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 ${\mathbf{A}}_4$, ${\mathbf{S}}_4$, and ${\mathbf{A}}_5$. 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 ${\mathbf{S}}_4$ model and reproduces the allowed values of the mixing angles, we predict $\delta =(90°–120°)$.

• Received 16 May 2012

DOI:https://doi.org/10.1103/PhysRevD.86.053014