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If massive neutrinos are the Majorana particles and have a normal massordering, the effective mass term $\langle m\rangle^{}_{ee}$ of a neutrinolessdouble-beta ($0\nu 2\beta$) decay may suffer significant cancellations amongits three components and thus sink into a decline, resulting in a "well" in thethree-dimensional graph of $|\langle m\rangle^{}_{ee}|$ against the smallestneutrino mass $m^{}_1$ and the relevant Majorana phase $\rho$. We present a newand complete analytical understanding of the fine issues inside such a well,and discover a novel threshold of $|\langle m\rangle^{}_{ee}|$ in terms of theneutrino masses and flavor mixing angles: $|\langle m\rangle^{}_{ee}|^{}_* =m^{}_3 \sin^2\theta^{}_{13}$ 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 $|\langle m\rangle^{}_{ee}|$, can be used tosignify observability or sensitivity of the future $0\nu 2\beta$-decayexperiments. Given current neutrino oscillation data, the possibility of$|\langle m\rangle^{}_{ee}| < |\langle m\rangle^{}_{ee}|^{}_*$ is found to bevery small.

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