Softly broken $\mu \leftrightarrow \tau$ symmetry in the minimal see-saw model

Abstract

Neutrino oscillations data indicates that neutrino mixings are consistent with an apparent ${\nu }_{\mu }-{\nu }_{\tau }$ exchange symmetry in neutrino mass matrix. We observe that in the mininimally extended standard model with the see-saw mechanism, one can impose $\mu \leftrightarrow \tau$ symmetry at the tree level on all Lagrangian terms, but for the mass difference among $\mu$ and $\tau$ 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 ${\theta }_{13}$, and for the deviation of ${\theta }_{ATM}$ 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.

Typos corrected. References and short discussions added. Final version, 6 pages, 2 figures

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