Hierarchical matrices in the see-saw mechanism, large neutrino mixing and leptogenesis

Abstract

We consider the see-saw mechanism for hierarchical Dirac and Majorana neutrino mass matrices m D and M R, including the CP violating phases. Simple arguments about the structure of the neutrino mass matrix and the requirement of successful leptogenesis lead to the situation that one of the right-handed Majorana neutrinos is much heavier than the other two, which in turn display a rather mild hierarchy. It is investigated how for the neutrino mixing one small and two large mixing angles are generated. The mixing matrix element |U e3|2 is larger than 10-3 and a characteristic ratio between the branching ratios of lepton flavor violating charged lepton decays $\ell_j \rightarrow \ell_i \gamma$ is found. Successful leptogenesis implies sizable CP violation in oscillation experiments. As in the original minimal see-saw model, the signs of the baryon asymmetry of the universe and of the CP asymmetry in neutrino oscillations are equal and there is no connection between the leptogenesis phase and the effective mass as measurable in neutrinoless double beta decay.