Abstract
An analytical expression for the three-loop form factors for ggH and γγH is derived for the contributions which involve massless quark loops. The result is expressed in terms of harmonic polylogarithms. It fully agrees with previously obtained kinematical expansions, and confirms a recent semi-numerical approximation which extends over the full kinematic range.
Highlights
Section is still a reduction by about 6%
The total cross section at NNLO requires the inclusion of three-loop virtual corrections to the ggH amplitude, two-loop corrections to singlereal emission, and the one-loop double-real emission contributions which occur for the first time at this order
After estimates based on 1/mt expansions of the cross section which indicated a break-down of this approximation for p⊥ 150 GeV [15, 16], it came as a surprise to find the K-factor of the exact calculation to be fairly independent of p⊥ [12, 13]. This provides yet another indication that for the total cross section, the QCD corrections are well described by their heavy-top limit
Summary
The amplitude for the processes ggH and γγH can be parameterized with the momenta q1,2 of the two external vector bosons as. Because of the trivial color structure in eq (2.1a) which can be projected out using (δab/NA)Maggb;Hμν, where NA is the number of gauge generators, we ignore the color structure in the following and focus only on the Lorentz structure of the amplitudes. Since gluons and photons do not directly couple to the Higgs boson, the Feynman diagrams contributing to the ggH and γγH amplitudes always involve at least one closed massive quark loop if higher orders in the electroweak coupling are neglected.
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