Exploring the neutrino mass matrix at M_R scale

We discuss the neutrino mass matrix which predicts zero or small values of |V_{13}| in MSSM and found the inequality, sin^2 2theta_{12} <= sin^2 2theta_sol, where sin^2 2theta_{12} is the mixing angle at M_R scale and sin^2 2theta_{sol} is the value determined by the solar neutrino oscillation. This constraint says that the model which predicts a larger value of tan^2 theta_{sol} at M_R than the experimental value is excluded. In particular, the bi-maximal mixing scheme at M_R scale is excluded, from the experimental value tan^2 theta_sol<1. In this model, |V_{13}| and a Dirac phase at m_Z are induced radiatively and turn out to be not small. The effective neutrino mass is expected to be of order 0.05 eV.Comment: revtex4, 20 pages, 6 figure

The Problem of Large Leptonic Mixing

Unlike in the quark sector where simple $S_3$ permutation symmetries can generate the general features of quark masses and mixings, we find it impossible (under conditions of hierarchy for the charged leptons and without considering the see-saw mechanism or a more elaborate extension of the SM) to guarantee large leptonic mixing angles with any general symmetry or transformation of only known particles. If such symmetries exist, they must be realized in more extended scenarios.Comment: RevTeX, 4 pages, no figure