Abstract
An inverse-scattering algorithm is used to construct the interquark potential from the masses and leptonic widths of vector mesons. There is substantial agreement between potentials constructed from the $1S$ and $2S$ levels of the $\ensuremath{\psi}$ family, and those based upon the $1S\ensuremath{-}4S$ levels of the $\ensuremath{\Upsilon}$ family. This agreement provides evidence that the quark-antiquark interaction is independent of heavy-quark flavor for interquark separations between about 0.1 and 1 fm. Self-consistency of the various determinations is explored at some length, and the uncertainties inherent in the method are investigated in detail. Predictions are made for electric-dipole transition rates in the $\ensuremath{\Upsilon}$ family, and the significance of future measurements for refining and extending present knowledge of the potential is discussed.
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