Coulomb gauge gluon propagator and the Gribov formula

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 $M=0.88(1)\mathrm{GeV}\simeq 2\sqrt{\sigma }$.

Comments: 10 pages, 2 figures. Slight change of notations, some point clarified. To appear on Phys. Rev. Lett