Final result of CUPID-0 phase-I in the search for the $^{82}$Se Neutrinoless Double Beta Decay

TL;DR

The CUPID-0 experiment used scintillating bolometers to search for neutrinoless double beta decay of $^{82}$Se, achieving the lowest background and setting new limits on the decay half-life, advancing the field of neutrino physics.

Contribution

This work demonstrates the effectiveness of scintillating bolometers in reducing background for neutrinoless double beta decay searches and provides the most stringent limits for $^{82}$Se to date.

Findings

Achieved the lowest background rate for calorimetric experiments.

Set a new lower limit on the half-life of $^{82}$Se neutrinoless double beta decay.

Estimated the effective Majorana neutrino mass range based on the results.

Abstract

CUPID-0 is the first pilot experiment of CUPID, a next-generation project for the measurement of neutrinoless double beta decay (0$\nu$DBD) with scintillating bolometers. The detector, consisting of 24 enriched and 2 natural ZnSe crystals, has been taking data at Laboratori Nazionali del Gran Sasso from June 2017 to December 2018, collecting a $^{82}$Se exposure of 5.29 kg$\times$yr. In this paper we present the phase-I results in the search for 0$\nu$DBD. We demonstrate that the technology implemented by CUPID-0 allows us to reach the lowest background for calorimetric experiments: $(3.5^{+1.0}_{-0.9})\times10^{-3}$ counts/(keV kg yr). Monitoring 3.88$\times$10$^{25}$ $^{82}$Se nuclei$\times$yr we reach a 90% credible interval median sensitivity of $\rm{T}^{0\nu}_{1/2}>5.0\times10^{24} \rm{yr}$ and set the most stringent limit on the half-life of $^{82}$Se 0$\nu$DBD : $\rm{T}^{0\nu}_{1/2}>3.5\times10^{24} \rm{yr}$ (90% credible interval), corresponding to m$_{\beta\beta} <$ (311-638) meV depending on the nuclear matrix element calculations.

Figures

Equations

$${\mathrm{T}}_{1/2}^{0\nu }>3.5\times 10^{24}\mathrm{yr}.$$

$$({\mathrm{T}}_{1/2}^{0\nu }{)}^{-1}={\mathrm{G}}_{0\nu }|{\mathcal{M}}_{0\nu }{|}^2{\left({\mathrm{g}}_{\mathrm{a}}\right)}^4{\left(\frac{{\mathrm{m}}_{\beta \beta }}{{\mathrm{m}}_{\mathrm{e}}}\right)}^2$$

Full text

neutrinoless double beta decay, Zn82Se scintillating cryogenic calorimeters; lepton number violation

Nowadays, neutrinoless double beta decay (0$\nu$DBD) is considered one of the most sensitive probes for Physics Beyond the Standard Model. This hypothetical nuclear transition foresees the simultaneous decay of two neutrons into protons and electrons without the emission of neutrinos Furry . Its detection would prove the non-conservation of the total lepton number, setting an important milestone for leptogenesis and baryogenesis theories Dell'Oro:2016dbc . The observation of 0$\nu$DBD would give precious insights also in Particle Physics, as this transition can occur only if neutrinos coincide with their own antiparticles, according to the Majorana hypothesis. As a consequence, its detection would allow to establish the fundamental nature of these particles Schechter:1982 . Furthermore, if the mechanism at the basis of 0$\nu$DBD is the exchange of light Majorana neutrinos, the half-life of the transition (T${}^{0\nu}_{1/2}$) would scale as T${}^{0\nu}_{1/2}\propto$ m${}_{\beta\beta}^{-2}$, where the parameter mββ (effective Majorana neutrino mass) is a superimposition of the neutrino mass eigenvalues mi weighted by the elements of the neutrino mixing matrix (Uei): mββ=$|\sum_{i}$U${}^{2}_{ei}$m${}_{i}|$ Feruglio:2002af . Thus, a measurement of T${}^{0\nu}_{1/2}$ would also allow to constrain the absolute mass scale of neutrinos.

