Interference in the reaction e+e-→γπ+π- and the final state interaction

We describe the interference between amplitudes e(+)e(-)-->rho-->gamma pi(+)pi(-) and e(+)e(-)-->phi-->gamma(f(0)+sigma) -->gamma pi(+)pi(-), with regard to the phase of the elastic pi pi scattering background and mixing of the f(0) and sigma mesons. It is shown that the Fermi-Watson theorem for the final state interaction in the reaction e(+)e(-)-->rho-->gamma pi(+)pi(-) is not valid in the case of soft photons, omega< 100 MeV, in the region of the phi meson. The interference patterns in the spectrum of the photon energy differential cross section and in the full cross section as a function beam energy are obtained.