Two-loop off-shell QCD amplitudes in FDR

TL;DR

This paper establishes a connection between FDR and dimensional regularization in QCD up to two loops, providing translation tools for renormalization schemes and fixing issues in the FDH method to maintain QCD's renormalizability.

Contribution

It introduces a method to relate FDR to dimensional regularization in QCD at two loops and proposes a fix for FDH to preserve renormalizability beyond one loop.

Findings

Derived coupling constant and quark mass shifts for FDR to MSbar translation.

Solved unitarity issues in FDH beyond one loop.

Presented a renormalizability-preserving fix for FDH.

Abstract

We link the FDR treatment of ultraviolet (UV) divergences to dimensional regularization up to two loops in QCD. This allows us to derive the one-loop and two-loop coupling constant and quark mass shifts necessary to translate infrared finite quantities computed in FDR to the MSbar renormalization scheme. As a by-product of our analysis, we solve a problem analogous to the breakdown of unitarity in the Four Dimensional Helicity (FDH) method beyond one loop. A fix to FDH is then presented that preserves the renormalizability properties of QCD without introducing evanescent quantities.