An approximation for NLO single Higgs boson inclusive transverse momentum distributions in hadron-hadron collisions

In the framework of the gluon-gluon fusion process for Higgs boson production there are two different prescriptions. They are given by the exact process where the gluons couple via top-quark loops to the Higgs boson and by the approximation where the top-quark mass mt is taken to infinity. In the latter case the coupling of the gluons to the Higgs boson is described by an effective Lagrangian. Both prescriptions have been used for the 2→2 body reactions to make predictions for Higgs boson production at hadron colliders. In next-to-leading order only the effective Lagrangian approach has been used to compute the single particle inclusive distributions. The exact computation of the latter has not been done yet because the n-dimensional extensions of 2→3 processes are not calculated and the two-loop virtual corrections are still missing. To remedy this we replace wherever possible the Born cross sections in the asymptotic top-quark mass limit by their exact analogues. These cross sections appear in the soft and virtual gluon contributions to the next-to-leading order distributions. This approximation is inspired by the fact that soft-plus-virtual gluons constitute the bulk of the higher order correction. Deviations from the asymptotic top-quark mass limit are discussed.