Abstract
The leptonic tensor for the process $e^+ e^- \to \gamma+\gamma^*$, which describes the next-to-leading order virtual and soft QED corrections to initial state radiation in $e^+ e^-$ annihilation with emission of an extra virtual photon decaying into hadrons, is calculated. A Monte Carlo generator for the reaction $e^+ e^- \to \gamma + \pi^+ \pi^-$ has been set up which includes these corrections. It thus describes configurations where the invariant mass of the hadrons plus photon is very close to $\sqrt{s}$. Predictions for cms energies of 1 to 10 GeV, corresponding to the energies of DAPHNE and B-meson factories, are presented. The possibility for an accurate measurement using tagged photons of $\sigma(e^+ e^- \to hadrons)$, which plays an important role in the theoretical description of the muon anomalous magnetic moment and the running of the electromagnetic coupling, is discussed.
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