Search for Neutrino-less 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 neutrino-less 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 11.34 kg$\times$yr to search for the neutrino-less double beta decay of ${}^{70}$Zn and for the neutrino-less positron-emitting electron capture of ${}^{64}$Zn. We found no evidence for these decays and set 90$\mathrm{\%}$ credible interval limits of ${\rm T}{1/2}^{0\nu\beta\beta}(^{70}{\rm Zn}) > 1.6 \times 10^{21}$yrand${\rm T}{1/2}^{0\nu EC \beta+}(^{64}{\rm Zn}) > 1.2 \times 10^{22}$ yr, surpassing by almost two orders of magnitude the previous experimental results