Two - loop QCD corrections to qq̄ → q ′ q̄ ′ ∗

We present the two-loop virtual QCD corrections to q ¯ q → q ′ ¯ q ′ scattering 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. (DG 12-MIHT). C.A. acknowledges the financial support of the Greek government and M.E.T. acknowledges financial support from CONACyT and the CVCP. We thank the British Council and German Academic Exchange Service for support under ARC project 1050.