Coulomb gauge gluon propagator and the Gribov formula

TL;DR

This paper investigates the Coulomb gauge gluon propagator in lattice SU(2) Yang-Mills theory, confirming the Gribov formula's validity and determining a mass scale of approximately 0.88 GeV.

Contribution

It demonstrates the multiplicative renormalizability of the static gluon propagator and validates the Gribov formula in lattice simulations.

Findings

Gluon propagator fits Gribov formula with M ≈ 0.88 GeV

Propagator is multiplicative renormalizable

Mass scale M relates to the string tension as M ≈ 2√σ

Abstract

We analyze the lattice SU(2) Yang-Mills theory in Coulomb gauge. We show that the static gluon propagator is multiplicative renormalizable and takes the simple form $D(|\vec{p}|)^{-1}=\sqrt{|\vec{p}|^2+M^4/|\vec{p}|^2}$, proposed by Gribov through heuristic arguments many years ago. We find $M=0.88(1) {\rm GeV} \simeq 2 \sqrt{\sigma}$.