Final Result of CUPID-0 Phase-I in the Search for the ${}^{82}\mathrm{Se}$ Neutrinoless Double-$\beta$ Decay

CUPID-0 is the first pilot experiment of CUPID, a next-generation project for the measurement of neutrinoless double beta decay ($0\nu \mathrm{DBD}$) 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 ${}^{82}\mathrm{Se}$ exposure of $5.29\mathrm{kg}\times \mathrm{yr}$. In this Letter we present the phase-I results in the search for $0\nu \mathrm{DBD}$. We demonstrate that the technology implemented by CUPID-0 allows us to reach the lowest background for calorimetric experiments: $({3.5}_{-0.9}^{+1.0})\times {10}^{-3}\mathrm{counts}/(\mathrm{keV}\mathrm{kg}\mathrm{yr})$. Monitoring $3.88\times {10}^{25}$ ${}^{82}\mathrm{Se}$ $\mathrm{nuclei}\times \mathrm{yr}$ we reach a 90% credible interval median sensitivity of $T_{1/2}^{0\nu }>5.0\times {10}^{24}\mathrm{yr}$ and set the most stringent limit on the half-life of ${}^{82}\mathrm{Se}$ $0\nu \mathrm{DBD}$: $T_{1/2}^{0\nu }>3.5\times {10}^{24}\mathrm{yr}$ (90% credible interval), corresponding to ${\mathrm{m}}_{\beta \beta }<(311–638)\mathrm{meV}$ depending on the nuclear matrix element calculations.

Figure 1

Left: energy resolution as a function of the energy for the most intense $\gamma$ peaks emitted by a ${}^{56}\mathrm{Co}$ source (sum spectrum of all the ZnSe channels). Right: Residuals of the calibration made with the coefficients derived from the ${}^{232}\mathrm{Th}$ calibrations. Green cross: Values corresponding to the ${}^{82}\mathrm{Se}$ $Q$ value, where we expect an energy resolution of $20.05\pm 0.34\mathrm{keV}$ and a residual of the calibration of $-1.03\pm 0.18\mathrm{keV}$.

Figure 2

Background measured by CUPID-0 (exposure of $9.95\mathrm{kg}\times \mathrm{yr}$ of $\mathrm{Zn}{}^{82}\mathrm{Se}$ crystals) after the three selection steps described in the text. The events below 2.8 MeV come from the tail of $2\nu \beta \beta$ decay. Inset: energy region of interest for the $0\nu \mathrm{DBD}$ search: from 2.8 to 3.2 MeV, a symmetric energy region around the $Q$ value of ${}^{82}\mathrm{Se}$ ($2997.9\pm 0.3\mathrm{keV}$).

Figure 3

Posterior probability density function (pdf) for ${\mathrm{\Gamma }}^{0\nu }$ as results from the simultaneous UEML fit in the ROI after the marginalization over the background index nuisance parameter. The posterior pdf accounts for all the statistics and systematic uncertainties arising from the energy scale, detector resolutions, efficiencies, and exposures measured for each data set. The yellow histogram represents the 90% area of the posterior pdf.