Admixture of quasi-Dirac and Majorana neutrinos with tri-bimaximal mixing

We propose a realization of the so-called bimodal/schizophrenic model proposed recently. We assume S4, the permutation group of four objects as flavor symmetry giving tri-bimaximal lepton mixing at leading order. In these models the second massive neutrino state is assumed quasi-Dirac and the remaining neutrinos are Majorana states. In the case of inverse mass hierarchy, the lower bound on the neutrinoless double beta decay parameter mee is about two times that of the usual lower bound, within the range of sensitivity of the next generation of experiments.