Quark mass generation with Schwinger-Dyson equations

TL;DR

This paper reviews how Schwinger-Dyson equations are used to understand chiral symmetry breaking and dynamical quark mass generation, emphasizing the role of the quark-gluon vertex and ghost sector contributions.

Contribution

It provides a detailed analysis of the impact of the quark-gluon vertex and ghost sector on quark mass generation using coupled integral equations.

Findings

The quark-gluon vertex significantly influences the gap equation.

Ghost sector contributions are crucial for accurate quark mass predictions.

The approach recovers correct renormalization group behavior of the dynamical mass.

Abstract

In this talk, we review some of the current efforts to understand the phenomenon of chiral symmetry breaking and the generation of a dynamical quark mass. To do that, we will use the standard framework of the Schwinger-Dyson equations. The key ingredient in this analysis is the quark-gluon vertex, whose non-transverse part may be determined exactly from the nonlinear Slavnov-Taylor identity that it satisfies. The resulting expressions for the form factors of this vertex involve not only the quark propagator, but also the ghost dressing function and the quark-ghost kernel. Solving the coupled system of integral equations formed by the quark propagator and the four form factors of the scattering kernel, we carry out a detailed study of the impact of the quark gluon vertex on the gap equation and the quark masses generated from it, putting particular emphasis on the contributions directly related with the ghost sector of the theory, and especially the quark-ghost kernel. Particular attention is dedicated on the way that the correct renormalization group behavior of the dynamical quark mass is recovered, and in the extraction of the phenomenological parameters such as the pion decay constant.