  Non-relativistic QCD (NRQCD) predicts colour octet contributions to be
significant not only in many production processes of heavy quarkonia but also
in their radiative decays. We investigate the photon energy distributions in
these processes in the endpoint region. There the velocity expansion of NRQCD
breaks down which requires a resummation of an infinite class of colour octet
operators to so-called shape functions. We model these non-perturbative
functions by the emission of a soft gluon cluster in the initial state. We
found that the spectrum in the endpoint region is poorly understood if the
values for the colour octet matrix elements are taken as large as indicated
from NRQCD scaling rules. Therefore the endpoint region should not be taken
into account for a fit of the strong coupling constant at the scale of the
heavy quark mass.
