  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.

High Energy Physics - Phenomenology