One-loop QCD amplitudes in the Feynman-Diagram gauge

TL;DR

This paper computes one-loop QCD scattering amplitudes in the Feynman-Diagram gauge, revealing unique ghost behavior and UV singularities, and demonstrates how to recover known amplitudes through specific corrections.

Contribution

It introduces a novel approach to calculating one-loop QCD amplitudes in the Feynman-Diagram gauge, highlighting non-decoupling ghosts and UV singularities, and shows how to obtain standard results.

Findings

Non-decoupling of Faddeev-Popov ghosts in FD gauge

Presence of non-conventional UV singularities

Recovery of known QCD amplitudes after corrections

Abstract

Scattering amplitudes for the massless QCD process, $q\bar{q}\to q^\prime\bar{q}^\prime$, are calculated in the one-loop order in the Feynman-Diagram (FD) gauge, where gluons are quantized on the light cone with opposite direction of the three-momenta. We find non-decoupling of the Faddeev-Popov ghosts and non-conventional UV singularities in dimensional regularization. The known QCD amplitudes with asymptotic freedom are reproduced only after summing propagator and vertex corrections. By quantizing gluons in the Feynman gauge on the FD gauge background, we obtain the one-loop improved FD gauge amplitudes.