$ \omega (\to \pi^+\pi^-\pi^0) $ meson photoproduction on proton

The cross section is estimated for the $\pi^+\pi^-\pi^0$ invariant mass distribution in the $\gamma p$ reaction in the GeV region. This reaction is assumed to proceed through the formation of the $\omega$ meson in the intermediate state, since the production cross section for this meson in the $\gamma p$ reaction in GeV region is significant and it has large branching ratio (88.8%) in the $\pi^+\pi^-\pi^0$ channel. The cross sections for this reaction have been calculated using the energy dependent reaction amplitude, i.e., $f_{\gamma p \to \omega p}(0)$, extracted from the latest $\omega$ meson photoproduction data. We use established procedure to calculate other factors, like width and propagator of the $\omega$ meson, so that our calculation can provide reliable cross section. The calculated results reproduce the measured $\pi^+\pi^-\pi^0$ invariant mass distribution spectra in the $\gamma p$ reaction.