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The ϒ → X γ photon spectrum in the soft-energy region

The dominant contribution of the next-to-leading order perturbative QCD corrections to the ϒ → X γ photon energy spectrum for photon energies ω ∼ m b α s can be obtained trivially from the knowledge of the corresponding O ( α ) correction to the positronium decay spectrum in the same region. The latter can be obtained from the NRQED computation of the orthopositronium photon spectrum, or by applying the threshold expansion to the 1-loop QED amplitude, as it is explained in this talk.