On the Quark-Gluon Vertex and Quark-Ghost Kernel: combining Lattice Simulations with Dyson-Schwinger equations

TL;DR

This paper combines lattice QCD simulations with Dyson-Schwinger equations to model the quark-gluon vertex, revealing a strong enhancement at low momenta and achieving a mass function consistent with lattice results.

Contribution

It introduces a novel combined approach using a generalized Ball-Chiu ansatz and regularization methods to better understand the quark-gluon vertex in QCD.

Findings

Compatible form factors from two numerical methods.

Strong vertex enhancement below 1 GeV.

Mass function aligns with lattice data.

Abstract

We investigate the dressed quark-gluon vertex combining two established non-perturbative approaches to QCD: the Dyson-Schwinger equation (DSE) for the quark propagator and lattice-regularized simulations for the quark, gluon and ghost propagators. The vertex is modeled using a generalized Ball-Chiu ansatz parameterized by a single form factor $\tilde X_0$ which effectively represents the quark-ghost scattering kernel. The solution space of the DSE inversion for $\tilde X_0$ is highly degenerate, which can be dealt with by a numerical regularization scheme. We consider two possibilities: (i) linear regularization and (ii) the Maximum Entropy Method. These two numerical approaches yield compatible $\tilde X_0$ functions for the range of momenta where lattice data is available and feature a strong enhancement of the generalized Ball-Chiu vertex for momenta below 1 GeV. Our ansatz for the quark-gluon vertex is then used to solve the quark DSE which yields a mass function in good agreement with lattice simulations and thus provides adequate dynamical chiral symmetry breaking.