Neutrino masses in the left-right symmetry model with a family symmetry

Abstract

Based on the SU (2) L ×SU(2) R × U (1) model with an U (1) family symmetry, we obtain the lepton flavor mixing matrix and research on the neutrino masses. In the model we consider, the Lagragian density which yields the Dirac masses for the leptons is U (1) family invariant, so both the mass matrix for the charge leptons and the Dirac mass matrix for the neutrinos are of the Fritzsch-type. But, generally speaking, neutrinos may have also Majorana masses. In that situation, the effective mass matrix for the light neutrinos is no longer of the Fritzsch type. We make some assumptions on the phases of the neutrino Majorana mass matrix to avoid diagonalizing the non-hermitian matrix. Then, we obtain the lepton flavor mixing matrix. The numerical calculation which is based on the lepton flavor mixing matrix shows that the model we consider may not fit the present result of the neutrino mixing experiment.