Optimization of the nonrelativistic potential model for $b\overline{b}$ quarkonia

Abstract

A systematic study of a wide class of nonrelativistic models of $b\overline{b}$ quarkonia is described. It is found that the potential $V(r) = 0.706380(\sqrt{r} - \frac{0.460442}{r}) + 8.81715$ (all in GeV) with the $b$-quark mass $m_b = 4.80303$ GeV gives a satisfactory description of the experimental data below the threshold for strong decays ($ \chi^2/DF = 6.5/7$). Limitations and implications of this observation are discussed.