Precision β-Decays Measurements with Low-Temperature Calorimeters: a Benchmark for Nuclear Models

This Ph.D. thesis presents a comprehensive investigation of two fundamental nuclear decay processes: the two-neutrino double-beta (2νββ) decay of 130Te, studied within the CUORE experiment, and the fourth-forbidden β-decay of 115In, explored through the ACCESS project. The main target is performing precise measurements of half-life and spectral shapes of these decays to refine nuclear matrix element calculations, test nuclear models, and probe the effective axial coupling constant within nuclear media. For the CUORE experiment, the development of a robust radioactive background model using 1038.4 kg y of exposure data is presented, and the work has been published in Phys. Rev. D 110, 052003. A simultaneous Bayesian fit to several energy spectra across a broad range, also exploiting the detector’s high granularity, provided exceptional sensitivity to bulk and surface material activities, detecting levels as low as 10 nBq kg−1 and 0.1 nBq cm−2, respectively. These advancements not only enhance the sensitivity of CUORE physics analyses, but also inform the design of the next-generation CUPID experiment. A dedicated fit optimization campaign achieved the most precise measurement of the 2νββ half-life of 130Te, T1/2 2νββ = 9.32 −0.04 +0.05 (stat) −0.08 +0.07 (syst) × 10^20 y. Spectral shape studies using the so-called improved formalism have been carried out for the first time in 130Te, demonstrating the potential of this technique to constrain nuclear models and axial coupling quenching. A paper on this analysis has been prepared, and it will be submitted to Phys. Rev. Lett. in the next few months. The ACCESS project focused on the fourth-forbidden β-decay of 115In using a cryogenic calorimeter based on indium iodide and the measurement is also presented in Phys. Rev. Lett. 133, 122501. Employing the enhanced spectrum-shape method, ACCESS achieved a high-precision determination of the spectral shape, axial coupling constant, and half-life of 115In. The analysis using the interacting shell model, which best fits the data, yielded a half-life of T 1/2 β = (5.26 ± 0.06) × 10^14 y. Together, these findings advance the understanding of nuclear decay processes similar to 0νββ, refine the knowledge about key nuclear parameters, and contribute to the broader effort of testing and improving theoretical nuclear models.