Half-Life and Precision Shape Measurement of the 2𝜈𝛽𝛽 Decay of 130 Te
Here, we present a new measurement of the 2𝜈𝛽𝛽 half-life of 130 Te (𝑇$^{2𝜈}_{1/2}$) using the first complete model of the CUORE data, based on 1038 kg yr of collected exposure. Thanks to optimized data selection, we achieve a factor of two improvement in precision, obtaining 𝑇$^{2𝜈}_{1/2}$ = (9.32$^{+0.05}_{−0.04}$stat $^{+0.07}_{−0.07}$syst)×10 20 yr. The signal-to-background ratio is increased by 70% compared to our previous results, enabling the first application of the improved 2𝜈𝛽𝛽 formalism to 130 Te . Within this framework, we determine a credibility interval for the effective axial coupling in the nuclear medium as a function of nuclear matrix elements. We also extract values for the higher-order nuclear matrix element ratios: second-to-first and third-to-first. The second-to-first ratio agrees with nuclear model predictions, while the third-to-first ratio deviates from theoretical expectations. These findings provide essential tests of nuclear models and key inputs for future 0𝜈𝛽𝛽 searches.