The CUORE experiment is a large bolometric array searching for the lepton number violating neutrino-less double beta decay ($0\nu\beta\beta$) in the isotope $\mathrm{ ^{ 130}Te}$. In this work we present the latest results on two searches for the double beta decay (DBD) of $\mathrm{ ^{ 130}Te}$ to the first $0^{ +}_2$ excited state of $\mathrm{ ^{ 130}Xe}$: the $0\nu\beta\beta$ decay and the Standard Model-allowed two-neutrinos double beta decay ($2\nu\beta\beta$). Both searches are based on a 372.5 kg$\times$yr TeO$_2$ exposure. The de-excitation gamma rays emitted by the excited Xe nucleus in the final state yield a unique signature, which can be searched for with low background by studying coincident events in two or more bolometers. The closely packed arrangement of the CUORE crystals constitutes a significant advantage in this regard. The median limit setting sensitivities at 90\% Credible Interval (C.I.) of the given searches were estimated as $\mathrm{ S^{ 0\nu}_{ 1/2} = 5.6 \times 10^{ 24} \: \mathrm{ yr}}$ for the ${ 0\nu\beta\beta}$ decay and $\mathrm{ S^{ 2\nu}_{ 1/2} = 2.1 \times 10^{ 24} \: \mathrm{ yr}}$ for the ${ 2\nu\beta\beta}$ decay. No significant evidence for either of the decay modes was observed and a Bayesian lower bound at $90\%$ C.I. on the decay half lives is obtained as: $\mathrm{ (T_{ 1/2})^{ 0\nu}_{ 0^+_2} > 5.9 \times 10^{ 24} \: \mathrm{ yr}}$ for the $0\nu\beta\beta$ mode and $\mathrm{ (T_{ 1/2})^{ 2\nu}_{ 0^+_2} > 1.3 \times 10^{ 24} \: \mathrm{ yr}}$ for the $2\nu\beta\beta$ mode. These represent the most stringent limits on the DBD of $^{ 130}$Te to excited states and improve by a factor $\sim5$ the previous results on this process.
Categories: nucl-ex