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Saturating the Bound on the Scale of Fermion Mass Generation

Recently, Jaeger and Willenbrock have shown that the Appelquist and Chanowitz bound on the scale of top-quark mass generation can formally be saturated in a particular limit of a two-Higgs doublet model. In this note I present an alternate derivation of their result. I perform a coupled channel analysis for f fbar to V_L V_L and V_L V_L to V_L V_L scattering and derive the conditions on the parameters required for f fbar to V_L V_L scattering to be relevant to unitarity. I also show that it is not possible to saturate the bound on fermion mass generation in the two-Higgs model while maintaining tree-level unitarity in Higgs scattering at high energies.