Fit to Gluon Propagator and Gribov Formula

TL;DR

This study numerically analyzes the SU(2) lattice gauge theory's gluon propagator, confirming Gribov's confinement scenario by showing the propagator vanishes at zero momentum, indicating gluons do not appear in the physical spectrum.

Contribution

It provides numerical evidence supporting Gribov's formula for the gluon propagator and its role in confinement within lattice gauge theory.

Findings

Gluon propagator vanishes at zero momentum after volume extrapolation.

Results agree with a discretized Gribov formula for the gluon propagator.

Supports the confinement scenario where gluons leave the physical spectrum.

Abstract

We report a numerical study of SU(2) lattice gauge theory in the minimal Coulomb gauge at beta = 2.2 and 9 different volumes. After extrapolation to infinite volume, our fit agrees with a lattice discretization of Gribov's formula for the transverse equal-time would-be physical gluon propagator, that vanishes like |k| at k = 0, whereas the free equal-time propagator (2|k|)^{-1} diverges. Our fit lends reality to a confinement scenario in which the would-be physical gluons leave the physical spectrum while the long-range Coulomb force confines color.