Hyperfine splittings in heavy-quark systems

Abstract

The hyperfine splittings in heavy-quark systems are calculated to fourth order in the strong coupling constant. The $\ensuremath{\psi}\ensuremath{-}{\ensuremath{\eta}}_{c}$ mass difference gives ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}=0.16\ifmmode\pm\else\textpm\fi{}0.02\ifmmode\pm\else\textpm\fi{}0.07$ GeV ($\stackrel{-}{\mathrm{MS}}$ refers to the modified minimal-subtraction scheme) where the first uncertainty is experimental and the second is a crude estimate of the uncertainty arising from scheme dependence. From the $\ensuremath{\Upsilon}\ensuremath{-}{\ensuremath{\eta}}_{b}$ mass difference we expect a more reliable and accurate determination of $\ensuremath{\Lambda}$.