Lepton mixing and discrete symmetries

Abstract

The pattern of lepton mixing can emerge from breaking a flavor symmetry in different ways in the neutrino and charged lepton Yukawa sectors. In this framework, we derive the conditions imposed on the mixing matrix by the structure of discrete groups of the von Dyck type which include A4, S4 and A5. We show that, in general, these conditions reduce to two equations for the mixing parameters (angles and CP phase δ). These constraints, which correspond to unbroken residual symmetries, are consistent with non-zero 13 mixing and deviations from maximal 2-3 mixing. For the allowed values of mixing angles we predict δ= 60 - 90^{\circ}.