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

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.