Heavy mesons in a simple quark-confining two-step potential model

Abstract

We study the mass spectra and decay widths of $\ensuremath{\Upsilon}$ resonances in a simple quark-confining, analytically solvable, two-step potential model used earlier to study the charmonium system and even the light mesons such as $\ensuremath{\pi}, \ensuremath{\rho}, K, \dots{}$. Results are found to be in good agreement with experiments and also with the values predicted by others. We predict the $B\overline{B}$ threshold at 10.242 GeV, which means in our model the first three radial $\ensuremath{\Upsilon}$ excitations $\ensuremath{\Upsilon}(9.4345)$, ${\ensuremath{\Upsilon}}^{\ensuremath{'}}(9.9930)$, and ${\ensuremath{\Upsilon}}^{\ensuremath{'}\ensuremath{'}}(10.1988)$ are stable with respect to the Zweig-rule-allowed decay $\ensuremath{\Upsilon}\ensuremath{\rightarrow}B\overline{B}$. The mass spectrum and thresholds of the anticipated $t\overline{t}$ states are also studied as a function of quark mass.