Beyondϒ: Heavier quarkonia and the interquark force

Abstract

A quarkonium potential constructed by inverse-scattering methods from the masses and leptonic decay widths of the $\Upsilon$ vector mesons provides a basis for extrapolation to heavier quark-antiquark bound states. Level spacings and leptonic widths are predicted for systems with ground-state masses up to 60 ${\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c}}^2$. It is found that present uncertainties in the potential at short distances would be most conclusively resolved by measurement of the $1{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ leptonic decay rate. Less definitive but still of value would be determinations of the $2S-1S$ or $2S-2P$ level spacings, and measurement of the ratio of $2S$ and $1S$ leptonic widths. Other properties of the next quarkonium family are less sensitive indicators of short-range behavior, and can be anticipated with some confidence from experimental results already in hand. These serve to test further the flavor independence of the interquark potential.