The role of $\sigma$-meson in $\omega\to \pi\pi\gamma$ decays and the coupling constant $g_{\omega\sigma\gamma}$

Abstract

We study the $\omega\to\pi\pi\gamma$ decays by adding to the amplitude calculated within the framework of chiral perturbation theory and vector meson dominance the amplitude of $\sigma$-meson intermediate state. We estimate the coupling constant $g_{\omega\sigma\gamma}$ utilizing the experimental value of the $\omega\to\pi^{0}\pi^{0}\gamma$ decay rate.