EQUIVALENCE THEOREM REDUX

The equivalence theorem states that amplitudes involving longitudinal vector bosons are equal to those with the corresponding unphysical scalars in the limit MW2s0. There are two ways to approach this limit, depending on whether MWMH'0 or MH2s'0. We show that the theorem has a different physical interpretation in each limit, but its validity in both depends only on the wave-function renormalization of the unphysical Goldstone bosons. We derive a condition that the renormalization parameters must satisfy in order for the theorem to hold. We show that this condition is satisfied in the first limit, appropriate to the heavy-Higgs-boson regime, if momentum subtraction at a scale mMH is used. With this prescription, the theorem is true to lowest nonzero order in g and to all orders in the Higgs-boson coupling. © 1990 The American Physical Society.