The effective neutrino mass of neutrinoless double-beta decays: how possible to fall into a well

Abstract

The neutrinoless double-beta (0nu 2beta ) decay is currently the only feasible process in particle and nuclear physics to probe whether massive neutrinos are the Majorana fermions. If they are of a Majorana nature and have a normal mass ordering, the effective neutrino mass term langle mrangle ^{}_{ee} of a 0nu 2beta decay may suffer significant cancellations among its three components and thus sink into a decline, resulting in a “well” in the three-dimensional graph of |langle mrangle ^{}_{ee}| against the smallest neutrino mass m^{}_1 and the relevant Majorana phase rho . We present a new and complete analytical understanding of the fine issues inside such a well, and identify a novel threshold of |langle mrangle ^{}_{ee}| in terms of the neutrino masses and flavor mixing angles: |langle mrangle ^{}_{ee}|^{}_* = m^{}_3 sin ^2theta ^{}_{13} in connection with tan theta ^{}_{12} = sqrt{m^{}_1/m^{}_2} and rho =pi . This threshold point, which links the local minimum and maximum of |langle mrangle ^{}_{ee}|, can be used to signify observability or sensitivity of the future 0nu 2beta -decay experiments. Given current neutrino oscillation data, the possibility of |langle mrangle ^{}_{ee}| < |langle mrangle ^{}_{ee}|^{}_* is found to be very small.