Testing static quark-antiquark potentials with bottomonium

We investigate the question of whether experimental data on the energy levels of bottomonium can discriminate between quark-antiquark potentials which are motivated by what we know about QCD and potentials which are purely phenomenological. We restrict ourselves to bottomonium because, of all the quarkonia observed thus far, bottomonium is the least relativistic and therefore the best testing ground for the static quarkonium potential. We consider two potentials whose functional form is motivated from perturbative QCD at short quark-antiquark separations and from nonperturbative lattice QCD at large separations. We also consider three strictly phenomenological potentials. We find that the best of the three phenomenological potentials, which has never been previously used, fits the spin-averaged data at least as well as the best of the QCD-motivated potentials. We propose further measurements on bottomonium energy levels to provide additional tests.