Abstract
We use the results of Maher et al. (preceding paper) to construct the matrix of partial-wave two-body and 2 → 3 scattering amplitudes for the scattering of longitudinally polarized gauge bosons , and Higgs bosons correct to two loops in the high-energy, heavy-Higgs-boson limit . We show explicitly that the energy dependence of the 2 → 2 amplitudes can be completely absorbed into a running quartic Higgs boson coupling 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 , but that three-loop corrections are necessary to restore unitarity for larger values of . That is, the interactions in the Higgs sector of the standard model are effectively strong with respect to the perturbative expansion for . The bound for a weakly interacting theory translates to a physical Higgs boson mass GeV if the bound is to hold for energies up to a few TeV, or GeV in perturbatively unified theories with mass scales of order GeV.
- Received 4 February 1993
DOI:https://doi.org/10.1103/PhysRevD.48.1084
©1993 American Physical Society