Previous work has suggested that perturbation theory is unreliable for Higgs- and Goldstone-boson scattering, at energies above the Higgs-boson mass, for relatively small values of the Higgs quartic coupling $\lambda \left(\mu \right)$. By performing a summation of nonlogarithmic terms, we show that perturbation theory is in fact reliable up to relatively large coupling. This eliminates the possibility of a strongly interacting standard Higgs model at energies above the Higgs-boson mass, complementing earlier studies which excluded strong interactions at energies near the Higgs-boson mass. The summation can be formulated in terms of an appropriate scale in the running coupling, $\mu =\sqrt{s}/e\approx \sqrt{s}/2.7\mathrm{}$, so it can be incorporated easily in renormalization-group-improved tree-level amplitudes as well as higher-order calculations.

• Received 9 August 1996

DOI:https://doi.org/10.1103/PhysRevD.55.311