Lorentz structure vs relativistic consistency of an effective power-law potential model for quark-antiquark systems

We show here that the relativistic consistency of an effective power-law potential V(r) = Ar/sup ν/+V0 (with A, ν>0) (used successfully to describe the heavy-meson spectra) in generating Dirac bound states of QQ-bar and Qq-bar systems implies, and also at the same time is implied by, an equally mixed vector-scalar Lorentz structure which was observed phenomenologically in the fine-hyperfine splittings of meson spectra