CP and Discrete Flavour Symmetries

TL;DR

This paper defines consistent generalized CP transformations within discrete flavor symmetries, linking them to automorphisms of the groups, and clarifies CP violation issues in various flavor models.

Contribution

It provides a systematic framework for understanding generalized CP transformations as automorphisms of discrete groups, resolving ambiguities in flavor symmetry models.

Findings

Generalized CP transformations correspond to automorphisms of discrete groups.

Clarification of CP violation in T', Delta(27), and A4 models.

Resolution of recent claims about geometrical CP violation.

Abstract

We give a consistent definition of generalised CP transformations in the context of discrete flavour symmetries. Non-trivial consistency conditions imply that every generalised CP transformation can be interpreted as a representation of an automorphism of the discrete group. This allows us to give consistent generalised CP transformations of popular flavour groups. We are able to clear up issues concerning recent claims about geometrical CP violation in models based on T', clarify the origin of 'calculable phases' in Delta(27) and explain why apparently CP violating scalar potentials of A4 result in a CP conserving ground state.