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

TL;DR

The paper computes all one-loop helicity amplitudes for 2→2 parton processes in QCD and N=1 SUSY Yang-Mills theory under three dimensional-regulation schemes (HV, DR, and 4D helicity). It develops universal transition rules to translate results to the conventional dimensional regularization scheme, enabling use with standard parton densities and PDFs. It explicitly verifies supersymmetry Ward identities in DR and demonstrates restoration in HV via finite renormalization, reinforcing the consistency of these regulators. Additionally, it derives and tests the scheme-dependent shifts in the next-to-leading order Altarelli-Parisi kernels, linking regulator choices to observable cross sections through factorization and renormalization, with practical guidance for phenomenology.

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.