Alternative Schemes of Predicting Lepton Mixing Parameters from Discrete Flavor and CP Symmetry

TL;DR

This paper proposes two new frameworks combining discrete flavor and CP symmetries to predict lepton mixing angles and CP phases, extending to quark mixing, and analyzes residual symmetry effects on mixing patterns.

Contribution

It introduces two alternative schemes for predicting lepton mixing parameters from combined flavor and CP symmetries, including criteria for residual symmetry equivalence.

Findings

Derived general criteria for residual symmetry equivalence.

Analyzed lepton mixing patterns from S4 flavor group with various residual symmetries.

Extended symmetry breaking patterns to quark sector.

Abstract

We suggest two alternative schemes to predict lepton mixing angles as well as $CP$ violating phases from a discrete flavor symmetry group combined with $CP$ symmetry. In the first scenario, the flavor and $CP$ symmetry is broken to the residual groups of the structure $Z_2\times CP$ in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters $\theta_{\nu}$ and $\theta_{l}$. This type of breaking pattern is extended to the quark sector. In the second scheme, an abelian subgroup contained in the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant $CP$ transformation, all lepton mixing parameter are determined in terms of three free parameters $\theta_{1, 2, 3}$. We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters $\theta_{\nu, l}$ and $\theta_{1, 2, 3}$ is taken into account. We have studied the lepton mixing patterns arising from the flavor group $S_4$ and $CP$ symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.