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Pion Pair Production with Higher Order Radiative Corrections in Low Energy e+e- Collisions

The complete one-loop QED initial state, final state and initial--final state interference corrections to the process e+e- -> pi+pi- are presented. Analytic formulae are given for the virtual and for the real photon corrections. The total cross section, the pion angular distribution and the pi+pi- invariant mass distribution are investigated in the regime of experimentally realistic kinematical cuts. It is shown that in addition to the full one-loop corrections also two-loop initial state corrections and even the resummation of higher order soft photon logarithms can be necessary if at least per cent accuracy is required. For the data analysis we focus on an inclusive treatment of all photons. The theoretical error concerning our treatment of radiative corrections is then estimated to be less than 2 per mille for both the measurement of the total cross section and the pi+pi- invariant mass distribution. In addition we discuss the model uncertainty due to the pion substructure. Altogether the precision of the theoretical prediction matches the requirements of low energy e+e- experiments like the ones going on at DAFNE or VEPP-2M.