Color-Coulomb Force Calculated from Lattice Coulomb Hamiltonian

Abstract

The static color-Coulomb potential is calculated as the solution of a non-linear integral equation. This equation has been derived recently as a self-consistency condition which arises in the Coulomb Hamiltonian formulation of lattice gauge theory when the restriction to the interior of the Gribov horizon is implemented. The potential obtained is in qualitative agreement with expectations, being Coulombic with logarithmic corrections at short range and confining at long range. The values obtained for the string tension and \(\Lambda_{\overline{MS}}\) are in semi-quantitative agreement with lattice Monte Carlo and phenomenological determinations.