Abstract
From observables we construct a unique spin-averaged quarkonia potential consistent with specified end-point behavior. At small quark-antiquark separation, we assume asymptotic freedom and at large separation, linear confinement. At intermediate radii the potential is expressed in terms of Fourier coefficients. Spin-averaged $\ensuremath{\psi}$ and $\ensuremath{\Upsilon}$ energy levels and relative leptonic widths determine a unique flavor-independent potential and $c$- and $b$-quark masses.
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