Simultaneous fit of the spectra of light and heavy self-conjugate mesons

Abstract

It is shown that a simultaneous nonrelativistic fit of the spectra of both the light and heavy self-conjugate mesons is possible by an effective non-Coulombic power-law potential of the form $V(r)={\mathrm{Ar}}^{0.1}+{V}_{0}$. This purely phenomenological potential is found to provide a very good account of the mass spectra and the leptonic decay widths of the ${\ensuremath{\rho}}^{0}$, $\ensuremath{\varphi}$, $\ensuremath{\psi}$, and $\ensuremath{\Upsilon}$ systems in a flavor-independent manner. In spite of the smallness of the constituent quark masses involved, the nonrelativistic fit for the light mesons of ${\ensuremath{\rho}}^{0}$ and $\ensuremath{\varphi}$ systems is excellent.