Interference in the reaction e+e-??p+p- and the final state interaction

We describe the interference between amplitudes ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\rho}}\ensuremath{\gamma}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\varphi}}\ensuremath{\gamma}{(f}_{0}+\ensuremath{\sigma})$$\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}},$ with regard to the phase of the elastic \ensuremath{\pi}\ensuremath{\pi} scattering background and mixing of the ${f}_{0}$ and \ensuremath{\sigma} mesons. It is shown that the Fermi-Watson theorem for the final state interaction in the reaction ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\rho}}\ensuremath{\gamma}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ is not valid in the case of soft photons, $\ensuremath{\omega}l100\mathrm{MeV},$ in the region of the \ensuremath{\varphi} 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.