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.
Highlights
Straightforward to set up and oftentimes more stable and efficient than the purely numerical approach
We present the analytic form of all leading-color two-loop five-parton helicity amplitudes in QCD
In this article we present the analytic expressions of the two-loop five-parton QCD amplitudes in the leading-color approximation
Summary
Straightforward to set up and oftentimes more stable and efficient than the purely numerical approach. Numerical algorithms were combined with functional reconstruction techniques [10] resulting in analytic expressions for the planar two-loop five-gluon single-minus helicity amplitude [11] and for all two-loop five-gluon helicity amplitudes [12] These calculations rely on the availability of the planar two-loop five-point master integrals, which have been given in refs. This is achieved by exploiting the analytic structure of amplitudes with five external massless partons in order to obtain target functions which are rational functions of Mandelstam variables This has a dramatic impact in reducing the degree of the multivariate polynomials that we reconstruct, allowing us to obtain all analytic expressions with a modest computational effort
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