Interference in the reactione+e−→γπ+π−and the final state interaction

We describe the interference between amplitudes $e^{+}{e}^{-}\to \overrightarrow{\rho }\gamma {\pi }^{+}{\pi }^{-}$ and $e^{+}{e}^{-}\to \overrightarrow{\phi }\gamma {(f}_0+\sigma )$ $\to \gamma {\pi }^{+}{\pi }^{-},$ 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 $e^{+}{e}^{-}\to \overrightarrow{\rho }\gamma {\pi }^{+}{\pi }^{-}$ is not valid in the case of soft photons, $\omega <100\mathrm{}\mathrm{MeV},$ in the region of the φ 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.