Measurement of the direct photon spectrum in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Υ</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mi>S</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>decays
Measurement of the direct photon spectrum in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Υ</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mi>S</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>decays
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 …