Improved QCD-motivated heavy-quark potentials with explicitΛMS―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 $c\overline{c}$ and $b\overline{b}$ spectra all fit the data very well for ${\Lambda }_{\overline{\mathrm{MS}}}$ in the range 100-500 MeV, where $\overline{\mathrm{MS}}$ denotes the modified minimal subtraction scheme. Furthermore, the potentials are described directly in coordinate space with explicit ${\Lambda }_{\overline{\mathrm{MS}}}$ 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 $\psi \left(1\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ and $\Upsilon \left(1\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ are higher than the center-of-gravity values of the $1{}_{}{}^3{}_{}{}^{}P_J^{}{}_{}{}^{}$ states by 0.9-1.8 MeV and 0.4-0.7 MeV, respectively, for ${\Lambda }_{\overline{\mathrm{MS}}}$ in the range 100-200 MeV.