QCD Corrections to Radiative $\Upsilon$ Decays

We calculate the next-to-leading order perturbative QCD corrections to the photon energy spectrum in radiative Upsilon decays We have calculated the next-to-leading order perturbative QCD corrections to the photon energy spectrum in radiative Upsilon decays. The higher-order corrections significantly modify the shape of the spectrum, in particular at large photon energies, and thereby reduce the discrepancy between experimental data and previous leading-order predictions. The next-to-leading order calculation of the photon energy spectrum allows a more reliable determination of the strong coupling constant from radiative Upsilon decays by restricting the analysis to the region of the energy spectrum that can be described by NLO perturbation theory.