Minimal seesaw textures with two heavy neutrinos

We systematically analyze the Dirac and the Majorana mass matrices in seesaw models with two heavy right-handed neutrinos. We perform thorough classification of the vanishing matrix elements which are compatible with the results from the current neutrino oscillation experiments. We include the possibility of a nondiagonal Majorana mass matrix which leads to new solutions viable with data. In a basis where the Majorana mass matrix is diagonal, these solutions imply a Dirac matrix with specific relationships amongst its elements. We find that at the level of total four zeros together in m(D) and M-R the mass matrices are almost consistent with the data but one mixing angle is predicted to be unsuitable. At the next level, i.e. with total three zeros, only seven patterns of mass matrices describe the experimental data well. The seven solutions have testable predictions for the future neutrino experiments. In particular, each solution has definite predictions about the observation of the 1-3 leptonic mixing angle and the effective mass measured in neutrinoless double beta decay. The solutions of the mass matrices contain novel texture forms and provide new insights into the lepton-generation structure. We also discuss possible connections between these textures and the tri-bimaximal mixing to search for symmetry principles behind the mass matrix structure.