There has been a great interest in three Higgs doublet models (3HDM) symmetric under an exact $$A_4$$
A
4
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.
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.
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.
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