Gupta-Radford-Repko potential and the properties of the Υ system

Because of recent improvements in the quality of the P-state splittings of the Υ system, we decided to reexamine some of the basic assumptions underlying an important recent calculation of the properties of the system by Gupta, Radford, and Repko (GRR). In particular, we want to examine the strategy chosen to determine the renormalization scale parameter. It is also of interest to know if one can develop a method for including Luescher or Luescher-type corrections to the form of the confinement potential that is consistent with some of the accomplishments of perturbation-theory potentials and the data. To this end, we have developed an abbreviated form of the GRR potential, which gives a fit to the measured energies that is somewhat better than the original GRR potential. By introducing a join radius, where the running coupling constant stops running, we are able to include a Coulomb term in the confinement potential. The amended Luescher coefficient is determined from a continuity condition at the join radius. Its value is found to be near 0.55, which is consistent with a recent calculation of Olsson and Suchyta