The scale of fermion mass generation

Appelquist and Chanowitz have derived an upper bound on the scale of fermion mass generation, proportional to v/mf , by considering the scattering of same-helicity fermions into pairs of longitudinal weak vector bosons in a theory without a standard Higgs boson. We show that the derivation of this bound is based on an inconsistent set of assumptions. We argue that there is no upper bound on the scale of (Dirac) fermion mass generation in the standard model. In contrast, there is an upper bound on the scale of Majorana-neutrino mass generation, given by ΛMaj ≡ 4πv/mν . In general, the upper bound on the scale of fermion mass generation depends on the dimensionality of the interaction responsible for generating the fermion mass. We explore the scale of fermion mass generation in a variety of excursions from the standard model: models with fermions in nonstandard representations, a theory with higherdimension interactions, a two-Higgs-doublet model, and models without a Higgs boson.