Pion pair production with higher order radiative corrections in low energy $e^+e^-$ collisions

Abstract.

The complete $O(\alpha)$ QED initial state (IS), final state (FS) and initial–final state (IFS) interference corrections to the process $e^+e^-\to\pi^+\pi^-$ are presented. Analytic formulae are given for the virtual and for the real photon corrections. The total cross section ($\sigma$), the pion angular distribution ($\mathrm{d}\sigma/\mathrm{d}\cos\Theta$) and the $\pi^+\pi^-$ invariant mass distribution ($\mathrm{d}\sigma/\mathrm{d}s'$) are investigated in the regime of experimentally realistic kinematical cuts.

It is shown that in addition to the full $O(\alpha)$ corrections also the $O(\alpha^2)$ and leading-log $O(\alpha^3)$ 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 we focus on an inclusive treatment of all photons. The theoretical error concerning our treatment of radiative corrections is then estimated to be 2 per mill 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 DA$\Phi$NE or VEPP-2M.