We provide complete analytic expressions for the isolated prompt photon production cross section in $e^{+}{e}^{-}$ annihilation reactions through one-loop order in quantum chromodynamics (QCD) perturbation theory. Functional dependences on the isolation cone size $\delta$ and isolation energy parameter $\epsilon$ are derived. The energy dependence as well as the full angular dependence of the cross section on ${\theta }_{\gamma }$ are displayed, where ${\theta }_{\gamma }$ specifies the direction of the photon with respect to the $e^{+}{e}^{-}$ collision axis. We point out that conventional perturbative QCD factorization breaks down for isolated photon production in $e^{+}{e}^{-}$ annihilation reactions in a specific region of phase space. We discuss the implications of this breakdown for the extraction of fragmentation functions from $e^{+}{e}^{-}$ annihilation data and for computations of prompt photon production in hadron-hadron reactions.

• Received 16 May 1996

DOI:https://doi.org/10.1103/PhysRevD.54.5470