Abstract
We compute the three-loop corrections to the helicity amplitudes for q overline{q} → Q overline{Q} scattering in massless QCD. In the Lorentz decomposition of the scattering amplitude we avoid evanescent Lorentz structures and map the corresponding form factors directly to the physical helicity amplitudes. We reduce the amplitudes to master integrals and express them in terms of harmonic polylogarithms. The renormalised amplitudes exhibit infrared divergences of dipole and quadrupole type, as predicted by previous work on the infrared structure of multileg scattering amplitudes. We derive the finite remainders and present explicit results for all relevant partonic channels, both for equal and different quark flavours.
Highlights
Beyond next-to-next-to-leading order (NNLO), predictions at third order in the perturbative couplings, i.e. at N3LO, are known only for a handful of important LHC processes [72,73,74,75,76,77,78,79,80]
A key ingredient for the study of jet production at N3LO is provided by the virtual three-loop corrections to the scattering amplitudes for the production of two jets in massless QCD
In appendices A and B we provide some details on the structure of infrared divergences up at three loops, in particular focusing on the explicit derivation of the quadrupole terms, which appear for the first time with the scattering of at least four coloured partons at three loops
Summary
We consider the massless quark-antiquark scattering process q(p1) + q(p2) −→ Q(−p3) + Q(−p4) ,. The minus signs appearing in the final-state momenta imply that all momenta are taken to be incoming, pμ1 + pμ2 + pμ3 + pμ4 = 0 This choice is convenient when performing the required crossings to obtain all the relevant partonic channels. The variables y, z are not needed for the computation of process (2.1), but will be convenient to describe all the other processes which can be derived from it using crossing symmetry In terms of these variables the physical scattering region is given by s > 0 , t, u < 0 which imply 0 < x < 1. We indicate with CF and CA the quadratic Casimir constants They are defined through (T a)ij(T a)jk = CF δik and facdfbcd = CAδab where fabc are the structure constants.
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