Generalised CP Symmetry in Modular-Invariant Models of Flavour

TL;DR

This paper develops a formalism combining finite modular and generalized CP symmetries in flavour models, showing that gCP constrains models and makes the modulus the sole source of CP violation.

Contribution

It introduces a consistent framework for combining modular and gCP symmetries in flavour theories, with explicit conditions and an illustrative $S_4$ model.

Findings

gCP symmetry imposes additional constraints on modular models

The modulus $ au$ becomes the only source of CP violation in these models

Viable models are more predictive due to symmetry constraints

Abstract

The formalism of combined finite modular and generalised CP (gCP) symmetries for theories of flavour is developed. The corresponding consistency conditions for the two symmetry transformations acting on the modulus $\tau$ and on the matter fields are derived. The implications of gCP symmetry in theories of flavour based on modular invariance described by finite modular groups are illustrated with the example of a modular $S_4$ model of lepton flavour. Due to the addition of the gCP symmetry, viable modular models turn out to be more constrained, with the modulus $\tau$ being the only source of CP violation.