Quantum Chromodynamic Corrections to the Gluonic Width of theϒMeson

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