Phase broken μ-τ Symmetry and the neutrino mass hierarchy

Inspired by the neutrino oscillations data, we consider the exact μ-τ 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 μ-τ symmetry by just modifying the phases of the neutrino mass matrix elements. This deviation is enough to allow for a nonvanishing neutrino mixing entry |Ve3| (i.e., θ13) but it also gives a very stringent (and eventually falsifiable) prediction for the atmospheric neutrino mixing element |Vμ3| as a function of |Ve3|. The breaking by phases is characterized by a single phase and is shown to lead to interesting lower bounds on the allowed mass of the lightest neutrino depending on the ordering of neutrino masses (normal or inverted) and on the value of the Dirac CP violating phase δCP. The allowed parameter space for the effective Majorana neutrino mass mee is also shown to be nontrivially constrained.