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

• Received 21 July 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.032002