Simultaneous Measurement of Half-Life and Spectral Shape of ${}^{115}$In $\beta$-decay with an Indium Iodide Cryogenic Calorimeter

Current bounds on neutrino Majorana mass are affected by significant uncertainties in the nuclear calculations for neutrinoless double-beta decay. A key issue for a data-driven improvement of the nuclear theory is the actual value of the axial coupling constant $g_A$, which can be investigated through forbidden $\beta$-decays. We present the first measurement of 4${}^{th}$-forbidden $\beta$-decay of ${}^{115}$In with a cryogenic calorimeter based on Indium Iodide. Exploiting the enhanced spectral shape method for the first time to this isotope, our study accurately determines simultaneously spectral shape, $g_A$, and half-life. The Interacting Shell Model, which best fits our data, indicates a half-life for this decay at $T_{1\mathrm{/}2}=(5.26\pm 0.06)\times {10}^{14}$,yr.