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 δ and isolation energy parameter
ϵ are derived. The energy dependence as well as the full angular
dependence of the cross section on θγ are displayed, where
θγ 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.Comment: 54 pages RevTeX plus 19 postscript figures submitted together in one
compressed fil