A Numerical Approach to Coulomb Gauge QCD

TL;DR

This paper introduces a numerical method to study Coulomb gauge QCD by calculating the ghost two-point function with Monte Carlo integration, exploring the behavior of the coupling constant and Coulomb potential.

Contribution

It presents a new numerical approach that extends previous analytic studies, enabling analysis of the ghost propagator and Coulomb potential without ladder-rainbow expansion.

Findings

IR enhancement of ghost correlator does not reproduce confinement quantitatively

Monte Carlo integration provides a feasible alternative to analytic methods

Study of critical behavior of the coupling constant in Coulomb gauge QCD

Abstract

We calculate the ghost two-point function in Coulomb gauge QCD with a simple model vacuum gluon wavefunction using Monte Carlo integration. This approach extends the previous analytic studies of the ghost propagator with this ansatz, where a ladder-rainbow expansion was unavoidable for calculating the path integral over gluon field configurations. The new approach allows us to study the possible critical behavior of the coupling constant, as well as the Coulomb potential derived from the ghost dressing function. We demonstrate that IR enhancement of the ghost correlator or Coulomb form factor fails to quantitatively reproduce confinement using Gaussian vacuum wavefunctional.