Lepton mixing patterns from the group $\Sigma(36\times3)$ with a generalized CP transformation

Abstract

The group $\Sigma(36\times3)$ with the generalized CP transformation is introduced to predict the mixing pattern of leptons. Various combinations of abelian residual flavor symmetries with CP transformations are surveyed. Six mixing patterns could accommodate the fit data of neutrinos oscillation at $3\sigma$ level. Among them, two patterns predict the nontrivial Dirac CP phase, around $\pm 57^{\circ}$ or $\pm 123^{\circ}$, which is in accordance with the result of the literature and the recent fit data. Furthermore, one pattern could satisfy the experimental constraints at $1\sigma$ level.