Inclusive Prompt Photon Production in Hadronic Final States of $e^{+}{e}^{-}$ Annihilation

Abstract

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

Comments: 40 pages, RevTex, 30 figures in postscript available in a separate file