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

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Abstract
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.

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