We reexamine the unitarity constraints on the high-energy scattering of longitudinally polarized W's and Z's and Higgs bosons in the standard model including one-loop corrections. Using an Argand diagram analysis, we find that the j = 0 scattering amplitudes are approximately unitary and weakly interacting at order-lambda-2 for Higgs-boson couplings lambda(s, M(H)2) less than or similar 2, but that corrections of order-lambda-3 or higher must be included to restore perturbative unitarity for larger values of lambda. We show also that two-loop [O(lambda-3)] corrections cannot extend the range of validity of perturbation theory beyond lambda almost-equal-to 2.2. An analysis of inelastic 2 --> 4 scattering in the W(L)+/-, Z(L), H system gives an independent but weaker limit lambda(s, M(H)2) less-than-or-similar 5. The limit lambda(s, M(H)2) < 2 translates to a physical-Higgs-boson mass M(H) less-than-or-similar 400 GeV if the bound is to hold up to energies of a few TeV, or M(H) less-than-or-similar 160 GeV in perturbatively unified theories with a mass scale of order 10(15) GeV. For masses much larger than these bounds, low-order perturbation theory fails and the Higgs sector of the standard model becomes effectively strongly interacting.
