the energies released in two crystals (E I +E II ), shown in Figure 3 -orange.In this spectrum the reader can still observe the γ peaks produced by 40 K, 65 Zn (which gives rise to a peaking background in the signal region) and 208 Tl, while the continuum due to the 2νββ decay of 82 Se is dramatically suppressed.
To further reduce the background in the region of interest for signature D, we required one of the two energies composing the sum spectrum to be comprised in a ±2σ interval centred around the 511 keV peak.This cut reduces the containment efficiency from (3.07±0.06)% to (0.88±0.03)% but, at the same time, suppresses the background by a factor 100, thus enhancing the sensitivity.The spectrum obtained imposing this requirement is reported in Figure 3 -blue.
Finally, signature E should result in a peak at 72.9+511 keV in the E I +E II spectrum (Figure 3 -orange).Due to the energy threshold at 200 keV, we could not trigger separately the 72.9 keV and the 511 keV energy deposits.For this reason, we did not exploit the same cut on the energy of the γ ray adopted in the analysis of the previous signature.
The E I +E II spectrum is expected to have a worse energy resolution compared to the spectrum in which the same amount of energy is released in a single crystal.For this reason, we repeated the study outlined in section 4 to determine the energy resolution at the energies of interest.We derived again the model describing a monochromatic energy release in the E I +E II spectrum and used it to fit the most intense peaks of the spectrum.We report in Table 2 the obtained energy resolution at the energies of interest for signatures C, D and E. In the same Table , we also report the values of the containment efficiency, derived through a Monte Carlo simulation accounting for the same smearing due to the resolution and for the same analysis threshold of the experimental data.Other contributions to the efficiency do not depend on the energy and include the trigger efficiency and the energy reconstruction efficiency.The combination of these two numbers results (98.971 +0.033 −0.034 %).In addition, for signature C we used the same basic cuts on the pulse shape described in section 4, obtaining an event selection efficiency of (95.1±0.8)%.Concerning signatures D and E on the contrary, we did not further select the events because of the lower background.
We performed a simultaneous fit to the three described spectra.The signal, as well as the peaking backgrounds such as the lines produced by the decay of 65 Zn (Figure 1 and 3), were modelled using a bi-gaussian function G with mean value fixed to the nominal peak position (µ) and width fixed to the one derived by the resolution studies (σ, see values reported in Table 2).We included in the fit functions also an exponential background with a number of background events (N bkg ) specific for each signature.The number of signal events is determined by a unique decay width (Γ64 Zn ): N i sig ∝ Γ64 Zn × i , where i is the total efficiency of the searched signature.The fitting functions can thus be Fig. 4 Result of the fit of signature C. The signal is expected at E=1094.9 keV.We modelled the background using an exponentially decreasing background and a peaking background due to 65 Zn.
written as follows: Also in this case we performed a simultaneous UEML fit.As described in section 4, we included the effects of possible systematic uncertainties by weighting the likelihood with a Gaussian probability density function for each influence parameter, taking into account a possible residual mis-calibration, as well as the uncertainties on energy resolution, efficiency and exposure.The results of the fits performed on signatures C, D and E are shown in Figures 4,5 and 6 respectively.
We chose a uniform prior for Γ64 Zn and integrated the likelihood marginalizing over the background index nuisance parameter (Figure 7).
We observed no evidence for signal and set a 90% credible interval Bayesian lower limit on the half-life of the 64 Zn electron capture -β + of T 0νECβ+ 1/2 ( 64 Zn)>1.2×10 22yr.This value largely surpasses the previous result of 8.5×10 20 years reported in Ref. [1], proving once more the potential of the bolometric technique.

Conclusions
In this work, we searched for the neutrino-less double beta decay of 70 Zn and for the electron captureβ + decay of 64 Zn, using the full exposure of the first CUPID-0 scientific run of 11.34 kg×yr.We found no evidence of the searched processes and set lower limits on their half-life of T Fig. 5 Result of the fit of signature D. The number of events is very small because we required the time-coincidence with a 511 keV γ-ray (see main text).The signal is expected at E=1094.9 keV.We modelled the background using an exponentially decreasing background and a peaking background due to 65 Zn.

57 Fig. 1
Fig.1Energy spectrum of the events detected by ZnSe crystals after data selection performed with basic cuts on the pulse shape and requiring that a single crystal in the array triggered the event.Red bar: Q-value of 70 Zn (997.1±2.1 keV).Dashed purple bar: energy of the γ ray produced by64 Zn in Signature C (Section 5).We highlight that Signature C is partly overlapped to the peak of65 Zn.

Fig. 2
Fig. 2 Posterior p.d.f. of the decay rate of 70 Zn.The 90% integral of the posterior is highlighted in yellow, and the red arrow indicates the value of the decay rate corresponding to the 90% credible interval.Inset: fit of the experimental data in a ±50 keV region centred around the Q-value.

Fig. 6
Fig.6Result of the fit of signature E (signal at E=583.9 keV over an exponentially decreasing background).

2 ΤFig. 7
Fig. 7 Posterior p.d.f. the decay rate.Yellow: integral of the posterior up to 90%.The red arrow indicates the value of the decay rate corresponding to the 90% credible interval.

Table 2
FWHM energy resolution and containment efficiency for the three signatures of64Zn decay.