Phase broken $\mu-\tau$ symmetry and the neutrino mass hierarchy

Understand

Inspired by the neutrino oscillations data, we consider the exact $\mu-\tau$ symmetry, implemented at the level of the neutrino mass matrix, as a good initial framework around which to study and describe neutrino phenomenology.

• Working in the diagonal basis for the charged leptons, we deviate from $\mu-\tau$ symmetry by just modifying the phases of the neutrino mass matrix elements.
• This deviation is enough to allow for a non-vanishing neutrino mixing entry $|V_{e3}|$ (i.e.
• $\theta_{13}$) but it also gives a very stringent (and eventually falsifiable) prediction for the atmospheric neutrino mixing element $|V_{\mu3}|$ as a function of $|V_{e3}|$.