Nontrivial ghost-gluon vertex and the match of RGZ, DSE and lattice Yang-Mills propagators

TL;DR

This paper demonstrates that incorporating a non-trivial ghost-gluon vertex is essential for aligning theoretical predictions of the ghost propagator with lattice data in SU(3) Yang-Mills theory, using DSE and RGZ approaches.

Contribution

It shows the necessity of a non-trivial ghost-gluon vertex for accurate ghost propagator predictions and provides RGZ fits for the gluon propagator consistent with lattice data.

Findings

Non-trivial ghost-gluon vertex is required for compatibility with lattice data.

RGZ fits accurately reproduce gluon lattice data.

Comparison between DSE and RGZ results confirms consistency.

Abstract

Either by solving the ghost propagator DSE or through a one-loop computation in the RGZ (Refined Gribov-Zwanziger) formalism, we show that a non-trivial ghost-gluon vertex is anyhow 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 DSE and RGZ results for the ghost propagator is furthermore provided. We also briefly discuss the connection between the RGZ and the OPE $d=2$ gluon condensate.