Conditions for global minimum in the A4 symmetric 3HDM

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.

Latex, 18 pages

References in corpus (6)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Symmetry breaking patterns in 3HDM
• Three-Higgs-doublet model with $A_4$ symmetry
• Exploring multi-Higgs models with softly broken large discrete symmetry groups
• Softly-broken $A_4$ or $S_4$ 3HDMs with stable states