Lepton mixing and discrete symmetries

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 model-independent conditions imposed on the mixing matrix by the structure of discrete groups of the von Dyck type which include A(4), S-4, and A(5). We show that, in general, these conditions lead to at least two equations for the mixing parameters (angles and CP phase delta). These constraints, which correspond to unbroken residual symmetries, are consistent with nonzero 13 mixing and deviations from maximal 2-3 mixing. For the simplest case, which leads to an S-4 model and reproduces the allowed values of the mixing angles, we predict delta = (90 degrees-120 degrees).