Infrared and ultraviolet asymptotic solutions to gluon and ghost propagators in Yang–Mills theory

Abstract

We examine the possibility that there may exist a logarithmic correction to the infrared asymptotic solution with power behavior which has recently been found for the gluon and Faddeev–Popov ghost propagators in the Landau gauge. We propose a new ansatz to find a pair of solutions for the gluon and ghost form factors by solving the coupled Schwinger–Dyson equation under a simple truncation. This ansatz enables us to derive the infrared and ultraviolet asymptotic solutions simultaneously and to understand why the power solution and the logarithmic solution is possible only in the infrared and ultraviolet limit, respectively. Even in the presence of the logarithmic correction, the gluon propagator vanishes and the ghost propagator is enhanced in the infrared limit, and the gluon–ghost–antighost coupling constant has an infrared fixed point (but with a different β function). This situation is consistent with Gribov–Zwanziger confinement scenario and color confinement criterion of Kugo and Ojima.