Improved QCD-motivated heavy-quark potentials with explicit ΛMbarS dependence

We propose two models for a heavy-quark potential with possible natural QCD interpretations. The potentials approach the two-loop perturbative QCD formula at short distance and a linear confining potential at large distance, and their predicted c bar c and b bar b spectra all fit the data very well for ΛMbarS in the range 100--500 MeV, where M bar S denotes the modified minimal subtraction scheme. Furthermore, the potentials are described directly in coordinate space with explicit ΛMbarS dependence so that they are convenient for practical calculations. Some of their phenomenological predictions are given, especially, in the picture regarding a confining potential as a scalar exchange. The predicted masses of ψ (1 1P1) and Υ(1 1P1) are higher than the center-of-gravity values of the 1 3PJ states by 0.9--1.8 MeV and 0.4--0.7 MeV, respectively, for ΛMbarS in the range 100--200 MeV