Four-particle scattering amplitudes in QCD at NNLO to higher orders in the dimensional regulator

Abstract

We compute all helicity amplitudes for four-particle scattering in massless QCD with $n_f$ fermion flavours to next-to-next-to-leading order (NNLO) in perturbation theory. In particular, we consider all possible configurations of external quarks and gluons. We evaluate the amplitudes in terms of a Laurent series in the dimensional regulator to the order required for future next-to-next-to-next-to-leading order (N${}^3$LO) calculations. The coefficients of the Laurent series are given in terms of harmonic polylogarithms that can readily be evaluated numerically. We present our findings in the conventional dimensional regularisation and in the t'Hooft-Veltman schemes.

22 pages, 3 figures, Journal Version, Fixed some typos

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• Three-loop helicity amplitudes for quark-gluon scattering in QCD
• The gluon Regge trajectory at three loops from planar Yang-Mills theory
• Three-loop soft function for energetic electroweak boson production at hadron colliders
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Three-loop helicity amplitudes for four-quark scattering in massless QCD