Charge asymmetry of pions in the process $e^-e^+\to e^-e^+\pi^+\pi^-$

Abstract. The study of the charge asymmetry of produced particles allows one to investigate the interference of different production mechanisms and to determine new features of the corresponding amplitudes. In the process $e^- e^+ \to e^- e^+ \pi^+ \pi^-$ the two-pion system is produced via two mechanisms: two-photon (C-even state) and bremsstrahlung (C-odd state) production. We study the charge asymmetry of pions differentially in the pion momenta cross section originating from interference between these two mechanisms. At low effective mass of the dipions this asymmetry is directly related to the s- andp-phases of elastic $\pi\pi$ scattering. At higher energies it can give new information about the $f_0$ meson family, the $f_2(1270)$ meson, etc. The asymmetry is expressed via the pion form factor $F_\pi$ and the helicity amplitudes $M_{ab}$ for the subprocess $\gamma^*\gamma\to \pi^+\pi^-$ as $\sum G_{ab}{\mathrm{Re}}(F_\pi^*M_{ab})$, where we have analytically calculated the coefficients $G_{ab}$ for the region giving the main contribution to the effect. Several distributions of the pions are presented performing a numerical analysis in a model with point-like pions. In the region near the dipion threshold the asymmetry is of the order of 1%. We show that with suitable cuts the signal to background ratio can be increased up to about 10%.