Search for Double-Beta Decay of $\mathrm{^{130}Te}$ to the $0^+$ States of $\mathrm{^{130}Xe}$ with CUORE

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 $$\sim 5$$ the previous results on this process.