Study of the $\pi \pi$ mass spectra in the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ at $\sqrt{s}\simeq 1020$ MeV

The invariant mass spectra of the ${\pi }^{+}{\pi }^{-}$ and ${\pi }^{\pm }{\pi }^0$ pairs in the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ were studied in the Spherical Neutral Detector experiment at the VEPP-2M collider in the energy region $\sqrt{s}\simeq 1020$ MeV. These studies were based on about $0.5\times {10}^6$ events. The spectra were analyzed in the framework of the vector meson dominance model. It was found that the experimental data can be described assuming the $e^{+}{e}^{-}\to \rho \overrightarrow{\pi }{\pi }^{+}{\pi }^{-}{\pi }^0$ transition only. An upper limit on the branching ratio of the $\phi \mathrm{}\left(1020\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay through intermediate states different from $\rho \pi$ was obtained at the $90\%$ confidence level: $B\left(\overrightarrow{\phi }{\pi }^{+}{\pi }^{-}{\pi }^0\right)<\mathrm{}6\mathrm{}\times {10}^{-4}.$ The ρ-meson mass and width which follow from the spectra analysis are $m_{\rho }=775.0\mathrm{}\pm 1.3$ MeV, ${\Gamma }_{\rho }=150.4\mathrm{}\pm 3.0$ MeV. The mass difference of the neutral and charged $\rho$ mesons was found to equal $m_{{\rho }^{\pm }}-m_{{\rho }^0}=-1.3\pm 2.3$ MeV. In the ${\pi }^{+}{\pi }^{-}$ mass spectrum the $\rho -\omega$ interference was seen at a two standard deviation level.