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 violated quark–lepton equality 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 determinant and hierarchical form with expansion parameter λ ∼ sin θ c ∼ m μ / m τ . The latter can be realized, e.g., in the model with U ( 1 ) family symmetry. The equality is violated at the ∼ λ 2 level. Large lepton mixing appears as a result of summation of the neutrino and charged lepton rotations which diagonalize corresponding mass matrices in contrast with the quark sector where the up quark and down quark rotations cancel each other. We show that the flip of the sign of rotation in the neutrino 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 ∼ ( 1 – 3 ) λ 2 , hierarchical neutrino mass spectrum, and m e e < 10 − 2 eV . The scenario is consistent with the thermal leptogenesis and (in SUSY context) bounds on lepton number violating processes, like μ → e γ .