Ghost dynamics from Schwinger-Dyson equations

TL;DR

This paper solves coupled Schwinger-Dyson equations for ghost functions in QCD, combining lattice data and approximations, achieving results that match lattice data and highlight the importance of artifact removal.

Contribution

It introduces a novel combined approach using lattice data and STI-derived ansatz to solve coupled ghost and vertex equations, providing new insights into ghost dynamics.

Findings

Excellent agreement with lattice data for ghost functions

Identification of the three-gluon vertex's quantitative impact

Validation of approximations through consistency checks

Abstract

We discuss the coupled dynamics of the ghost dressing function and the ghost-gluon vertex through the Schwinger-Dyson equations that they satisfy. In order to close the system of equations, we combine recent lattice data for the gluon propagator and an approximate STI-derived Ansatz for the general kinematics three-gluon vertex. The numerical solution of the resulting coupled system exhibits excellent agreement to lattice data, for both the ghost dressing function and the ghost-gluon vertex, and allows the determination of the coupling constant. Next, in the soft gluon limit the full three-gluon vertex appearing in the ghost-gluon equation reduces to a special projection that is tightly constrained by lattice simulations. Specializing the ghost-gluon Schwinger-Dyson equation to this limit provides a nontrivial consistency check on the approximations employed for the three-gluon interaction and shows that the latter has an important quantitative effect on the ghost-gluon vertex. Finally, our results stress the importance of eliminating artifacts when confronting lattice data with continuum predictions.