Three-Higgs-doublet model under A4 symmetry implies alignment

TL;DR

This paper demonstrates that a three-Higgs-doublet model with A4 symmetry naturally leads to scalar alignment, satisfying positivity and unitarity constraints, and offering a constrained scalar potential framework.

Contribution

It introduces an A4 symmetric three-Higgs-doublet model where alignment emerges naturally from the potential's global minima, with all physical constraints satisfied.

Findings

Alignment arises as a natural consequence of the potential's minima

Positivity and unitarity constraints are satisfied in the model

The A4 symmetry restricts the scalar potential form

Abstract

A model with three scalar doublets can be conveniently accommodated within an A4 symmetric framework. The A4 symmetry permits only a restricted form for the scalar potential. We show that for the global minima of this potential alignment follows as a natural consequence. We also verify that in every case positivity and unitarity constraints are satisfactorily met.