Quantum Chromodynamic Corrections to the Gluonic Width of theϒMeson

Abstract

The corrections to the gluonic width of $\ensuremath{\Upsilon}$-like mesons in quantum chromodynamics (QCD) through first order in ${\ensuremath{\alpha}}_{s}$ are calculated, with the result ${\ensuremath{\Gamma}}_{g}={{\ensuremath{\Gamma}}_{g}}^{0}[1+(3.8\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{\ensuremath{\alpha}}_{s}\frac{({M}_{\ensuremath{\Upsilon}})}{\ensuremath{\pi}}]$, using the $\stackrel{-}{\mathrm{MS}}$ scheme definition of ${\ensuremath{\alpha}}_{s}$, renormalized at ${M}_{\ensuremath{\Upsilon}}$. With this correction, the measured value of the leptonic branching ratio of the $\ensuremath{\Upsilon}$ can be used to determine ${\ensuremath{\alpha}}_{s}$, or, equivalently, the QCD scale parameter ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}$. The result is ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}=100$ MeV, with experimental errors of $_{\ensuremath{-}25}^{+34}\mathrm{MeV}$ and comparable theoretical uncertainties. Analysis of the $\ensuremath{\psi}$ and ${\ensuremath{\psi}}^{\ensuremath{'}}$ data is consistent with this value.