Dalitz Plot Analysis of the Decay \(\omega \rightarrow \pi^{+}\pi^{-}\pi^{0}\)

Using a low-background sample of \(2.6\times 10^5\) \(J/\psi\rightarrow\omega\eta(\omega\rightarrow\pi^{+}\pi^{-}\pi^{0},\eta\rightarrow\gamma\gamma)\) events, about 5 times larger statistics than previous experiments, we present a Dalitz plot analysis of the decay \(\omega\rightarrow\pi^{+}\pi^{-}\pi^{0}\). It is found that the Dalitz plot distribution differs from the pure \(P\)-wave phase space with a statistical significance of \(18.9\sigma\). The parameters from the fit to data are in reasonable agreement with those without the cross-channel effect within the dispersive framework, which indicates that the cross-channel effect in \(\omega\rightarrow\pi^+\pi^-\pi^0\) is not significant.