Goldstone-boson equivalence theorem and the Higgs resonance

The Goldstone-boson equivalence theorem equates the amplitude for longitudinal-vector-boson scattering to the corresponding amplitude for the scattering of the Goldstone bosons of the Rξ gauge. When the Higgs-boson width is included in the Higgs-boson propagator, this equality is apparently lost. We show that this apparent violation of the theorem is a result of making an inconsistent perturbative expansion of the amplitude. We demonstrate this for the process WL+WL-→WL+WL- both on resonance (s=mH2) and far below (s much-lt mH2). We also reformulate the scalar sector of the standard model in such a way that the equivalence theorem is manifestly upheld in the presence of a Higgs-boson width