Isolated prompt photon production in hadronic final states of e+e- annihilation

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.