Final Result of CUPID-0 Phase-I in the Search for the Se 82 Neutrinoless Double- β Decay

CUPID-0 is the first pilot experiment of CUPID, a next-generation project for the measurement of neutrinoless double beta decay (0νDBD) 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 Se82 exposure of 5.29 kg×yr. In this Letter we present the phase-I results in the search for 0νDBD. 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)×10-3 counts/(keV kg yr). Monitoring 3.88×1025 Se82 nuclei×yr we reach a 90% credible interval median sensitivity of T1/20ν>5.0×1024 yr and set the most stringent limit on the half-life of Se82 0νDBD: T1/20ν>3.5×1024 yr (90% credible interval), corresponding to mββ<(311-638) meV depending on the nuclear matrix element calculations.