Infrared-suppressed gluon propagator in 4d Yang-Mills theory in a Landau-like gauge

Abstract

The infrared behavior of the gluon propagator is directly related to confinement in QCD. Indeed, the Gribov-Zwanziger scenario of confinement predicts an infrared vanishing (transverse) gluon propagator in Landau-like gauges, implying violation of reflection positivity and gluon confinement. Finite-volume effects make it very difficult to observe (in the minimal Landau gauge) an infrared suppressed gluon propagator in lattice simulations of the four-dimensional case. Here we report results for the SU(2) gluon propagator in a gauge that interpolates between the minimal Landau gauge (for gauge parameter lambda equal to 1) and the minimal Coulomb gauge (corresponding to lambda = 0). For small values of lambda we find that the spatially-transverse gluon propagator D^tr(0,|\vec p|), considered as a function of the spatial momenta |\vec p|, is clearly infrared suppressed. This result is in agreement with the Gribov-Zwanziger scenario and with previous numerical results in the minimal Coulomb gauge. We also discuss the nature of the limit lambda -> 0 (complete Coulomb gauge) and its relation to the standard Coulomb gauge (lambda = 0). Our findings are corroborated by similar results in the three-dimensional case, where the infrared suppression is observed for all considered values of lambda.Comment: 5 pages, 2 figures, one figure with additional results and extended discussion of some aspects of the results added and some minor clarifications. In v3: Various small changes and addition