Measurement of the direct photon spectrum inΥ(1S)decays

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Abstract

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

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