Static potentials and scaling in SU(2) lattice gauge theory

Abstract

The potentials between static colour sources are studied using SU(2) colour in a Monte Carlo evaluation with a combined variational and multi-hit technique. This allows accurate determinations of the potentials both for relatively large separation R and for β-values up to 2.575 where the lattice spacing a is relatively small. The best determined potential is that between static fundamental colour sources and this is used to study scaling. By measuring the potential at separations along the lattice axis and off-axis, we find small departures from rotational invariance at low values of R a . These are well described by using a lattice Coulomb component in the potential. Our results for the potential are consistent with scaling between the β-values 2.3, 2.4 and 2.575 and we present results for the shape of the continuum potential. Comparison with the asymptotic scaling expected from perturbation theory shows a small but well-determined discrepancy of about 10% in the ratio of lattice spacings at adjacent β-values. We also present results for (i) the excited modes of the potential between fundamental colour sources which are relevant to hybrid mesons, and (ii) the potential between adjoint colour sources.