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

## TL;DR

This paper investigates the minima of scalar potentials in multi-Higgs models with triplet fields under various non-Abelian discrete symmetries, providing insights applicable to electroweak and flavor physics models.

## Contribution

It offers a comprehensive analysis of potential minima for multi-Higgs models with triplet fields under a broad class of discrete symmetries, including $ ext{Delta}(3n^2)$ and $ ext{Delta}(6n^2)$ for $n>3$, extending previous studies.

## Key findings

- Classified minima for various discrete symmetry groups.
- Identified conditions for stable scalar configurations.
- Provided analytical tools for model building in particle physics.

## Abstract

We analyse the minima of scalar potentials for multi-Higgs models where the scalars are arranged as either one triplet or two triplets of the discrete symmetries $A_4$, $S_4$, $\Delta(27)$, $\Delta(54)$, as well as $\Delta(3n^2)$ and $\Delta(6n^2)$ with $n>3$. The results should be useful for both multi-Higgs models involving electroweak doublets and multi-flavon models involving electroweak singlets, where in both cases the fields transform as triplets under some non-Abelian discrete symmetry.