Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory

TL;DR

This work delivers the complete two-loop helicity amplitudes for quark-gluon scattering and quark-antiquark annihilation to gluons in QCD, along with corresponding gluino-gluon amplitudes in pure N=1 SYM. The authors provide results in both HV and FDH dimensional regularization schemes and establish explicit scheme-conversion rules, grounded in Catani’s infrared-factorization framework. They present all-orders-in-ε one-loop amplitudes, finite two-loop remainders, and detailed color-helicity decompositions, with cross-checks against existing CDR results. The FDH scheme is shown to preserve supersymmetry Ward identities at two loops, and the HV results are shown to be consistent with prior HV/CDR results, enabling robust NNLO jet predictions and SUSY-consistency tests.

Abstract

We present the two-loop QCD helicity amplitudes for quark-gluon scattering, and for quark-antiquark annihilation into two gluons. These amplitudes are relevant for next-to-next-to-leading order corrections to (polarized) jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity (FDH) variants of dimensional regularization. The transition rules for converting the amplitudes between the different variants are much more intricate than for the previously discussed case of gluon-gluon scattering. Summing our two-loop expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Anastasiou, Glover, Oleari and Tejeda-Yeomans. We describe the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric Yang-Mills theory, obtained from the QCD amplitudes by modifying the color representation and multiplicities, and verify supersymmetry Ward identities in the FDH scheme.