Infrared Behavior of 3-Point Functions in Landau Gauge Yang-Mills Theory

TL;DR

This paper analytically investigates the infrared behavior of three-gluon and ghost-gluon vertices in Landau gauge Yang-Mills theory, revealing uniform and asymmetric divergences and expanding the understanding of infrared fixed points.

Contribution

It provides an analytical determination of the momentum dependence of vertex dressing functions and identifies additional infrared singularities at asymmetric momentum configurations.

Findings

Identified uniform infrared divergence in vertex functions.

Discovered additional singularities at asymmetric momentum points.

Results consistent across two and three dimensions.

Abstract

The three-gluon and ghost-gluon vertices of Landau gauge Yang-Mills theory are investigated in the low momentum regime. Due to ghost dominance in the infrared we can use the known power law behavior for the propagators to determine analytically the complete momentum dependence of the dressing functions. Besides a uniform, i. e. all momenta going to zero, divergence, we find additional singularities, if one momentum alone goes to zero, while the other two remain constant. At these asymmetric points we can extract additional infrared exponents, which corroborate previous results and expand the known fixed point solution of Landau gauge Yang-Mills theory, where the uniform infrared exponents for all vertex functions are known. Calculations in two and three dimensions yield qualitatively similar results.