Two-loop QCD corrections to the scattering of massless distinct quarks

TL;DR

This paper delivers the two-loop QCD corrections for massless 2->2 quark scattering in conventional dimensional regularisation and the $\overline{\rm MS}$ scheme, providing the infrared pole structure in agreement with Catani's predictions and the full finite remainders for the $s$-, $t$-, and $u$-channel processes in analytic form. The finite parts are expressed in terms of polylogarithms up to weight 4 using a basis based on $x=-t/s$ and $y=-u/s$, enabling precise NNLO predictions for jet production in hadron collisions. These results constitute a critical ingredient for next-to-next-to-leading order jet cross sections and must be combined with real-emission contributions and PDF evolution to yield physical observables; the work also cross-checks the QED limit against BDG as a consistency test. Overall, the study advances the theoretical precision of QCD predictions relevant for high-energy collider phenomenology.

Abstract

We present the two-loop virtual QCD corrections to the scattering of massless distinct quarks in conventional dimensional regularisation. The structure of the infrared divergences agrees with that predicted by Catani while expressions for the finite remainder are given for each of the s-, t- and u-channels in terms of polylogarithms. The results presented here form a vital part of the next-to-next-to-leading order contribution to inclusive jet production in hadron colliders and will play a crucial role in improving the theoretical prediction for jet cross sections in hadron-hadron collisions.