The increasing interest in the search for 0$\nu$DBD motivated a huge international effort in the development of several technologies Albert:2017owj ; KamLAND-Zen:2016pfg ; Aalseth:2017btx ; Alduino:2017ehq ; Agostini:2018tnm to study some of the candidate isotopes: elements with even atomic number and even neutron number, for which the single beta decay is strongly forbidden by energy conservation law. These experiments are now envisioning next-generation detectors to probe half-lives exceeding 1027 yr and, thus, the whole range of the inverted hierarchy region of neutrino masses, whose lower bound is at m${}_{\beta\beta}\sim$10 meV. The main handles to improve the sensitivity are the detector exposure, the background in the region of interest and the energy resolution Cremonesi:2013vla . To ensure a competitive discovery potential, next-generation detectors will need more than 1027 emitters (hundreds of kg of source), a background as close as possible to zero in 5-10 years of data-taking, and an energy resolution of $\sim 1$%, in order to disentangle the monochromatic peak produced by 0$\nu$DBD from environmental background and from the irreducible background due to the Standard Model allowed 2$\nu$DBD decay Alduino:2017qet .

Cryogenic calorimeters (historically also called bolometers Fiorini:1983yj ) are one of the leading technologies in the search for 0$\nu$DBD. These devices consist of dielectric and diamagnetic crystals cooled down at cryogenic temperatures (10 mK) and equipped with a sensor to convert thermal variations into electrical signals. The sensors chosen for CUPID-0 are Neutron Transmutation Doped (NTD) Ge thermistors thermistor . The most impressive implementation of this technology is CUORE Artusa:2014lgv , an array of 988 TeO2 cryogenic calorimeters, for a total active mass of 742 kg, that is taking data at Laboratori Nazionali del Gran Sasso (LNGS, Italy) to study the 130Te 0$\nu$DBD. With an average energy resolution of 7.7$\pm$0.5 keV in the region of interest, in 2018 CUORE set a 90% credible interval (C. I.) lower limit on T${}^{0\nu}_{1/2}$ of 1.5$\times$1025 yr Alduino:2017ehq . The success of CUORE motivated the proposal of CUPID (CUORE Upgrade with Particle IDentification Wang:2015raa ; Wang:2015taa ; Artusa:2014wnl ; Alduino:2016vtd ), which aims at exploring the inverted hierarchy region of neutrino masses by reaching a 0$\nu$DBD sensitivity larger than 1027 yr. CUPID will increase the active mass through isotopic enrichment and, at the same time, decrease the background by two orders of magnitude with respect to CUORE. Since the CUORE background in the region of 0$\nu$DBD is dominated by $\alpha$ decays occurring on the detector surfaces Alduino:2017qet , the first milestone of CUPID is the development of an active technique which enables the identification of such interactions. In the last years, scintillating bolometers proved to be a viable path for the $\alpha$ background suppression, as the simultaneous measurement of the calorimetric signal and the scintillation light allows to keep a high energy resolution while identifying the nature of the interaction Bobin:1997qm ; Pirro:2005ar . The promising R$\&$D activity performed by the LUCIFER Beeman:2013sba ; Beeman:2013vda ; Beeman:2012ci ; Beeman:2012jd ; Beeman:2011bg ; Cardani:2013mja ; Cardani:2013dia ; Artusa:2016maw and LUMINEU Barabash:2014una ; Armengaud:2017hit ; Buse:2018nzg ; Armengaud:2015hda ; Bekker:2014tfa experiments in the development of scintillating bolometers allowed to construct a first medium-scale demonstrator of this technology: CUPID-0.

