Implications of Dark- \(\theta _{12}\) Solution on Two-zero Texture Inverse Neutrino Mass Matrix

We investigate the possibility of two-zeros in inverse neutrino mass matrix ( \(M_{\nu }^{-1}\) ) in light of “dark” large mixing angle (dark- \(\theta _{12}\) ) solution to the solar neutrino problem where solar mixing angle lies in the second octant ( \(\sin ^{2}{\theta _{12}}\simeq 0.7\) ). The zeros in right-handed Majorana neutrino mass matrix \(M_{R}\) corresponds to the zeros in \(M_{\nu }^{-1}\) if Dirac and charged lepton mass matrices are diagonal. Out of fifteen possible two-zero textures, only seven are found to be consistent with dark- \(\theta _{12}\) solution. All the textures with vanishing (1,1) element are found to be inconsistent with dark- \(\theta _{12}\) solution. We, also, obtained predictions of the model for neutrinoless double beta ( \(0\nu \beta \beta \) ) decay amplitude \(|M_{ee}|\) . For five out of seven allowed textures, the predicted 3 \(\sigma \) lower bound on \(0\nu \beta \beta \) amplitude \(|M_{ee}|\) is \(\mathcal {O}(10^{-2})\) which is within the sensitivity reach of \(0\nu \beta \beta \) decay experiments like SuperNEMO, KamLAND-Zen, NEXT and nEXO. Furthermore, these textures are found to be necessarily CP-violating. Within Type-I seesaw setting, we have shown that the allowed \(M_{\nu }^{-1}\) textures can be realized using \(A_{4}\) discrete flavor symmetry wherein the standard model particle content has been enlarged with three right-handed neutrinos and a scalar singlet field.