| Summary: | We study the soft and collinear contributions to inclusive Higgs-boson production in gluon-gluon fusion at four loops. Using recent progress for the quark and gluon form factors and Mellin moments of splitting functions, we are able to complete the soft-gluon enhanced contributions exactly in the limit of a large number of colours, and to a sufficiently accurate numerical accuracy for QCD. The four-loop soft and virtual contributions increase the QCD cross section at 14 TeV by 2.7% and 0.2% for the standard choices μR=mH and μR=mH/2 of the renormalization scale, and reduce the scale uncertainty to below ±3%. As by-products, we derive the complete δ(1−x) term for the gluon-gluon splitting function at four loops and its purely Abelian contributions at five loops, and provide a numerical result for the single pole of the four-loop gluon form factor in dimensional regularization. Finally we present the closely related fourth-order coefficients D4 for the soft-gluon exponentiation of Higgs-boson and Drell-Yan lepton-pair production.
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