Softly-broken $A_4$ or $S_4$ 3HDMs with stable states

TL;DR

This paper investigates multi-Higgs models with softly-broken $A_4$ or $S_4$ symmetries, revealing conditions under which stable states are protected by residual symmetries, with implications for particle physics phenomenology.

Contribution

It introduces a novel analysis of softly-broken $A_4$ and $S_4$ symmetric 3HDMs, identifying stable states protected by residual symmetries.

Findings

Identification of stable states protected by residual symmetries

Analysis of mass spectra and decay channels of physical states

Comparison with previously studied symmetry-breaking scenarios

Abstract

We study multi-Higgs models with a triplet of $A_4$ or $S_4$ symmetry that is softly-broken. Focusing on parameters that softly break the respective symmetries but preserve the directions of the vacuum expectation values of the triplet we analyse the masses of physical states and discuss their decays. In contrast with previously studied symmetries, we find some cases with stable states that are protected by residual symmetries left unbroken by both the soft-breaking parameters and by the vacuum.