Final-state radiation in electron-positron annihilation into pion pair

The process of $e^+ e^-$ annihilation into $\pi^+ \pi^-$ pair with radiation of the photon is considered. The amplitude of the reaction $e^+ e^- \to \pi^+ \pi^- \gamma$ consists of the model independent initial-state radiation (ISR) and model dependent final-state radiation (FSR). The general structure of the FSR tensor is constructed from Lorentz covariance, gauge invariance and discrete symmetries in terms of the three invariant functions. To calculate these functions we apply Chiral Perturbation Theory (ChPT) with vector and axial-vector mesons. The contribution of $e^+ e^- \to \pi^+ \pi^- \gamma$ process to the muon anomalous magnetic moment is evaluated, and results are compared with the dominant contribution in framework of a hybrid model, consisting of VMD and point-like scalar electrodynamics. The developed approach allows us also to calculate the $\pi^+ \pi^-$ charge asymmetry.