A Gribov equation for the photon Green's function

Details A Gribov equation for the photon Green's function A Gribov equation for the photon Green's function

2008-05-09

arxiv.org/abs/0805.1382v3

Eur.Phys.J.C65:181-193,2010

Physics

High Energy Physics

High Energy Physics - Phenomenology

12 pages, 5 figures; version to be published in Eur. Phys. J. C

Scientific paper

10.1140/epjc/s10052-009-1188-7

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.

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