Measurement of the direct photon spectrum in ${\rm Y}\mathrm{}\left(1S\right)\mathrm{}$ decays

Using data taken with the CLEO II detector at the Cornell Electron Storage Ring, we have determined the ratio of branching fractions: $R_{\gamma }\equiv \Gamma \left({\rm Y}\mathrm{}\right(1S)\mathrm{}\to \gamma \mathrm{gg})/\Gamma \left({\rm Y}\mathrm{}\right(1S)\mathrm{}\to \mathrm{ggg})=[2.75\pm 0.04(\mathrm{stat})\pm 0.15(\mathrm{syst}\left)\right]\%$. From this ratio, we have determined the QCD scale parameter ${\Lambda }_{\overline{\mathrm{MS}}}$ (defined in the modified minimal subtraction scheme) to be ${\Lambda }_{\overline{\mathrm{MS}}}=233\mathrm{}\pm 11\pm 59$ MeV, from which we determine a value for the strong coupling constant ${\alpha }_s{(M}_{{\rm Y}\mathrm{}\left(1S\right)\mathrm{}})=0.163\mathrm{}\pm 0.002\pm 0.014$, or ${\alpha }_s{(M}_Z)=0.110\mathrm{}\pm 0.001\pm 0.007$.