The CUPID-0 collaboration focused on 82Se, which features one of the highest Q-values for 0$\nu$DBD decay (2997.9$\pm$0.3 keV Lincoln:2012fq ). This choice allows to work in an energy region barely affected by the $\beta/\gamma$ background induced by the natural radioactivity, that drops of more than an order of magnitude above 2.6 MeV. The main limitation of 82Se, i.e. its poor natural isotopic abundance, can be overcome through isotopic enrichment. The CUPID-0 collaboration exploits 96.3$\%$ enriched Se to synthesise ZnSe powder Beeman:2015xjv and grow 24 cylindrical Zn82Se crystals 95% enriched in 82Se Dafinei:2017xpc . These crystals (plus two natural ones) are surrounded by 3M Vikuiti plastic reflective foils and interleaved by bolometric light detectors (LD) similar to those described in Ref. Beeman:2013zva . Both the ZnSe crystals and the LD are equipped with a NTD Ge thermistor and with a P-doped Si Joule heater injecting a periodic reference pulse to correct for temperature variations Arnaboldi:2003yp ; Andreotti2012 . The detectors are arranged in five towers using a mechanical copper structure, and anchored to the coldest point of an Oxford 3He/4He dilution refrigerator located in the Hall-A of LNGS (previously used for the CUORE-0 experiment Alfonso:2015wka ). Details about the detector construction, commissioning and operation can be found in Ref. Azzolini:2018tum .

The CUPID-0 detector has been taking data from June 2017 to December 2018. Physics data are divided in nine blocks called “data sets”. At the beginning and at the end of each data set we perform an energy calibration exposing the detector to an external (removable) 232Th source which provide $\gamma$ lines up to 2615 keV. For the 0$\nu$DBD search, we discard from the analysis the data acquired by the two natural crystals and also by two enriched crystals that are not featuring a satisfactory bolometric performance. Thus, the final active mass used for the described analysis is 8.74 kg, corresponding to 4.65 kg of 82Se. With a live-time for physics runs of 74%, we collected a total 82Se exposure of 5.29 kg$\times$yr (3.88$\times$1025 82Se nuclei$\times$yr). The first four data sets, referring to 1.83 kg$\times$yr of 82Se, were used to extract a preliminary limit on the half-life of 82Se 0$\nu$DBD both to the ground and exited states of 82Kr Azzolini:2018dyb ; Azzolini:2018oph . Since then, we increased by almost a factor 3 the statistics and we improved the analysis algorithms to enhance the energy resolution and the background discrimination capability. In this paper we present the final result of CUPID-0 phase-I for the search of 0$\nu$DBD.

The signals produced by particle interactions are amplified, filtered with a 120 dB/decade, six-pole anti-aliasing active Bessel filter, and fed in a 18 bit analog-to-digital converter board with a sampling frequency of 1 ksps for ZnSe and 2 ksps for the (faster) LDs. The electronics is described in Refs. Arnaboldi:2018yp ; Carniti2016 ; arnaboldi20018 ; arnaboldi2015 ; arnaboldi2010 ; Arnaboldi:2004jj ; AProgFE . Data are saved on disk using a custom DAQ software package DiDomizio:2018ldc . The ZnSe signals are acquired using a derivative trigger with channel-dependent parameters. Since the pulses recorded by the LD have a lower signal to noise ratio (as the majority of the energy is released in the heat channel), we used a different trigger, forcing the acquisition of the LD waveforms every time the trigger of the corresponding ZnSe fires.

The data analysis follows a slightly different path for heat and light pulses. Heat pulses recorded by the ZnSe are processed using a software matched filter algorithm Gatti:1986cw ; Radeka:1966 , corrected by temperature instabilities using the reference pulse periodically injected by the Si resistor, and energy-calibrated. To this aim, we exploit the periodical calibration with 232Th sources: we identify the most intense peaks produced by the sources and use a zero-intercept parabolic function to convert the signal amplitude into energy. Finally, we compute time-coincidences among crystals using a coincidence window of 20 ms, in order to reject the background due to multi-site events simultaneously triggering different detectors.

Light pulses are acquired in time-coincidence with ZnSe and filtered using a slightly modified version of the matched filter algorithm Azzolini:2018yye . After improving the amplitude estimation by taking advantage from the known time jitter between heat and light channels Azzolini:2018yye , we inter-calibrate the light detectors using the 2.6 MeV line produced by the 232Th sources. Finally, we remove the correlation between light and heat signals by performing a rotation in the light energy vs. heat energy scatter plot to enhance the energy resolution Beretta:2019bmm .

