Measurement of the Direct Photon Momentum Spectrum in Upsilon(1S), Upsilon(2S), and Upsilon(3S) Decays

Using data taken with the CLEO III detector at the Cornell Electron Storage Ring, we have investigated the direct photon spectrum in the decays Upsilon(1S) -> gggamma, Upsilon(2S) -> gggamma, Upsilon}(3S) -> gggamma. The latter two of these are first measurements. Our analysis procedures differ from previous ones in the following ways: a) background estimates (primarily from pi^0 decays are based on isospin symmetry rather than a determination of the pi^0 spectrum, which permits measurement of the Upsilon(2S) and Upsilon(3S) direct photon spectra without explicit corrections for pi^0 backgrounds from, e.g., chi_bJ states, b) we estimate the branching fractions with a parametrized functional form (exponential) used for the background, c) we use the high-statistics sample of Upsilon(2S) -> pi+ pi- Upsilon(1S) to obtain a tagged-sample of Upsilon(1S) -> gamma + X events, for which there are no QED backgrounds. We determine values for the ratio of the inclusive direct photon decay rate to that of the dominant three-gluon decay Upsilon -> ggg (R_gamma=B(gggamma)/B(ggg)) to be: R_gamma(1S)=(2.70+/-0.01+/-0.13+/-0.24)%, R_gamma(2S)=(3.18+/-0.04+/-0.22+/-0.41)%, and R_gamma(3S)=(2.72+/-0.06+/-0.32+/-0.37)%, where the errors shown are statistical, systematic, and theoretical model-dependent, respectively. Given a value of Q^2, one can estimate a value for the strong coupling constant alpha_s(Q^2) from R_gamma.