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

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 = 125GeV and the h → W W, ZZ signal. We also checked numerically that, for each point that passes all the constraints, the minimum is a global minimum of the potential.

Dispersive constraints on fermion masses

“…For example, a flavor U(1) symmetry with a scalar field called flavon was introduced and then spontaneously broken in the Froggatt-Nielsen model [1]. The aforementioned flavor structures were generated in various models with modular flavor symmetry [2], which has attracted great attention [3][4][5][6][7]. The smooth confinement mechanism without chiral symmetry breaking [8][9][10] was implemented to explain the small Yukawa couplings of the first-and second-family fermions, which are composite of ultraviolet fields, while the third family fermions are elementary to be consistent with the O(1) top Yukawa coupling [11].…”