Infrared exponent for gluon and ghost propagation in Landau gauge QCD

Abstract

In the covariant description of confinement, one expects the ghost correlations to be infrared enhanced. Assuming ghost dominance, the long-range behavior of gluon and ghost correlations in Landau gauge QCD is determined by one exponent \ensuremath{\kappa}. The gluon propagator is infrared finite (vanishing) for $\ensuremath{\kappa}=1/2 (\ensuremath{\kappa}>1/2)$ which is still under debate. Here, we study the critical exponent and coupling for the infrared conformal behavior from the asymptotic form of the solutions to the Dyson-Schwinger equations in an ultraviolet finite expansion scheme. The value for \ensuremath{\kappa} is directly related to the ghost-gluon vertex. Assuming that it is regular in the infrared, one obtains $\ensuremath{\kappa}\ensuremath{\simeq}0.595.$ This value maximizes the critical coupling ${\ensuremath{\alpha}}_{c}(\ensuremath{\kappa}),$ yielding ${\ensuremath{\alpha}}_{c}^{\mathrm{max}}\ensuremath{\simeq}(4\ensuremath{\pi}{/N}_{c})0.709\ensuremath{\approx}2.97$ for ${N}_{c}=3.$ For larger \ensuremath{\kappa} the vertex acquires an infrared singularity in the gluon momentum; smaller ones imply infrared singular ghost legs. Variations in ${\ensuremath{\alpha}}_{c}$ remain within 5% from $\ensuremath{\kappa}=0.5$ to $0.7.$ Above this range, ${\ensuremath{\alpha}}_{c}$ decreases more rapidly with ${\ensuremath{\alpha}}_{c}\ensuremath{\rightarrow}{0}^{+}$ as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}{1}^{\ensuremath{-}}$ which sets the upper bound on \ensuremath{\kappa}.