Saturating the bound on the scale of fermion mass generation

Recently, Jäger and Willenbrock have shown that the Appelquist and Chanowitz bound on the scale of top-quark mass generation can formally be saturated at tree-level 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 ff̄→VLVL and VLVL→VLVL scattering and derive the conditions on the parameters required for ff̄→VLVL scattering to be relevant to unitarity. I also show that it is not possible to saturate the bound on fermion mass generation in a two-Higgs model while maintaining tree-level unitarity in Higgs scattering at high energies.