Flavor symmetryLe−Lμ−Lτ, atmospheric neutrino mixing, andCPviolation in the lepton sector

Abstract

The PMNS neutrino mixing matrix is given, in general, by the product of two unitary matrices associated with the diagonalization of the charged lepton and neutrino mass matrices. Assuming that the active flavor neutrinos possess a Majorana mass matrix which is diagonalized by a bimaximal mixing matrix, we give the allowed forms of the charged lepton mixing matrix and the corresponding implied forms of the charged lepton mass matrix. We then assume that the origin of bimaximal mixing is a weakly broken flavor symmetry corresponding to the conservation of the non–standard lepton charge L ′ = Le − Lµ − Lτ. The latter does not predict, in general, the atmospheric neutrino mixing to be maximal. We study the impact of this fact on the allowed forms of the charged lepton mixing matrix and on the neutrino mixing observables, analyzing the case of CP–violation in detail. When compared with the case of exact bimaximal mixing, the deviations from zero Ue3 and from maximal atmospheric neutrino mixing are typically  