One-loop helicity amplitudes for all 2 -> 2 processes in QCD and N=1 supersymmetric Yang-Mills theory

Abstract

One loop corrections to the helicity amplitudes of all 2 -> 2 subprocesses are calculated in QCD and in N=1 supersymmetric Yang-Mills theory using two versions of dimensional regularization: the `t~Hooft-Veltman scheme and dimensional reduction. Studying the structure of the soft and collinear singularities, we found universal transition rules for the squared matrix element which can be used to translate the results obtained in these schemes to the results valid in the conventional dimensional regularization scheme. With explicit calculation it is demonstrated that the one loop helicity amplitudes of the 2 -> 2 subprocesses calculated using dimensional reduction in the N=1 supersymmetric $SU(N)$ gauge theory respect the supersymmetry Ward identities. Our transition rules can also be used to calculate the next-to-leading order Altarelli-Parisi kernels in the dimensional reduction scheme when they satisfy supersymmetry Ward identities as well.