Interference in the reaction $e^{+}{e}^{-}\to \gamma {\pi }^{+}{\pi }^{-}$ and the final state interaction

Abstract

We describe the interference between amplitudes $e^{+}{e}^{-}\to \rho \to \gamma {\pi }^{+}{\pi }^{-}$ and $e^{+}{e}^{-}\to \varphi \to \gamma (f_0+\sigma )\to \gamma {\pi }^{+}{\pi }^{-}$, 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 $e^{+}{e}^{-}\to \rho \to \gamma {\pi }^{+}{\pi }^{-}$ is not valid in the case of soft photons, $\omega <100$ MeV, in the $\varphi$ 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.

Comments: 10 pages, revtex, 2 ps files of figures