One-loop QCD corrections to quark scattering at NNLO

TL;DR

The paper delivers analytic NNLO virtual corrections for massless 2→2 quark scattering by calculating the interference of one-loop amplitudes with themselves, completing the virtual piece when combined with existing two-loop–tree contributions. Using conventional dimensional regularization and an MSbar renormalization, the authors reduce one-loop integrals to two master integrals, Box$^6$ and Bub, enabling a clean separation of infrared poles and a full epsilon expansion across kinematic regions. They present explicit expressions for the like and unlike quark channels (A^{8(1x1)} and B^{8(1x1)}) and verify that the infrared structure matches Catani’s predictions, including a detailed accounting of finite parts. Together with known two-loop results, these findings complete the 2→2 massless quark–quark virtual corrections at NNLO, facilitating precise phenomenology and cross-channel extrapolations.

Abstract

We present the O(as^4) virtual QCD corrections to unlike-quark and like-quark scattering due to the interference of one-loop amplitudes with one-loop amplitudes. The structure of the infrared divergences agrees with that predicted by Catani. The results are expressed in an analytic form so that the relevant expressions for crossed scattering processes can be obtained in a straightforward manner. The one-loop contributions presented here, together with the interference of tree with two-loop amplitudes given recently, complete the 2 to 2 virtual QCD corrections at NNLO for the massless quark scattering processes.