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

TL;DR

This paper explores lepton mixing patterns derived from the group (36) with generalized CP symmetry, identifying specific patterns consistent with neutrino oscillation data and predicting CP phases.

Contribution

It introduces the group (36) with CP symmetry and systematically analyzes residual symmetries to predict viable lepton mixing patterns.

Findings

Six mixing patterns fit neutrino oscillation data at 3 level.

Two patterns predict CP phases around b1 57b0 or 123b0.

One pattern matches experimental constraints at 1 level.

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.