Scales of fermion mass generation and electroweak symmetry breaking

The scale of mass generation for fermions (including neutrinos) and the scale for electroweak symmetry breaking (EWSB) can be bounded from above by the unitarity of scattering involving longitudinal weak gauge bosons or their corresponding would-be Goldstone bosons. Including the exact n-body phase space we analyze the 2 -> n (n >= 2) processes for the fermion-(anti)fermion scattering into multiple gauge boson final states. Contrary to naive energy power counting, we demonstrate that as n becomes large, the competition between an increasing energy factor and a phase-space suppression leads to a strong new upper bound on the scale of fermion mass generation at a finite value n=n(s), which is independent of the EWSB scale, v = (root 2G(F))(-1/2). For quarks, leptons, and Majorana neutrinos, the strongest 2 -> n limits range from about 3 TeV to 130-170 TeV (with 2 less than or similar to n(s) less than or similar to 24), depending on the measured fermion masses. Strikingly, given the tiny neutrino masses as constrained by the neutrino oscillations, neutrinoless double-beta decays and astrophysical observations, the unitarity violation of nu(L)nu(L) -> nW(L)(a) scattering actually occurs at a scale no higher than similar to 170 TeV. Implications for various mechanisms of neutrino mass generation are analyzed. On the other hand, for the 2 -> n pure Goldstone boson scattering, we find that the decreasing phase-space factor always dominates over the growing overall energy factor when n becomes large, so that the best unitarity bound on the scale of EWSB remains at n = 2.