Interference in the reaction $e^+e^-\toγπ^+π^-$ and the final state interaction

Abstract

We describe the interference between amplitudes $e^ + e^-\toρ\toγπ^+π^-$ and $e^ + e^-\toϕ\toγ(f_0 + σ) \toγπ^ + π^-$, with regard to the phase of the elastic $ππ$ scattering background and mixing of the $f_0$ and $σ$ mesons. It is shown that the Fermi-Watson theorem for the final state interaction in the reaction $e^ + e^-\toρ\toγπ^ + π^-$ is not valid in the case of soft photons, $ω< 100$ MeV, in the $ϕ$ meson region. The interference patterns in the spectrum of the photon energy differential cross-section and in the full cross-section as a function of the beam energy are obtained.