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 $m_t$ 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 $2 to 2$ 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 $2 to 3$ 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.