Three-point vertices in Landau-gauge Yang-Mills theory

TL;DR

This paper uses lattice gauge theory simulations to analyze three-point vertices in Landau-gauge SU(2) Yang-Mills theory, revealing that ghost-gluon vertices are nearly tree-level and three-gluon vertices are suppressed or change sign at low momenta.

Contribution

It provides non-perturbative numerical results for three-point vertices in Landau-gauge SU(2) Yang-Mills theory across different dimensions and kinematic configurations.

Findings

Ghost-gluon vertex is essentially tree-level-like.

Three-gluon vertex is suppressed at intermediate momenta.

Some three-gluon-vertex tensor structures change sign at low momenta in three dimensions.

Abstract

Vertices are of central importance for constructing QCD bound states out of the individual constituents of the theory, i.e. quarks and gluons. In particular, the determination of three-point vertices is crucial in non-perturbative investigations of QCD. We use numerical simulations of lattice gauge theory to obtain results for the 3-point vertices in Landau-gauge SU(2) Yang-Mills theory in three and four space-time dimensions for various kinematic configurations. In all cases considered, the ghost-gluon vertex is found to be essentially tree-level-like, while the three-gluon vertex is suppressed at intermediate momenta. For the smallest physical momenta, reachable only in three dimensions, we find that some of the three-gluon-vertex tensor structures change sign.