Softly broken $μ\leftrightarrowτ$ symmetry in the minimal see-saw model

Abstract

Neutrino oscillations data indicates that neutrino mixings are consistent with an apparent $ν_μ- ν_τ$ exchange symmetry in neutrino mass matrix. We observe that in the mininimally extended standard model with the see-saw mechanism, one can impose $μ\leftrightarrowτ$ symmetry at the tree level on all Lagrangian terms, but for the mass difference among $μ$ and $τ$ leptons. In the absence of any new extra physics, this mass difference becomes the only source for the breaking of such a symmetry, which induces, via radiative corrections, small but predictable values for $θ_{13}$, and for the deviation of $θ_{ATM}$ from maximallity. In the CP conserving case, the predictions only depend on neutrino mass hierarchy and may provide a unique way to test for new physics with neutrino experiments.