To check the goodness of the energy reconstruction we made a calibration with a 56Co source (T${}_{1/2}\sim 77.3$ days, Q-value $\sim$ 4.6 MeV) emitting $\gamma$ rays with significant branching ratio up to 3.3 MeV. We calibrate the spectrum of each crystal using the coefficients derived from the 232Th calibrations, then apply these calibration coefficients to the runs performed with the 56Co source and obtain the sum spectrum of all the calibrated channels. To derive the FWHM energy resolution and the residuals of the calibration, we fit the most prominent $\gamma$ peaks of the spectrum. Bolometric detectors often show a non perfectly Gaussian response to monochromatic energy deposits Alduino:2016zrl ; Casali:2013zzr . For this reason, instead of using a single Gaussian function, we fit the 56Co peaks using the signal model of CUPID-0 that, as explained in Ref Azzolini:2018yye , consists in a double Gaussian function. The FWHM energy resolution and the residuals of the calibration are shown in Fig. 1.

The energy resolution is modelled as a function of the energy using a linear dependency. The value extracted at the Q-value of 82Se is 20.05$\pm$0.34 keV FWHM, about 10$\%$ better with respect to the one used for the analysis described in Ref. Azzolini:2018dyb thanks to the de-correlation of heat and light signals Beretta:2019bmm .

The residuals of the 56Co peaks show a small parabolic dependency on the energy, that could be removed by a further improvement of the calibration function. Nevertheless, the residual at the Q-value of 82Se is $-1.03\pm 0.18$ keV, which is negligible considering the $\sim$20 keV energy resolution. For this reason, instead of acting on the calibration function to further decrease the residual at the Q-value, we decided to treat this parameter as a systematic uncertainty.

We monitored possible drifts in the calibration parameters during all the physics runs with periodical 232Th calibrations, and we observed variations in the peaks positions lower than $\pm$0.1$\%$. The use of the 56Co calibration allowed us to narrow the systematic uncertainty on the 0$\nu$DBD position by a factor 3 compared to the previous analysis described in Ref. Azzolini:2018dyb . Nonetheless, this technique could not be used as routine calibration for CUPID-0 for the sake of physics data live time, since the time needed to collect sufficient $\gamma$ peaks near our region of interest was of the order of three weeks.

To select the events of interest for the 0$\nu$DBD search, we apply the following data selection criteria. First, we reject non-physics events (due for example to electronics noise) by applying basic cuts to the shape parameters of the heat pulses, such as the slope of the baseline before the time of interaction, and the rise-time of the pulse. We also require that a single crystal in the array triggered that event, as from GEANT4 simulations we expect the two electrons of 0$\nu$DBD  to be contained in a single ZnSe crystals with a probability of (81.0$\pm$0.2)$\%$

Then, we select electron-like events by exploiting the time-development of the light pulses which, being dominated by the crystal scintillation, allows to discriminate electrons from $\alpha$ particles. To this purpose we use a shape parameter defined in Ref. Azzolini:2018yye , which is very sensitive to the time development of the light pulse. To improve the discrimination capability we combine the shape parameters of the two light detectors: since they result to be uncorrelated, we simply average them. To select a pure $\beta/\gamma$ sample, we use electromagnetic showers induced by muons interacting in the material close to the detector, easily recognisable as they induce simultaneous triggers in more than one detector. In order to make this selection more robust, we only choose events triggered by more than four crystals. We set a cut on the shape parameter of light pulses in order to keep a signal efficiency of 98$\%$. The probability for an $\alpha$ particle to pass this selection is lower than 10*-7*, proving the potential of the light and heat read-out in suppressing the $\alpha$ background in view of the next-generation experiment CUPID. After the removal of $\alpha$ particles, the background in the region of interest decreases from 3.2$\times$10*-2* counts/(keV kg yr) to 1.3$\times$10*-2* counts/(keV kg yr). The residual background is dominated by 208Tl decays due to internal and surface contaminations of the crystals.

