Search for Double-Beta Decay of ${}^{130}\mathrm{T}\mathrm{e}$ to the $0^{+}$ States of ${}^{130}\mathrm{X}\mathrm{e}$ 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 ${}^{130}\mathrm{T}\mathrm{e}$. In this work we present the latest results on two searches for the double beta decay (DBD) of ${}^{130}\mathrm{T}\mathrm{e}$ to the first $0_2^{+}$ excited state of ${}^{130}\mathrm{X}\mathrm{e}$: 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} : $\mathrm{y}\mathrm{r}$}$forthe${0\nu\beta\beta}$decayand$${\mathrm{S}}_{1\mathrm{/}2}^{2\nu }=2.1\times {10}^{24}\mathrm{y}\mathrm{r}$$forthe${2\nu\beta\beta}$ decay. No significant evidence for either of the decay modes was observed and a Bayesian lower bound at $90\mathrm{\%}$ C.I. on the decay half lives is obtained as: $\mathrm{(T{1/2})^{0\nu}_{0^+_2} > 5.9 \times 10^{24} : $\mathrm{y}\mathrm{r}$}$forthe$0\nu\beta\beta$modeand$$({\mathrm{T}}_{1\mathrm{/}2}{)}_{0_2^{+}}^{2\nu }>1.3\times {10}^{24}\mathrm{y}\mathrm{r}$$forthe$2\nu\beta\beta$mode\mathrm{.}TheserepresentthemoststringentlimitsontheDBDof$^{130}$Tetoexcitedstatesandimprovebyafactor$\sim5$ the previous results on this process.