Measurement of the $2\nu \beta \beta$ decay rate and spectral shape of ${}^{100}$Mo from the CUPID-Mo experiment

Neutrinoless double beta decay ($0\nu \beta \beta$) is a yet unobserved nuclear process which would demonstrate Lepton Number violation, a clear evidence of beyond Standard Model physics. The process two neutrino double beta decay ($2\nu \beta \beta )$ is allowed by the Standard Model and has been measured in numerous experiments. In this letter, we report a measurement of $2\nu \beta \beta$ decay half-life of ${}^{100}$Mo to the ground state of ${}^{100}$Ru of $(7.07\pm 0.02\text{ (stat.) }\pm 0.11\text{ (syst.)})\times {10}^{18}$~yr by the CUPID-Mo experiment. With a relative precision of $\pm 1.6$ % this is the most precise measurement to date of a $2\nu \beta \beta$ decay rate in ${}^{100}$Mo. In addition, we constrain higher-order corrections to the spectral shape which provides complementary nuclear structure information. We report a novel measurement of the shape factor ${\xi }_{3,1}=0.45\pm 0.03\text{ (stat.) }\pm 0.05\text{ (syst.)}$, which is compared to theoretical predictions for different nuclear models. We also extract the first value for the effective axial vector coupling constant obtained from a spectral shape study of $2\nu \beta \beta$ decay.