Radiative corrections to hadron production in e+e- annihilations at DA_Ph63NE energies

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Radiative corrections to low energy hadron production as measured at the e+e?– colliders DA?NE and VEPP-2M are investigated. The goal of this work is to provide the theoretical condition for extracting hadronic cross sections undressed from QED corrections from the measured data with a precision of per mill level. High precision hadronic data are required to reduce the theoretical error of the running fine structure constant ?(s) and the muon anomalous magnetic moment aµ and therefore represent a key to a possible discovery of “new physics”. Especially the channel of charged pion pair production e+e? ? ?+?? below 1 GeV appears to be of great importance. To this process the complete O(?) QED initial state, final state and initial–final state interference corrections are calculated. Analytic formulae are given for the virtual and for the real photon corrections. The total cross section (?), the pion angular distribution (d?/d cos ?) and the ?+?? invariant mass distribution (d?/ds?) are investigated in the regime of experimentally realistic kinematical cuts. It is shown that in addition to the full O(?) corrections also the O(?2) and leading log O(?3) photonic corrections as well as the contributions from IS e+e? pair production have to be taken into account if at least per cent accuracy is required. For the data analysis I focus on an inclusive treatment of all photons. The theoretical error concerning this treatment of radiative corrections is then estimated to be 2 per mill for both the measurement of the total cross section and the ?+?? invariant mass distribution. In addition the model uncertainty due to the pion substructure is discussed. To be able to extract the pion form factor from the experimental data with the desired accuracy a dedicated Fortran program was written which allows to take into account experimentally realistic kinematical cuts. Altogether the precision of the theoretical prediction matches the requirements of low energy e+e? experiments like the ones at DA?NE and VEPP-2M.