Flavor dependence of the static quark-antiquark potential

Abstract

We investigate to what extent a static quark-antiquark potential can account for the spin-averaged energy levels in bottomonium and charmonium. For comparison, we treat the problem with four different potentials, solving the Schrödinger equation in each case with relativistic as well as nonrelativistic kinematics. Each potential contains two or three parameters which are adjusted to obtain best agreement with the experimental data. We find that none of the potentials provide a good quantitative fit to the data, although all of them lead to qualitative agreement with experiment. Furthermore, for each potential, we find that the parameters which give the best fit to the data are not the same for charmonium and bottomonium. In the case of nonrelativistic kinematics the fit to the combined data is appreciably worse than the individual fits. On the other hand, in the case of relativistic kinematics, the combined fits are about as good as the individual fits for three of the four potentials. We conclude that the flavor dependence of the potential is a function of the form of the potential and of the prescription used to calculate the energy eigenvalues.