A viable $A_4$ 3HDM theory of quark mass matrices

TL;DR

This paper demonstrates that a three Higgs doublet model with softly broken $A_4$ symmetry can successfully reproduce realistic quark masses and mixing, aligning with observed Higgs properties.

Contribution

It introduces a viable $A_4$-symmetric 3HDM with softly broken terms that accommodates quark masses and CKM mixing, overcoming previous incompatibility issues.

Findings

The model fits quark mass matrices and CKM matrix.

The Higgs boson mass and decay signals are consistent with observations.

Numerical analysis confirms global minima of the potential.

Abstract

It is known that a three Higgs doublet model (3HDM)symmetric under an exact $A_4$ symmetry is not compatible with nonzero quark masses and/or non-block-diagonal CKM matrix. We show that a 3HDM with softly broken $A_4$ terms in the scalar potential does allow for a fit of quark mass matrices. Moreover, the result is consistent with $m_h=125\textrm{GeV}$ and the $h \rightarrow WW, ZZ$ signal. We also checked numerically that, for each point that passes all the constraints, the minimum is a global minimum of the potential.