Abstract
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.
Highlights
We study the soft and collinear (SV) contributions to inclusive Higgs-boson production in gluongluon fusion at four loops
We present the corresponding expression for the Drell-Yan (DY) process, pp → γ∗ + X, which is closely related to the gluon-gluon fusion (ggF) process in the threshold limit, and the N4LL soft-gluon exponentiation coefficient D4 for both processes
As by-products, we obtain a complete result for the so-called gluon virtual anomalous dimension, i.e. the δ(1−z) terms of the gluon-gluon splitting function at four loops in Quantum Chromodynamics (QCD), together with partial information at five loops, and we derive a numerical result for the single pole 1/ε of the dimensionally regulated gluon form factor at four loops
Summary
We study the soft and collinear (SV) contributions to inclusive Higgs-boson production in gluongluon fusion at four loops. The observed relation between the gluon virtual anomalous dimension Bng and the corresponding coefficient of the β-function for purely Abelian terms leads to new predictions at five loops.
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