A Gribov equation for the photon Green's function

TL;DR

This paper derives a Gribov equation for the photon and gluon Green's functions, enabling non-perturbative analysis of their running couplings in QCD and QED, revealing singularities and decoupling behaviors.

Contribution

It introduces a novel derivation of the Gribov equation based on the second derivative of a gauge-invariant quantity, allowing non-perturbative insights into gauge boson dynamics.

Findings

QCD coupling exhibits a space-like singularity indicating super-criticality.

QED coupling shows a Q^2 behavior in the UV, leading to photon decoupling.

The approach connects Gribov's confinement scenario with non-perturbative Green's function analysis.

Abstract

We present a derivation of the Gribov equation for the gluon/photon Green's function D(q). Our derivation is based on the second derivative of the gauge-invariant quantity Tr ln D(q), which we interpret as the gauge-boson `self-loop'. By considering the higher-order corrections to this quantity, we are able to obtain a Gribov equation which sums the logarithmically enhanced corrections. By solving this equation, we obtain the non-perturbative running coupling in both QCD and QED. In the case of QCD, alpha_S has a singularity in the space-like region corresponding to super-criticality, which is argued to be resolved in Gribov's light-quark confinement scenario. For the QED coupling in the UV limit, we obtain a \propto Q^2 behaviour for space-like Q^2=-q^2. This implies the decoupling of the photon and an NJLVL-type effective theory in the UV limit.