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Radiative return at NLO and the measurement of the hadronic cross-section in electron-positron annihilation

Electron-positron annihilation into hadrons plus an energetic photon from initial state radiation allows the hadronic cross-section to be measured over a wide range of energies. The full next-to-leading order QED corrections for the cross-section for e^+ e^- annihilation into a real tagged photon and a virtual photon converting into hadrons are calculated where the tagged photon is radiated off the initial electron or positron. This includes virtual and soft photon corrections to the process e^+ e^- \to γ+γ^* and the emission of two real hard photons: e^+ e^- \to γ+ γ+ γ^*. A Monte Carlo generator has been constructed, which incorporates these corrections and simulates the production of two charged pions or muons plus one or two photons. Predictions are presented for centre-of-mass energies between 1 and 10 GeV, corresponding to the energies of DAPHNE, CLEO-C and B-meson factories.