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

Neutrinoless double beta decay ($0νββ$) 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 ($2νββ)$ is allowed by the Standard Model and has been measured in numerous experiments. In this letter, we report a measurement of $2νββ$ 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 $2νββ$ 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 $ξ_{3,1}=0.45~\pm 0.03~\text{(stat.)} \ \pm 0.05 \ \text{(syst.)}$, 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 $2νββ$ decay.