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

TL;DR

This paper analytically investigates the low-momentum behavior of three-point functions in Landau gauge Yang-Mills theory, revealing scaling and kinematic divergences with implications for infrared dynamics.

Contribution

It provides explicit hypergeometric series solutions for three-gluon and ghost-gluon vertices, including their divergences and kinematic dependencies, extending to various dimensions and ghost exponents.

Findings

Identification of scaling behavior in vertices

Discovery of additional kinematic divergences

Dependence of dressing functions on kinematic configurations

Abstract

Analytic solutions for the three-gluon and ghost-gluon vertices in Landau gauge Yang-Mills theory at low momenta are presented in terms of hypergeometric series. They do not only show the expected scaling behavior but also additional kinematic divergences when only one momentum goes to zero. These singularities, which have also been proposed previously, induce a strong dependence on the kinematics in many dressing functions. The results are generalized to two and three dimensions and a range of values for the ghost propagator's infrared exponent kappa.