No abstract

We study the infrared behaviour of the pure Yang-Mills correlators using relations that are well defined in the non-perturbative domain. These are the Slavnov-Taylor identity for three-gluon vertex and the Schwinger-Dyson equation for ghost propagator in the Landau gauge. We also use several inputs from lattice simulations. We show that lattice data are in serious conflict with a widely spread analytical relation between the gluon and ghost infrared critical exponeessencnts. We conjecture that this is explained by a singular behaviour of the ghost-ghost-gluon vertex function in the infrared. We show that, anyhow, this discrepancy is not due to some lattice artefact since lattice Green functions satisfy the ghost propagator Schwinger-Dyson equation. We also report on a puzzle concerning the infrared gluon propagator: lattice data seem to favor a constant non vanishing zero momentum gluon propagator, while the Slavnov-Taylor identity (complemented with some regularity hypothesis of scalar functions) implies that it should diverge.

We study the flavorless gluon propagator in the Landau gauge from high statistics lattice calculations. Hypercubic artifacts are efficiently eliminated by taking the ͚ p 4 →0 limit. The propagator is fitted to the three-loops perturbative formula in an energy window ranging from ϳ2.5 GeV up to ϳ5.5 GeV. ␣ s is extracted from the best fit in a continuous set of renormalization schemes. The fits are very good, with a 2 per DOF smaller than 1. We propose a more stringent test of asymptotic scaling based on scheme independence of the resulting ⌳ MS . This method shows that asymptotic scaling at three loops is not reached by the gluon propagator although we use rather large energies. We are only able to obtain an effective flavorless three-loops estimate ⌳ MS (3) ϭ353Ϯ2 Ϫ10 ϩ25 MeV. We argue that the real asymptotic value for ⌳ MS should plausibly be smaller.