In CUPID-0, this background can be suppressed with a final data selection, made by applying a time-veto. Indeed, if the contamination is internal or very close to the crystal, it is possible to tag the mother of 208Tl (212Bi) thanks to its $\alpha$ decay, and then exploit the short half-life of 208Tl (3.05 min) to reject subsequent $\beta$ and $\gamma$ deposits. If the contamination is internal, the decay of 212Bi is expected to produce an $\alpha$ event with an energy corresponding to the Q-value of the transition; if the contamination is on the crystal surface, part of the energy can be lost, and a 212Bi decay results in an $\alpha$ event with lower energy. In CUPID-0 we can exploit the particle identification capability to tag all the $\alpha$ particles down to 2 MeV, enhancing the rejection of 212Bi - 208Tl events.

Then we open a time-veto of 7 208Tl half-lives for each tagged $\alpha$ event. When an $\alpha$ particle is detected, the probability for a 208Tl decay to occur after 7 half-lives is 0.8$\%$. Thus, a time-veto of 7 half-lives offers a tagging efficiency exceeding 99% with a reasonable dead-time of 6$\%$. We highlight that, despite the strong particle identification capability offered by CUPID-0, there is still a small probability that surface $\alpha$ particles escape detection. According to our background model, surface contaminations of the crystals in Th produce a residual background at the level of 3.4$\times$10*-4* counts/(keV kg yr) Azzolini:2019nmi .

The total efficiency on the signal selection thus includes:

• •

the trigger and energy reconstruction efficiency ($\sim 99.5$%), computed using the reference pulses injected by the Si resistor (as done, for example, in Ref. Alduino:2016zrl );

• •

the data selection efficiency of heat pulses, comprising the efficiency of the cuts on the pulse shape, and the dead-time introduced by the time-veto of 7 half-lives used to reject 212Bi - 208Tl events ($\sim 88$%). This number was evaluated using the $\sim$1 MeV $\gamma$-peak produced by 65Zn decay in the physics spectrum Azzolini:2018yye ;

• •

the $\beta/\gamma$ selection efficiency ($\sim 98\%$), computed on a sample of pure $\gamma$ events. To define this event class, we exploit electromagnetic showers induced by cosmic muons; such events are easily identifiable as they result in interactions in a large number of crystals (see details in Ref. Azzolini:2018yye ).

The total efficiency, averaging the nine data sets, summed up to (86$\pm$1)$\%$. This number is combined with the (81.0$\pm$0.2)$\%$ probability that the two electrons emitted in 0$\nu$DBD are contained in a single crystal. Thus, the final CUPID-0 signal efficiency results (70$\pm$1)%. The background spectrum between 2.7 MeV and 4.0 MeV after the three selection steps is shown in Fig. 2.

In the ROI for the 0$\nu$DBD search (from 2.8 to 3.2 MeV, see inset in Fig. 2) we observe 14 counts. Performing a simultaneous unbinned extended maximum likelihood (UEML) fit in the ROI, modelled with the only contribution of a flat background, we obtain $(3.5^{+1.0}_{-0.9})\times 10^{-3}$ counts/(keV kg yr), the lowest background achieved by 0$\nu$DBD experiments based on cryogenic calorimeters. We then repeat the simultaneous UEML fit in the ROI adding the signal hypothesis to the model. For each data set, the fit includes the bi-Gaussian line shape for the 0$\nu$DBD signal Azzolini:2018dyb , and the flat background component. The efficiency, the exposure and the energy resolution are data set dependent. On the contrary, the decay rate $\Gamma^{0\nu}$ ($\Gamma^{0\nu}=1/T^{0\nu}_{1/2}$ ) and the background index are treated as free parameters common to all the detectors and data sets.

