Neutrino masses and mixing: Singular mass matrices and Quark-lepton symmetry

Abstract

We suggest an approach to explain the observed pattern of the neutrino masses and mixing which employs the weakly broken quark-lepton symmetry and does not require introduction of an ad hoc symmetry of the neutrino sector. The mass matrices are nearly equal for all quarks and leptons. They have very small determinants and hierarchical form with expansion parameter lambda = 0.26. The latter can be realized, e.g., in the model with U(1) family symmetry. The symmetry is broken at the lambda^2 level. Large lepton mixing appears as a result of summation of the neutrino and charged lepton rotations which diagonalize the mass matrices in contrast with quark sector where the up quarks and down quarks rotations cancel each other. We show that the flip of the sign of rotation in the lepton sector is a result of the seesaw mechanism which also enhances the neutrino mixing. In this approach one expects, in general, deviation of the 2-3 mixing from maximal, s_{13} \sim (1-3) lambda^2, hierarchical neutrino mass spectrum, and m_{ee} < 10^{-2} eV. The scenario is consistent with the thermal leptogenesis and (in SUSY context) bounds on lepton number violating processes, like mu to e gamma.