Scalar isovector resonance photoproduction through the final state meson-meson interactions

We construct the amplitudes of $\pi\eta$ photoproduction taking into account the effects of the $\pi\eta$ - $K\bar K$ interchannel coupling. The idea of our model is close to the molecular description of scalar resonances with exception that apart from the pseudoscalar loops we include also vector mesons in the intermediate state loops. These amplitudes are used to calculate the $S$-wave cross sections and mass distributions in the $\pi\eta$ effective mass region corresponding to the scalar resonances $a_0(980)$ and $a_0(1450)$. The values we obtained for $a_0(980)$ are comparable with predictions of other models while the cross section for $a_0(1450)$ is about an order of magnitude larger than prediction based on the quark model. We show that the amplitudes with loops containing vector mesons calculated in the on-shell approximation are not suppressed in contrast to amplitudes containing only pseudoscalar loops. We estimate the cross sections for the $P$- and $D$- waves in the $\pi\eta$ channel.