Consequences Of Fully Dressing Quark-Gluon Vertex Function With Two-Point Gluon Lines

TL;DR

This paper investigates how fully dressing the quark-gluon vertex with two-point gluon lines influences the solutions of the Dyson-Schwinger equation for the quark propagator, highlighting the importance of additional diagrams.

Contribution

It introduces a comprehensive construction of the quark-gluon vertex including all two-point gluon line diagrams, emphasizing their significant impact on DSE solutions.

Findings

Additional diagrams with crossed gluon lines significantly affect the quark propagator solutions.

The inclusion of these diagrams alters the infrared behavior of the solutions.

Color factors and diagram proliferation amplify their importance.

Abstract

We extend recent studies of the effects of quark-gluon vertex dressing upon the solutions of the Dyson-Schwinger equation for the quark propagator. A momentum delta function is used to represent the dominant infrared strength of the effective gluon propagator so that the resulting integral equations become algebraic. The quark-gluon vertex is constructed from the complete set of diagrams involving only 2-point gluon lines. The additional diagrams, including those with crossed gluon lines, are shown to make an important contribution to the DSE solutions for the quark propagator, because of their large color factors and the rapid growth in their number.