Effective potential for heavy-quark-antiquark bound systems

An analytic form for the quark-antiquark interaction potential is proposed based on the renormalization-group equation of quantum chromodynamics (QCD) and the confinement assumption. With validity of the nonrelativistic approximation assumed, energy spectra, leptonic decay width, and $E1$ transition rates are computed. The results are compared with experimental data of $\psi$ and $\Upsilon$ resonances. A possible spin-spin interaction of non-QCD origin is then discussed.