Precise measurement of $2\nu \beta \beta$ decay of ${}^{100}$Mo with the CUPID-Mo detection technology

We report the measurement of the two-neutrino double-beta ($2\nu \beta \beta$) decay of ${}^{100}$Mo to the ground state of ${}^{100}$Ru using lithium molybdate (\crystal) scintillating bolometers. The detectors were developed for the CUPID-Mo program and operated at the EDELWEISS-III low background facility in the Modane underground laboratory. From a total exposure of $42.235$ kg$\times$d, the half-life of ${}^{100}$Mo is determined to be $T_{1\mathrm{/}2}^{2\nu }=[7.12_{-0.14}^{+0.18}(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.10(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})]\times {10}^{18}$ years. This is the most accurate determination of the $2\nu \beta \beta$ half-life of ${}^{100}$Mo to date. We also confirm, with the statistical significance of $>3\sigma$, that the single-state dominance model of the $2\nu \beta \beta$ decay of ${}^{100}$Mo is favored over the high-state dominance model.