Nontrivial ghost-gluon vertex and the match of the Refined-Gribov-Zwanziger, Dyson-Schwinger equations, and lattice Yang-Mills propagators

Abstract

Either by solving the ghost propagator Dyson-Schwinger equations or through a one-loop computation in the refined Gribov-Zwanziger (RGZ) formalism, we show that a nontrivial ghost-gluon vertex is required to obtain a ghost propagator prediction compatible with the available corresponding lattice data in the SU(3) case. For the necessary gluon propagator input, we present RGZ tree-level fits which account well for the gluon lattice data. Interestingly, this propagator can be rewritten in terms of a running gluon mass. A comparison of both Dyson-Schwinger equations and RGZ results for the ghost propagator is furthermore provided. We also briefly discuss the connection between the RGZ and the operator product expansion d=2 gluon condensate.