Measurement of the Direct Photon Spectrum in $Υ(1S)$ Decays

Using data taken with the CLEO II detector at the Cornell Electron Storage Ring, we have determined the ratio of branching fractions: $R_γ \equiv Γ(Υ(1S) \rightarrow γgg)/Γ(Υ(1S) \rightarrow ggg) = (2.75 \pm 0.04(stat.) \pm 0.15(syst.))%$. From this ratio, we have determined the QCD scale parameter $Λ_{\overline{MS}}$ (defined in the modified minimal subtraction scheme) to be $Λ_{\overline{MS}}= 233 \pm 11 \pm 59$ MeV, from which we determine a value for the strong coupling constant $α_{s}(M_{Υ(1S)}) = 0.163 \pm 0.002 \pm 0.014$, or $α_{s}(M_{Z}) = 0.110 \pm 0.001 \pm 0.007$.