A flavor symmetry for quasi-degenerate neutrinos: Lμ - Lτ

We consider the flavor symmetry L μ - L τ for the neutrino mass matrix. The most general neutrino mass matrix conserving L μ - L τ predicts quasi-degenerate neutrino masses with one maximal and two zero mixing angles. The presence of L μ - L τ can also be motivated by the near-bimaximal form of the neutrino mixing matrix. Furthermore, it is a special case of μτ symmetric mass matrices. Breaking the flavor symmetry by adding a small flavor-blind term to the neutrino mass matrix and/or by applying radiative corrections is shown to reproduce the observed neutrino oscillation phenomenology. Both the normal and inverted mass ordering can be accommodated within this scheme. Moderate cancellation for neutrinoless double beta decay is expected. The observables |U e3 | 2 and |1/2 - sin 2 θ 23 | are proportional to the inverse of the fourth power of the common neutrino mass scale. We comment on whether the atmospheric neutrino mixing is expected to lie above or below π/4. We finally present a model based on the see-saw mechanism which generates a light neutrino mass matrix with an (approximate) L μ - L τ flavor symmetry. This is a minimal model with just one standard Higgs doublet and three heavy right-handed neutrinos. It needs only small values for the soft L μ - L τ breaking terms to reproduce the phenomenological viable mass textures analyzed.