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

TL;DR

The article delivers complete two-loop helicity amplitudes for quark-quark and quark-antiquark scattering in QCD, along with gluino-gluino amplitudes in ${ m N}=1$ SYM, in both HV and FDH schemes. It implements Catani's infrared subtraction to obtain finite remainders and analyzes scheme dependence, providing explicit all-orders-in-$oldsymbol{ extepsilon}$ one-loop results and sophisticated two-loop finite remainders expressed in terms of color structures, logs, and polylogarithms. The work also investigates ambiguities in $D$-dimensional Dirac algebra, showing that, with consistent prescriptions, the finite remainders are free of these ambiguities and, in the FDH scheme, satisfy supersymmetry Ward identities. The results support precise NNLO QCD jet predictions and demonstrate the FDH scheme’s compatibility with SUSY constraints, with potential applications in polarized jet production and NNLO Monte Carlo implementations.

Abstract

We present the two-loop QCD helicity amplitudes for quark-quark and quark-antiquark scattering. 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 and present the scheme dependence of the results. We verify that the finite remainder, after subtracting the divergences using Catani's formula, are in agreement with previous results. We also provide the amplitudes for gluino-gluino scattering in pure N=1 supersymmetric Yang-Mills theory. We describe ambiguities in continuing the Dirac algebra to D dimensions, including ones which violate fermion helicity conservation. The finite remainders after subtracting the divergences using Catani's formula, which enter into physical quantities, are free of these ambiguities. We show that in the FDH scheme, for gluino-gluino scattering, the finite remainders satisfy the expected supersymmetry Ward identities.