Three-Higgs-doublet model with $A_4$ symmetry

TL;DR

This paper explores a three-Higgs-doublet extension of the Standard Model with $A_4$ symmetry, analyzing scalar mass spectra and the implications for neutrino mass generation, including scenarios with light or massless scalars.

Contribution

It provides a detailed analysis of the scalar sector in a three-Higgs-doublet model with $A_4$ symmetry, highlighting potential light scalars and their phenomenological implications.

Findings

No light scalars in one scenario

Possible light or massless scalars in others

Quantum effects may influence scalar masses

Abstract

We worked out in detail the three-Higgs-doublet extension of the standard model when the $A_4$ symmetry, which is imposed to solve the flavor problem, is extended to the scalar sector. The three doublets may be related to the fermion mass generation and, in particular, they may be the unique responsible for the generation of the neutrino masses. If this is the case, the respective VEVs have to be quite smaller than the electroweak scale if no fine tuning in the Yukawa couplings is assumed. We consider here the mass spectra in the scalar sector in three different situations. In one of them there are no light scalars at all, but in the other ones a light or two massless scalars, at the tree level, may survive. The later fields are safe, from the phenomenological point of view, since it couples mainly with neutrinos and/or becomes enough massive at the tree level if there exist trilinear interactions. Quantum effects may be important too.