Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP

TL;DR

This paper explores lepton mixing patterns derived from discrete flavor groups Delta(3n^2) and Delta(6n^2) combined with CP symmetry, analyzing how residual symmetries influence mixing angles and phases for various group parameters.

Contribution

It provides a comprehensive analysis of lepton mixing arising from specific discrete flavor groups and CP symmetries, identifying conditions for realistic mixing patterns and CP phases.

Findings

Mixing patterns depend on group indices and a continuous parameter.

Certain group combinations yield trimaximal columns in mixing matrices.

Experimental data can be fitted for small group indices n ≤ 11.

Abstract

We perform a detailed study of lepton mixing patterns arising from a scenario with three Majorana neutrinos in which a discrete flavor group Gf=Delta (3 n^2) or Gf=Delta(6 n^2) and a CP symmetry are broken to residual symmetries Ge=Z3 and Gnu=Z2 x CP in the charged lepton and neutrino sectors, respectively. While we consider all possible Z3 and Z2 generating elements, we focus on a certain set of CP transformations. The resulting lepton mixing depends on group theoretical indices and one continuous parameter. In order to study the mixing patterns comprehensively for all admitted Ge and Gnu, it is sufficient to discuss only three types of combinations. One of them requires as flavor group Delta (6 n^2). Two types of combinations lead to mixing patterns with a trimaximal column, while the third one allows for a much richer structure. For the first type of combinations the Dirac as well as one Majorana phase are trivial, whereas the other two ones predict in general all CP phases to be non-trivial and also non-maximal. Already for small values of the index n of the group, n <= 11, experimental data on lepton mixing can be accommodated well for particular choices of the parameters of the theory. We also comment on the relation of the used CP transformations to the automorphisms of Delta (3 n^2) and Delta (6 n^2).