Non-vanishing $\theta _{13}$ and CP-Violation in Inverse Neutrino Mass Matrix

Abstract

We examine the generic predictions of inverse Majorana neutrino mass matrix, $M_{\nu }^{-1}$ with texture two zeros in the basis where charged lepton mass matrix is diagonal. The mass models studied in the present work predict non-zero values of $\theta _{13}$ and have interesting implications for CP violation. $J_{CP}=0$ is disallowed for type I and II neutrino mass models and are thus, necessarily CP violating. For neutrino mass model of type III, $\theta _{13}=0$ is disallowed, as discussed earlier, but $\delta =0^{\circ }$ or $360^{\circ }$ is still allowed which impel $J_{CP}$ to vanish in the region where $\theta _{23}$ is below maximality. However, this case becomes necessarily CP-violating for the region where $\theta _{23}$ is above maximality.