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

Abstract

If massive neutrinos are the Majorana particles and have a normal mass ordering, the effective mass term $⟨m{⟩}_{ee}^{}$ of a neutrinoless double-beta ($0\nu 2\beta$) 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 $|⟨m{⟩}_{ee}^{}|$ 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 discover a novel threshold of $|⟨m{⟩}_{ee}^{}|$ in terms of the neutrino masses and flavor mixing angles: $|⟨m{⟩}_{ee}^{}{|}_{\ast }^{}=m_3^{}{\sin }^2{\theta }_{13}^{}$ in connection with $\tan {\theta }_{12}^{}=\sqrt{m_1^{}/m_2^{}}$ and $\rho =\pi$. This threshold point, which links the {\it local} minimum and maximum of $|⟨m{⟩}_{ee}^{}|$, can be used to signify observability or sensitivity of the future $0\nu 2\beta$-decay experiments. Given current neutrino oscillation data, the possibility of $|⟨m{⟩}_{ee}^{}|<|⟨m{⟩}_{ee}^{}{|}_{\ast }^{}$ is found to be very small.

Comments: 9 pages, 3 figures, version to appear in Eur. Phys. J. C