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 generally bounded from above by the unitarity of scatterings involving longitudinal weak gauge bosons or their corresponding would-be Goldstone bosons. We reanalyze these scatterings for 2 → n processes (n > 2) with multiple gauge boson final states including the exact n-body phase space. Contrary to the näıve energy power counting, we demonstrate that as n becomes large, the competition between an overall increasing energy factor and a phase-space suppression leads to the strongest new upper bound on the scale of fermion mass generation at a finite value n = ns, which is independent of the EWSB scale, v = ( √ 2GF ) − 1 2 . For quarks, leptons and Majorana neutrinos, the strongest 2 → n limits range from about 3TeV to 130 − 170TeV (with 2 . ns . 24), depending on the measured fermion masses. Strikingly, given the current constraints on neutrino masses from neutrino oscillations, neutrinoless doublebeta decays and astrophysical observations, the unitarity violation of ν L ν L → nW a L scattering actually occurs at a scale no higher than ∼ 170TeV. Implications for various mechanisms of neutrino mass generation are analyzed. On the other hand, for pure Goldstone scattering, we find that the decreasing phase space factor dominates over the growing overall energy factor when n becomes large, suggesting that the best unitarity bound on the scale of the EWSB remains at n = 2 . PACS number(s): 12.15.Ff, 14.60.Pq, 11.80.-m, 12.60.-i Electronic address: [email protected] Electronic address: [email protected]