Two-loop Improved Truncation of the Ghost-Gluon Dyson-Schwinger Equations: Multiplicatively Renormalizable Propagators and Nonperturbative Running Coupling

Abstract

The coupled Dyson-Schwinger equations for the gluon and ghost propagators are investigated in the Landau gauge using a two-loop improved truncation that preserves the multiplicative renormalizability of the propagators. In this truncation all diagrams contribute to the leading order infrared analysis. The infrared contributions of the nonperturbative two-loop diagrams to the gluon vacuum polarization are computed analytically, and this reveals that infrared power behaved propagator solutions only exist when the squint diagram contribution is taken into account. For small momenta the gluon and ghost dressing functions behave respectively like (p^2)^{2\kappa} and (p^2)^{-\kappa}, and the running coupling exhibits a fixed point. The values of the infrared exponent and fixed point depend on the precise details of the truncation. The coupled ghost-gluon system is solved numerically for all momenta, and the solutions have infrared behaviors consistent with the predictions of the infrared analysis. For truncation parameters chosen such that \kappa=0.5, the two-loop improved truncation is able to produce solutions for the propagators and running coupling which are in very good agreement with recent lattice simulations.Comment: 41 pages, LateX; minor corrections; accepted for publication in Few-Body System