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Higgs Mass Bounds in the Three- and Six-Higgs Doublet Models for Family Structure

We reanalyze our recently proposed mass matrix model based on spontaneously broken discrete chiral family symmetry, taking into account the additional flavor changing neutral current constraint implied by the bound on the $D_1-D_2$ mass difference, and including several corrections to our earlier analysis. When combined, the $K_1-K_2$ and $D_1-D_2$ constraints force the masses of the Higgs particles that contribute most strongly to flavor changing neutral currents (the $ϕ$ Higgs states) to lie above 17 TeV, well beyond the limit of validity of conventional perturbative Higgs physics. The analogous constraints on the masses of the $η$ Higgs states and the neutral pseudo Goldstone Higgs state depend on the mechanism for realizing small first family masses. If the $η$ Higgs is the primary contributor to second family masses, the pseudo Goldstone and $η$ Higgs states must have masses above 220 GeV, with numerical fits suggesting masses above 1 TeV, while if the $η$ Higgs is responsible solely for first family masses, the corresponding mass bounds drop to the range detectable at the LHC. We show that naturalness of small first family masses favors the latter alternative, and give an illustrative mass matrix texture model.