Regularization Scheme Independence and Unitarity in QCD Cross Sections

TL;DR

The paper analyzes how next-to-leading order QCD cross sections can be made independent of the choice of infrared regularization scheme, provided the scheme is unitary. It introduces the dipole subtraction formalism to isolate scheme-dependent pieces and derives a universal master function ${\\cal F}(\\{p\\})$ whose finiteness and scheme-independence ensure overall unitarity. By relating the regularization dependence to the Altarelli--Parisi splitting functions and their dimensional regularization variants, the authors provide explicit rules to transition between schemes without performing loop calculations. The framework not only guarantees RS independence of physical observables but also offers a practical, process-independent recipe to maintain unitarity across different regularization prescriptions. These insights pave the way for reliable cross-section computations in alternative schemes and set the stage for future NNLO extensions and potential numerical approaches that bypass explicit loop evaluations.

Abstract

When calculating next-to-leading order QCD cross sections, divergences in intermediate steps of the calculation must be regularized. The final result is independent of the regularization scheme used, provided that it is unitary. In this paper we explore the relationship between regularization scheme independence and unitarity. We show how the regularization scheme dependence can be isolated in simple universal components, and how unitarity can be guaranteed for any regularization prescription that can consistently be introduced in one-loop amplitudes. Finally, we show how to derive transition rules between different schemes without having to do any loop calculations.