Minima of multi-Higgs potentials with triplets of $\Delta(3n^2)$ and $\Delta(6n^2)$

TL;DR

This paper systematically analyzes the minima of multi-Higgs potentials with specific discrete symmetries, identifying cases of spontaneous CP violation and introducing new geometrical CP violation scenarios, including for 6 Higgs doublets.

Contribution

It provides the first classification of minima and spontaneous CP violation in 3 and 6 Higgs doublet models with $ riangle(3n^2)$ and $ riangle(6n^2)$ symmetries using the invariant approach.

Findings

Identified new cases of spontaneous geometrical CP violation.

Determined conditions for calculable phases in VEVs.

First analysis of 6 Higgs doublet models with these symmetries.

Abstract

I present a list of minima for 3 Higgs doublet models and 6 Higgs doublet models that are invariant under the discrete symmetries $\Delta(3n^2)$ and $\Delta(6n^2)$. I use the invariant approach formalism on the scalar sector and, with relevant Spontaneous CP-odd invariants, determine if the minima lead to Spontaneous CP violation. I identify in which cases the VEVs have calculable phases, finding several new cases of Spontaneous Geometrical CP Violation, including the first cases for 6 Higgs doublet models.