Conditions for global minimum in the A4 symmetric 3HDM

TL;DR

This paper derives exact conditions for the global minimum in A4 symmetric three Higgs doublet models, addressing subtleties and providing numerical examples, and discusses boundedness from below in charge-breaking directions.

Contribution

It provides the first complete analytic criteria for global minima in A4 symmetric 3HDMs and explores boundedness conditions with numerical support.

Findings

Analytic necessary and sufficient conditions for neutral global minima.

A safe analytical sufficient condition for bounded from below potentials.

Numerical evidence supporting a conjecture on charge-breaking directions.

Abstract

There has been a great interest in three Higgs doublet models (3HDM) symmetric under an exact A4 symmetry. We provide the complete analytic necessary and sufficient conditions for a point to be the global minimum along the neutral directions in such models, discussing many of the subtleties involved. We also present a number of numerical examples, to highlight those issues. We then turn to the directions which break electric charge, presenting a safe analytical sufficient condition for bounded from below (BFB) potentials. Based on extensive numerical simulations, we discuss one conjecture on BFB along charge breaking directions.