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 $^{ 76}\mathrm{ Ge}$. Assuming no signals, current and future experiments could place a $90\%$ lower limit on the half life $T^{ 0\nu}_{ 1/2} \gtrsim 4\times 10^{ 26}~{ \rm yr}$ and $T^{ 0\nu}_{ 1/2} \gtrsim 7\times 10^{ 27}~{ \rm yr}$, 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 $10^{ 4}~{ \rm kg}\cdot{ \rm yr}$ and a background rate of $10^{ -4}~{ \rm counts}/({ \rm keV}\cdot{ \rm kg}\cdot{ \rm yr})$, we find that a moderate evidence for normal neutrino mass ordering (i.e., with a Bayes factor ${ \cal B}$ given by $\ln({ \cal B}) \simeq 2.5$ or a probability about $92.3\%$ according to the Jeffreys scale) can be achieved if the true value of effective neutrino mass $m^{ }_{ \beta\beta}$ turns out to be below $0.01~{ \rm eV}$.
Categories: hep-ph hep-ex