QCD Corrections to Photon Production in Association with Hadrons in   $e^+e^-$ Annihilation
  A detailed investigation of the theoretical ambiguities present in the QCD description of photon production in $e^+e^-$ annihilation is given. It is pointed out that in a well-defined perturbative analysis it is necessary to subtract the quark-photon collinear singularities. This subtraction requires the introduction of an unphysical parameter in the perturbative part of the cross section. The subtracted term is factored into non-perturbative fragmentation function. The dependence on the unphysical parameter cancels in the sum of non-perturbative and perturbative parts. It is pointed out that for $E_{\gamma}\le \sqrt{s}/(2(1+\epsilon_c))$ the non-perturbative contributions are suppressed. Using a general purpose next-to-leading order Monte Carlo program, we calculate various physical quantities that were measured in LEP experiments recently. 
Zoltan Kunszt and Zolt\'an Tr\'ocs\'anyi