Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity

TL;DR

This paper presents a comprehensive numerical unitarity-based calculation of two-loop five-parton amplitudes in QCD, crucial for precise three-jet production predictions at hadron colliders.

Contribution

It introduces a method to compute two-loop five-parton amplitudes with external fermions using a numerical unitarity approach and integrand decomposition, advancing precision in QCD calculations.

Findings

Successfully computed all independent five-parton amplitudes

Validated results by recomputing four-parton amplitudes

Included contributions with massless closed fermion loops

Abstract

We compute a complete set of independent leading-color two-loop five-parton amplitudes in QCD. These constitute a fundamental ingredient for the next-to-next-to-leading order QCD corrections to three-jet production at hadron colliders. We show how to consistently consider helicity amplitudes with external fermions in dimensional regularization, allowing the application of a numerical variant of the unitarity approach. Amplitudes are computed by exploiting a decomposition of the integrand into master and surface terms that is independent of the parton type. Master integral coefficients are numerically computed in either finite-field or floating-point arithmetic and combined with known analytic master integrals. We recompute two-loop leading-color four-parton amplitudes as a check of our implementation. Results are presented for all independent four- and five-parton processes including contributions with massless closed fermion loops.