etermination of neutrino mass ordering in future $^76$Ge-based neutrinoless double-beta decay experiments

Motivated by recent intensive experimental efforts on searching for neutrinoless double-beta decays, we perform a detailed analysis of the physics potential of the experiments based on?76Ge. Assuming no signals, current and future experiments could place a?90%?lower limit on the half life?T0ν1/2?4×1026?yr?and?T0ν1/2?7×1027?yr, respectively. Then, how to report an evidence for neutrinoless double-beta decays is addressed by following the Bayesian statistical approach. For the first time, we present a quantitative description of experimental power to distinguish between normal and inverted neutrino mass orderings. Taking an exposure of?104?kg?yr?and a background rate of?10?4?counts/(keV?kg?yr), we find that a moderate evidence for normal neutrino mass ordering (i.e., with a Bayes factor?B?given by?ln(B)?2.5?or a probability about?92.3%?according to the Jeffreys scale) can be achieved if the true value of effective neutrino mass?mββ?turns out to be below?0.01?eV.