Suppression of $0\nu 2\beta$ Decay from CP Violation

The observed phenomenon of neutrino oscillations is interpreted as the proof that neutrinos must have mass. As this is true for the neutrinos in the mass basis, the mass matrix in the flavor (weak) basis may still contain zeros. This can happen if the CP violating phases, usually neglected, come into play and result in suppression of processes which half-life depends on the masses of ${\nu }_e$, ${\nu }_{\mu }$, or ${\nu }_{\tau }$. In the present paper we investigate the possibility of such suppression of the neutrinoless double beta decay ($0\nu 2\beta$).