Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD

Abstract

We present the analytic form of all leading-color two-loop five-parton helicity amplitudes in QCD. The results are analytically reconstructed from exact numerical evaluations over finite fields. Combining a judicious choice of variables with a new approach to the treatment of particle states in $D$ dimensions for the numerical evaluation of amplitudes, we obtain the analytic expressions with a modest computational effort. Their systematic simplification using multivariate partial-fraction decomposition leads to a particularly compact form. Our results provide all two-loop amplitudes required for the calculation of next-to-next-to-leading order QCD corrections to the production of three jets at hadron colliders in the leading-color approximation.

v2: Minor text changes, matches published version

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Cited by in corpus (5)

• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• NNLO QCD corrections to three-photon production at the LHC
• Multi-Quark Colour Decompositions from Unitarity
• Color Dressed Unitarity and Recursion for Yang-Mills Two-Loop All-Plus Amplitudes
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes