Final–state Radiation in Electron–positron Annihilation into Pion Pair

In this article the final-state radiation (FSR) of the hard photon in e−(p1) + e(p2) → γ ∗(Q) → π(p+) + π −(p−) + γ(k) reaction is considered in the framework of ChPT with vector ρ and axial–vector a1 mesons 1) (the FSR diagrams are shown in Fig.1). Our consideration of FSR is motivated by the necessity to study model dependence of the next-to-leading order hadronic contribution a μ to anomalous magnetic moment (AMM) of the muon (a μ is the hadronic contribution, where additional photon is attached to hadrons). Also FSR is a main unrestricted background to scan the hadronic cross–section at meson factories by the radiative return method 2). In this method only ISR (initial-state radiation) events have to be chosen and the FSR processes have to be rejected. Different methods have been suggested to separate ISR and FSR contributions for the dominant hadronic channel at low energies – the pion-pair production. One of them is to choose kinematics, where photon is radiated outside the narrow cones along the momenta of the pions. In these conditions the FSR contribution is suppressed. If the FSR background can be reliably calculated in some theoretical model then it can be subtracted from experimental cross section of ee → ππγ or incorporated in the Monte Carlo event generator used in analysis. Finally, the theoretical predictions for FSR can be tested by studying the C–odd interference of ISR and FSR 3). The FSR cross section has been calculated 3) in framework of the scalar QED (sQED), in which the pions are treated as point-like particles, and the