Scale of fermion mass generation

Abstract

Unitarity of longitudinal weak vector boson scattering implies an upper bound on the scale of electroweak symmetry breaking, $\Lambda_{EWSB}\equiv \sqrt{8\pi}v\approx$ 1 TeV. Appelquist and Chanowitz have derived an analogous upper bound on the scale of fermion mass generation, proportional to $v^2/m_f$, 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 there is no upper bound, beyond that on the scale of electroweak symmetry breaking, in such a theory. This result is obtained by considering the same process, but with a large number of longitudinal weak vector bosons in the final state. We further argue that there is no 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 $\Lambda_{Maj}\equiv 4\pi v^2/m_\nu$. 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 higher-dimension interactions, a two-Higgs-doublet model, and models without a Higgs boson.