On the validity of the effective W approximation

Abstract

We analyze the validity of the effective W approximation in the standard model under the conditions appropriate to a search for a very heavy Higgs boson at the SSC. Specifically, we consider the cross section for the inclusive reaction pp→WWX when the transverse momenta of the produced W's are of the order of the Higgs boson mass and each of these are very large compared to the W boson mass. We point out that the potential problem of bad off-shell behavior of the WW scattering amplitude is gauge dependent and can be avoided by the use of axial gauge. We give a derivation of the effective W approximation, with a corresponding definition of the gauge boson distribution functions. We conclude that the approximation is valid up to corrections of order m 2 W M 2 H − and also corrections of order α s ( m W) to the lowest order calculation of the gauge boson distribution functions. We work to all orders in soft QCD corrections but to lowest order in the electroweak coupling g. The conclusions are established in the most detail at lowest order in the Higgs sector coupling λ, but it appears that the approximation remains valid to all orders in λ, as is needed if the Higgs boson is so large that the Higgs sector is strongly interacting.