Infrared exponent for gluon and ghost propagation in Landau gauge QCD

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 kappa. The gluon propagator is infrared finite (vanishing) for kappa=1/2 (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 kappa is directly related to the ghost-gluon vertex. Assuming that it is regular in the infrared, one obtains kappasimilar or equal to0.595. This value maximizes the critical coupling alpha(c)(kappa), yielding alpha(c)(max)similar or equal to(4pi/N-c)0.709approximate to2.97 for N-c=3. For larger kappa the vertex acquires an infrared singularity in the gluon momentum; smaller ones imply infrared singular ghost legs. Variations in alpha(c) remain within 5% from kappa=0.5 to 0.7. Above this range, alpha(c) decreases more rapidly with alpha(c)-->0(+) as kappa-->1(-) which sets the upper bound on kappa.