Quarkonia and quantum chromodynamics

Abstract

The $\ensuremath{\psi}$ and $\ensuremath{\Upsilon}$ spectroscopies are analyzed in the framework of a recently proposed potential model which incorporates linear confinement and asymptotic freedom. Given the Regge slope ${\ensuremath{\alpha}}^{\ensuremath{'}}$ (${\ensuremath{\alpha}}^{\ensuremath{'}}$ taken to be 1 ${\mathrm{GeV}}^{\ensuremath{-}2}$) and the quantum-chromodynamics (QCD) scale parameter $\ensuremath{\Lambda}$ (${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}$ taken to be 0.5 GeV, where $\stackrel{-}{\mathrm{MS}}$ refers to the modified minimal-subtraction scheme) the potential is completely determined. Excellent agreement with experiment is found, including in particular leptonic widths and hyperfine splittings. This supports a short-distance behavior of the quark-antiquark potential as predicted by QCD. We also demonstrate in a model-independent way that the $\ensuremath{\Psi}$ and $\ensuremath{\Upsilon}$ spectra provide a lower bound on the QCD scale parameter $\ensuremath{\Lambda}$; we find ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}g0.1$ GeV. The properties of ($b\overline{c}$) and possible ($t\overline{t}$), ($t\overline{c}$), and ($t\overline{b}$) spectroscopies are studied, including weak-interaction effects. The implications of the $\ensuremath{\Psi}$, $\ensuremath{\Upsilon}$, and possible heavier quarkonium families for quantitative tests of QCD are discussed. It is shown that a ($t\overline{t}$) system with $m(t\overline{t})\ensuremath{\ge}40$ GeV would provide an accurate determination of ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}$.