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The scale of fermion mass generation can, as shown by Appelquist andChanowitz, be bounded from above by relating it to the scale of unitarityviolation in the helicity nonconserving amplitude for fermion-anti-fermionpairs to scatter into pairs of longitudinally polarized electroweak gaugebosons. In this paper, we examine the process t tbar -> W_L W_L in a family ofphenomenologically-viable deconstructed Higgsless models and we show that scaleof unitarity violation depends on the mass of the additional vector-likefermion states that occur in these theories (the states that are thedeconstructed analogs of Kaluza-Klein partners of the ordinary fermions in afive-dimensional theory). For sufficiently light vector fermions, and for adeconstructed theory with sufficiently many lattice sites (that is,sufficiently close to the continuum limit), the Appelquist-Chanowitz bound canbe substantially weakened. More precisely, we find that, as one varies the massof the vector-like fermion for fixed top-quark and gauge-boson masses, thebound on the scale of top-quark mass generation interpolates smoothly betweenthe Appelquist-Chanowitz bound and one that can, potentially, be much higher.In these theories, therefore, the bound on the scale of fermion mass generationis independent of the bound on the scale of gauge-boson mass generation. Whileour analysis focuses on deconstructed Higgsless models, any theory in whichtop-quark mass generation proceeds via the mixing of chiral and vector fermionswill give similar results.Comment: 12 pages, 11 eps figures included, revtex. Refrences added; wording  modified slightly to emphasize focus on top-quar

Unitarity and bounds on the scale of fermion mass generation