The contributions of virtual corrections and soft gluon emission to the inclusive Higgs boson production cross section $p\overrightarrow{p}H+X$ are computed at next-to-next-to-leading order in the heavy top quark limit. We show that this part of the total cross section is well behaved in the sense of perturbative convergence, with the NNLO corrections amounting to an enhancement of the NLO cross section by $\sim 5\%$ for the CERN LHC and 10–20 % for the Fermilab Tevatron. We compare our results with an existing estimate of the full NNLO effects and argue that an analytic evaluation of the hard scattering contributions is needed.

• Received 20 February 2001

DOI:https://doi.org/10.1103/PhysRevD.64.013015