The ghost-gluon vertex in Hamiltonian Yang-Mills theory in Coulomb gauge

TL;DR

This paper solves the Dyson-Schwinger equation for the ghost-gluon vertex in Hamiltonian Yang-Mills theory within Coulomb gauge, revealing an IR finite but IR enhanced vertex compared to the bare one, based on non-perturbative propagators.

Contribution

It provides a one-loop level solution for the ghost-gluon vertex using non-perturbative propagators from a variational approach in Coulomb gauge.

Findings

The ghost-gluon vertex is IR finite.

The vertex is IR enhanced by 15-25%.

Results depend on the kinematical momentum regime.

Abstract

The Dyson-Schwinger equation for the ghost-gluon vertex of the Hamiltonian approach to Yang-Mills theory in Coulomb gauge is solved at one-loop level using as input the non-perturbative ghost and gluon propagators previously determined within the variational approach. The obtained ghost-gluon vertex is IR finite but IR enhanced compared to the bare one by 15% to 25%, depending on the kinematical momentum regime.