Quantum-chromodynamic predictions for direct photons ine+e−collisions

We analyze the direct photon production in $e^{+}{e}^{-}$ collisions in quantum chromodynamics using the cut-vertex formalism and the renormalization-group method. The two-loop anomalous dimensions of timelike cut vertices are calculated from the two-loop parton decay probability functions. The moments of the transverse structure function ${{\overline{W}}^{\gamma }}_T$ are calculated up to the next-to-leading order. The nonleading corrections to ${{\overline{W}}^{\gamma }}_T$ turn out to be large, and even larger than those to the photon structure function ${F^{\gamma }}_2$ in photon-photon scattering. Also, the moments of the longitudinal structure function ${{\overline{W}}^{\gamma }}_L$ are calculated in the leading order. The corrections are found to be small.