2-LOOP UNITARITY CONSTRAINTS ON THE HIGGS-BOSON COUPLING

We use the results of Maher et al. (preceding paper) to construct the matrix of j = 0 partial-wave two-body and 2 --> 3 scattering amplitudes for the scattering of longitudinally polarized gauge bosons W(L)+/-, Z(L) and Higgs bosons H correct to two loops in the high-energy, heavy-Higgs-boson limit square-root s much greater than M(H) much greater than M(W). We show explicitly that the energy dependence of the 2 --> 2 amplitudes can be completely absorbed into a running quartic Higgs boson coupling lambda(s) = lambda(s) (s, M(H)2) and factors which involve small anomalous dimensions and remain near unity. After diagonalizing the matrix of partial-wave amplitudes we use an Argand-diagram analysis to show that the elastic scattering amplitudes are approximately unitary and weakly interacting for lambda(s) less than or similar to 2.3, but that three-loop corrections are necessary to restore unitarity for larger values of lambda(s). That is, the interactions in the Higgs sector of the standard model are effectively strong with respect to the perturbative expansion for lambda(s) greater than or similar to 2.3. The bound lambda(s) less than or similar to 2.3 for a weakly interacting theory translates to a physical Higgs boson mass M(H) less than or similar to 380 GeV if the bound is to hold for energies up to a few TeV, or M(H) less-than-or-equal-to 155 GeV in perturbatively unified theories with mass scales of order 10(16) GeV.