Mixing Patterns from the Groups Sigma (n phi)

TL;DR

This paper surveys specific discrete groups and their mixing patterns, identifying those compatible with experimental lepton mixing data, especially predicting the reactor angle, and discusses their automorphisms and implications for CP violation.

Contribution

It provides a comprehensive analysis of mixing patterns derived from Sigma groups, highlighting those compatible with data and exploring their automorphisms and CP properties.

Findings

Certain Sigma group patterns match experimental lepton mixing angles.

Predicted reactor angle theta_{13} ranges from 0.1 to 0.2.

Most patterns lead to a trivial Dirac phase, with CP violation patterns fitting data less well.

Abstract

We survey the mixing patterns which can be derived from the discrete groups Sigma (36 x 3), Sigma (72 x 3), Sigma (216 x 3) and Sigma (360 x 3), if these are broken to abelian subgroups Ge and Gnu in the charged lepton and neutrino sector, respectively. Since only Sigma (360 x 3) possesses Klein subgroups, only this group allows neutrinos to be Majorana particles. We find a few patterns that can agree well with the experimental data on lepton mixing in scenarios with small corrections and that predict the reactor mixing angle theta_{13} to be 0.1 <= theta_{13} <= 0.2. All these patterns lead to a trivial Dirac phase. Patterns which instead reveal CP violation tend to accommodate the data not well. We also comment on the outer automorphisms of the discussed groups, since they can be useful for relating inequivalent representations of these groups.