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 $T_{1/2}^{2\nu}=[7.12^{+0.18}_{-0.14}\,\mathrm{(stat.)}\pm0.10\,\mathrm{(syst.)}]\times10^{18}$ 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.