We provide complete analytic expressions for the inclusive prompt photon production cross section in hadronic final states of ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$ annihilation reactions through one-loop order in quantum chromodynamics perturbation theory. Computed explicitly are direct photon production through first order in the electromagnetic strength ${\mathrm{\alpha }}_{\mathrm{em}}$ and the quark-to-photon and gluon-to-photon fragmentation contributions through first order in the strong coupling ${\mathrm{\alpha }}_{\mathit{s}}$. The full angular dependence of the cross sections is displayed, separated into transverse (1+${\cos }^2$${\mathrm{\theta }}_{\gamma }$) and longitudinal (${\sin }^2$${\mathrm{\theta }}_{\gamma }$) components, where ${\mathrm{\theta }}_{\gamma }$ specifies the direction of the photon with respect to the ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$ collision axis. We discuss extraction of fragmentation functions from ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$ data. © 1996 The American Physical Society.

• Received 27 July 1995

DOI:https://doi.org/10.1103/PhysRevD.53.1124