We account for the systematics due to the uncertainty on the energy scale, the detector resolutions, the efficiencies, and the exposures. For each influence parameter, we weight the likelihood with a Gaussian probability density function with the mean and width fixed to the best estimated values and uncertainties, respectively. In contrast to the analysis described in Ref. Azzolini:2018dyb , we treat the energy resolution and the uncertainty on the energy scale separately, as the former is a data-set dependent parameter, while the latter refers to the entire statistics. We then integrate the likelihood via numerical integration using a uniform prior in the physical region of $\Gamma^{0\nu}$ (between 0 and 0.5 $\times 10^{-24}$ yr*-1*) and marginalize over the background index nuisance parameter. The resulting posterior probability density function (pdf) is shown in Fig. 3. The fit converges to a value of $\Gamma^{0\nu}$ of $4.7^{+7.9}_{-5.3}\times 10^{-26}$ yr*-1*. We found no evidence for 0$\nu$DBD and we set a 90% C. I. Bayesian upper limit on $\Gamma^{0\nu}<0.20\times 10^{-24}$ yr*-1*, corresponding to a lower limit on the 82Se half-life of

[TABLE]

We also take into account the hypothesis of an exponential background distribution instead of a flat one, obtaining the same results.

Exploiting a toy MC in which we simulate 1000 experiments with the same performances and exposure measured by CUPID-0, we evaluate the 90$\%$ C. I. median sensitivity to be $\rm{T}^{0\nu}_{1/2}>5.0\times 10^{24}~{}\rm{yr}$. We evaluate also the probability to reach a higher limit with respect to the one measured in this work, obtaining 80%. As far as the limit on the effective neutrino mass is concerned, we recall that in the models where the 0$\nu$DBD is mediated by the exchange of a light Majorana neutrino, the effective neutrino mass mββ is related to T${}^{0\nu}_{1/2}$ by:

[TABLE]

where G0ν, M0ν, ga and me are the phase space factor of the decay, the dimensionless nuclear matrix element (NME), the effective axial coupling constant and the electron mass respectively. Using G0ν from Refs. Kotila:2012zza , the NME from Refs. Engel:2016xgb ; Yao:2014uta ; Menendez:2008jp ; Simkovic:2013qiy ; Rodriguez:2010mn ; Meroni:2012qf and an axial coupling constant ga=1.269 we set an upper limit on m${}_{\beta\beta}<~{}$(311-638) meV.

Summarizing, CUPID-0 set the most stringent limit on the 0$\nu$DBD half-life of 82Se. Thanks to the capability to reject the background coming from $\alpha$ radioactive contaminations granted by the scintillating cryogenic calorimeter technique, we reach an unprecedented background level for bolometric experiments: $(3.5^{+1.0}_{-0.9})\times 10^{-3}$ counts/(keV kg yr).

According to our background reconstruction model Azzolini:2019nmi , the main contribution in the ROI is due to $\mu$ interactions: $(1.53\pm 0.13~{}\rm{stat}\pm 0.25~{}\rm{syst})\times 10^{-3}$ counts/(keV kg yr). The contaminations of the crystals dominate the residual background. In order to assess the individual contributions to the measured background, at the beginning of 2019 we upgraded the CUPID-0 detector by installing a muon veto and removing the reflecting foil that prevents the analysis of coincidences of surface events among crystals. In such a way, we plan to improve the capability of recognize the sources of the $\beta/\gamma$ background measured by CUPID-0. Measuring residual background contributions with such a high sensitivity will be of crucial importance in anticipation of the next-generation CUPID experiment.

This work was partially supported by the European Research Council (FP7/2007-2013), Contract No. 247115. We are particularly grateful to S. Grigioni and M. Veronelli for their help in the design and construction of the sensor-to-absorber gluing system, M. Iannone for the help in all the stages of the detector construction, A. Pelosi for the construction of the assembly line, M. Guetti for the assistance in the cryogenic operations, R. Gaigher for the calibration system mechanics, M. Lindozzi for the development of cryostat monitoring system, M. Perego for his invaluable help, the mechanical workshop of LNGS (E. Tatananni, A. Rotilio, A. Corsi, and B. Romualdi) for the continuous help in the overall setup design. We acknowledge the Dark Side Collaboration for the use of the low-radon clean room. This work makes use of the DIANA data analysis and APOLLO data acquisition software which has been developed by the CUORICINO, CUORE, LUCIFER, and CUPID-0 Collaborations.