The Upsilon -> X gamma photon spectrum in the soft-energy region

TL;DR

This paper discusses how next-to-leading order QCD corrections to the Upsilon decay photon spectrum can be derived from positronium decay calculations, using NRQED or threshold expansion methods.

Contribution

It introduces a straightforward method to obtain QCD corrections for Upsilon decay spectra from known QED positronium decay results.

Findings

QCD corrections can be derived from QED positronium decay data

NRQED and threshold expansion methods are effective

Simplifies calculations of photon spectra in heavy quarkonium decays

Abstract

The dominant contribution of the next-to-leading order perturbative QCD corrections to the Upsilon -> X gamma photon energy spectrum for photon energies w ~ m_b alpha_s can be obtained trivially from the knowledge of the corresponding O(alpha) 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.