Quarkonium annihilation rates

Recent measurements of ratios of quarkonium annihilation rates are used to evaluate the strong fine-structure constant ${\alpha }_s$. Expressions are presented for QCD radiative corrections with ${\alpha }_s$ referred to the quark-mass scale. We find ${\mathrm{\alpha }}_{\mathit{s}}$(${\mathit{m}}_{\mathit{b}}$)=0.${179}_{\mathrm{-}0.008}^{+0.009\mathrm{}}$ from the ratio Γ(Υ→γgg)/ Γ(Υ→ggg). The corresponding range of ${\Lambda }_{\mathrm{MS}{¯}^{\mathrm{}\left(4\right)\mathrm{}}}$ (the QCD scale factor for four light-quark flavors) is 146–210 MeV, where MS¯ denotes the modified-minimal-subtraction scheme. The experimentally more precise but theoretically more questionable ratio of the gluonic and muonic widths of J/ψ and Υ yields ${\alpha }_s$($m_c$)=0.29±0.02, ${\alpha }_s$($m_b$)=0.189±0.008 when $v^2$/$c^2$ corrections to these ratios for J/ψ and Υ are parametrized linearly. Further predictions are made for ratios of rates.