A viable $$A_4$$ A 4 3HDM theory of quark mass matrices

Abstract

Abstract It is known that a three Higgs doublet model (3HDM) symmetric under an exact $$A_4$$ 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 $$A_4$$ A 4 terms in the scalar potential does allow for a fit of quark mass matrices. Moreover, the result is consistent with $$m_h=125\,\text {GeV}$$ m h = 125 GeV and the $$h \rightarrow WW,ZZ$$ h → W W , Z Z signal. We also checked numerically that, for each point that passes all the constraints, the minimum is a global minimum of the potential.