The CUORE experiment is a closely packed array of 988 cryogenic calorimeters aimed at investigating lepton number violation via neutrino-less double beta decay (0νββ) in 130Te. We present the latest results on searches for the double beta decay (DBD) of 130Te to the first 0+ excited state of 130Xe in the 0νββ and Standard Model channels and discuss future perspectives. 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. With a 372.5 kg×yr TeO2 exposure the median limit setting sensitivities at 90\% Credible Interval (C.I.) were estimated as 5.6 × 10^24 yr for the 0νββ decay and 2.1 × 10^24 yr for the 2νββ 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: (T1/2)0ν0+ > 5.9 × 10^24 yr for the 0νββ mode and (T1/2)2ν0+ > 1.3 × 10^24 yr for the 2νββ mode. These represent the most stringent limits on the DBD of 130Te to excited states and improve by a factor ∼5 the previous results on this process.
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