Generalized CP Symmetries in Three-Higgs-Doublet Models

TL;DR

This paper explores the scalar and Yukawa sectors of three-Higgs-doublet models with generalized CP symmetry, revealing a richer structure and more possibilities than in two-Higgs-doublet models, including 40 Yukawa texture classes.

Contribution

It classifies all Yukawa textures in three-Higgs-doublet models with generalized CP symmetry, identifying 40 distinct possibilities, expanding the understanding beyond two-Higgs-doublet models.

Findings

Four classes of scalar potentials identified.

Two main Yukawa scenarios in 2HDM; many more in 3HDM.

40 Yukawa texture possibilities in 3HDM, some with only 10 real parameters.

Abstract

We study the scalar and Yukawa sectors of three Higgs doublets models with a generalized CP symmetry. We show that there are only four classes of scalar potentials, merely one more than in two Higgs doublet models (2HDM). In 2HDM with generalized CP symmetries extended to the Yukawa sector, there are only two possible cases: the usual CP, with 18 real Yukawa couplings; and a minimal generalized CP model, with 12 real Yukawa parameters. In contrast, with three Higgs there is a rich variety of allowed models. We classify all possible Yukawa textures, showing that there are 40 possibilities, several of which have only 10 real Yukawa couplings.