Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model

TL;DR

This paper completes the classification of all finite reparametrization symmetry groups in the three-Higgs-doublet model, providing a detailed analysis of symmetries, including generalized-CP, and their implications for CP-conservation.

Contribution

It introduces a comprehensive classification of all realizable finite symmetry groups in 3HDM, extending previous work from 2HDM and including the role of solvable groups and CP symmetries.

Findings

Classification of all finite symmetry groups in 3HDM

Presence of Z_4 symmetry guarantees CP-conservation

Detailed analysis of solvable groups in symmetry realization

Abstract

Symmetries play a crucial role in electroweak symmetry breaking models with non-minimal Higgs content. Within each class of these models, it is desirable to know which symmetry groups can be implemented via the scalar sector. In N-Higgs-doublet models, this classification problem was solved only for N=2 doublets. Very recently, we suggested a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM). Here, we present this classification in all detail together with an introduction to the theory of solvable groups, which play the key role in our derivation. We also consider generalized-CP symmetries, and discuss the interplay between Higgs-family symmetries and CP-conservation. In particular, we prove that presence of the Z_4 symmetry guarantees the explicit CP-conservation of the potential. This work completes classification of finite reparametrization symmetry groups in 3HDM.