Effective non-Coulombic power-law potential for the study of light and heavy mesons

From purely phenomenological considerations we have shown that it is possible to describe successfully the heavy-meson spectra of $c\overline{c}$ and $b\overline{b}$ systems in the framework of an effective non-Coulombic power-law potential in the form $V\left(r\right)=V_0+a{r}^{\nu }$ (with $a$, $\nu >0\mathrm{}$). The nonsingular short-distance behavior of this potential, which is in apparent contradiction with the predictions of quantum chromodynamics, does not pose any problem in explaining the fine-hyperfine splittings, if we prescribe the spin dependence to be generated through this static confining potential in the form of an approximately equal admixture of scalar and vector parts with no contributions from the anomalous quark magnetic moments. This nonrelativistic formalism, when extended to a unified study of the entire meson spectra including the ordinary light and the heavy mesons, gives a very good account of the meson masses, fine-hyperfine splittings, electromagnetic transition rates, and leptonic decay widths without reflecting any inadequacy in the short- and long-range behavior of this simple effective power-law potential.