Ruling Out a Strongly-Interacting Standard Higgs Model

Previous work has suggested that perturbation theory is unreliable for Higgs- and Goldstone-boson scattering, at energies above the Higgs mass, for relatively small values of the Higgs quartic coupling $\lambda(\mu)$. 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 mass, complementing earlier studies which excluded strong interactions at energies near the Higgs mass. The summation can be formulated in terms of an appropriate scale in the running coupling, $\mu=\sqrt{s}/e\approx\sqrt{s}/2.7$, so it can easily be incorporated in renormalization-group improved tree-level amplitudes as well as higher-order calculations.