Higher-order soft corrections to lepton pair and Higgs boson production

Utilizing recent three-loop results on the quark and gluon splitting functions and form factors, we derive the complete threshold-enhanced third-order (N3LO) QCD corrections to the total cross sections for the production of lepton pairs and the Higgs boson in hadron collisions. These results, for the latter case obtained in the heavy top-quark limit, are employed to extend the threshold resummation for these processes to the fourth logarithmic order. We investigate the numerical impact of the higher-order corrections for Higgs boson production at the Tevatron and the LHC. Our results, suitably treated in Mellin N-space, provide a sufficiently accurate approximation to the full N3LO contributions. Corrections of about 5% at the LHC and 10% at the Tevatron are found for typical Higgs masses. The N3LO predictions exhibit a considerably reduced dependence on the renormalization scale with, for the first time, stationary points close to the Higgs mass.