Non-perturbative Landau gauge and infrared critical exponents in QCD

TL;DR

This paper investigates the non-perturbative Landau gauge in QCD, deriving infrared critical exponents for gluon and ghost propagators using Schwinger-Dyson equations, and discusses the implications of Gribov's horizon prescription.

Contribution

It introduces a non-perturbative Landau gauge formulation incorporating Gribov horizon effects and computes infrared critical exponents in various dimensions.

Findings

Infrared exponents for gluon and ghost propagators in d=2,3,4 dimensions.

Two solutions for critical exponents in 4D QCD.

Non-perturbative Landau gauge includes a correction term for Gribov copies.

Abstract

We discuss Faddeev-Popov quantization at the non-perturbative level and show that Gribov's prescription of cutting off the functional integral at the Gribov horizon does not change the Schwinger-Dyson equations, but rather resolves an ambiguity in the solution of these equations. We note that Gribov's prescription is not exact, and we therefore turn to the method of stochastic quantization in its time-independent formulation, and recall the proof that it is correct at the non-perturbative level. The non-perturbative Landau gauge is derived as a limiting case, and it is found that it yields the Faddeev-Popov method in Landau gauge with a cut-off at the Gribov horizon, plus a novel term that corrects for over-counting of Gribov copies inside the Gribov horizon. Non-perturbative but truncated coupled Schwinger-Dyson equations for the gluon and ghost propagators $D(k)$ and $G(k)$ in Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by $D(k) \sim 1/(k^2)^{1 + a_D}$ and $G(k) \sim 1/(k^2)^{1 + a_G}$ are obtained in space-time dimensions $d = 2, 3, 4$. Two possible solutions are obtained with the values, in $d = 4$ dimensions, $a_G = 1, a_D = -2$, or $ a_G = [93 - (1201)^{1/2}]/98 \approx 0.595353, a_D = - 2a_G$.