Unitarity and bounds on the scale of fermion mass generation

The scale of fermion mass generation can, as shown by Appelquist and Chanowitz, be bounded from above by relating it to the scale of unitarity violation in the helicity nonconserving amplitude for fermion-anti-fermion pairs to scatter into pairs of longitudinally polarized electroweak gauge bosons. In this paper, we examine the process t (t) over bar -> WL+WL- in a family of phenomenologically-viable deconstructed Higgsless models and we show that scale of unitarity violation depends on the mass of the additional vectorlike fermion states that occur in these theories (the states that are the deconstructed analogs of Kaluza-Klein partners of the ordinary fermions in a five-dimensional theory). For sufficiently light vector fermions, and for a deconstructed theory with sufficiently many lattice sites (that is, sufficiently close to the continuum limit), the Appelquist-Chanowitz bound can be substantially weakened. More precisely, we find that, as one varies the mass of the vectorlike fermion for fixed top-quark and gauge-boson masses, the bound on the scale of top-quark mass generation interpolates smoothly between the Appelquist-Chanowitz bound and one that can, potentially, be much higher. In these theories, therefore, the bound on the scale of fermion mass generation is independent of the bound on the scale of gauge-boson mass generation. While our analysis focuses on deconstructed Higgsless models, any theory in which top-quark mass generation proceeds via the mixing of chiral and vector fermions will give similar results.