Radiative corrections to the effective approximation

We derive the O(αs) corrections to the W and Z gauge boson distribution functions in the effective W approximation. The QCD radiative corrections are calculated in the soft gluon limit which correctly gives the terms of O(αsπ). We compare the radiatively corrected rates for Higgs production from vector boson fusion and for the background from the qanti q → W+W- subprocess. In the soft gluon limit, the Higgs signal is unchanged by O(αs) corrections, while the calculation of Barger, Lopez and Putikka finds that the background from qanti q → W+W- is increased by a factor of 1+8/9αsπ. (orig.)