Abstract
We compute in conventional dimensional regularisation the tree-level splitting amplitudes for a quark parent in the limit where four partons become collinear to each other. This is part of the universal infrared behaviour of the QCD scattering amplitudes at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant. Further, we consider the iterated limit when m′ massless partons become collinear to each other within a bigger set of m collinear partons, as well as the limits when one gluon or a q overline{q} pair or two gluons become soft within a set of m collinear partons.
Highlights
The inclusive Higgs production cross section is known at next-to-leading order (NLO) [5, 6] in the strong coupling constant αs of perturbative QCD, with full heavy-quark mass dependence
In the limit in which the heavy-quark mass is much larger than the other scales in the process, i.e. by replacing the loop-mediated Higgs-gluon coupling by a tree-level effective coupling, which is often termed Higgs Effective Field Theory (HEFT), inclusive Higgs production from gluon fusion is known at next-to-next-to-next-to-leading order (N3LO) [7, 8], whose accuracy has reached the 5% level [9]
The next-to-largest production mode of the Higgs boson in hadron collisions is from vector-boson fusion, for which inclusive Higgs [10] and double-Higgs [11] production are known at N3LO in the deep inelastic scattering (DIS) approximation
Summary
The aim of this paper is to study the behaviour of tree-level QCD amplitudes in the limit where a certain number of massless partons become collinear. This naive counting seems to be at odds with the fact that a set of m light-like momenta (that do not sum up to zero) depend on (D −1)m degrees of freedom This apparent conundrum is resolved upon noting that the collinear limit is invariant under longitudinal boosts in the direction of the parent momentum P =. The quantity Pfs1s.′..fm in eq (2.6) is the (polarised) splitting amplitude for the squared matrix element It depends on the transverse momenta k⊥i and momentum fractions zi of the particles in the collinear set as well as the spin indices of the parent. We could alternatively have defined an explicitly transverse splitting amplitude by replacing gμν by −dμν(P , n) in eq (2.23), at the price of introducing terms proportional to the gauge vector n that cancel when contracted with a transverse quantity
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