Measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ cross section in the energy region from 0.56 to 1.1 GeV with the SND detector

The precise measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ cross section is performed in the center-of-mass energy range $E=560$–1100 MeV using a data sample of 66 pb${}^{-1}$ collected in the experiment with the SND detector at the VEPP-2000 $e^{+}{e}^{-}$ collider. The systematic uncertainty of the cross section measurement is 0.9% at the maximum of the $\omega$ resonance and 1.2% at the maximum of the $\phi$ resonance. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ cross section measured by SND from 0.62 to 1.975 GeV is $(45.95\pm 0.06\pm 0.46)\times {10}^{-10}$. From the fit to the cross section data with the vector meson dominance model, the parameters of the $\omega$, $\rho$, and $\phi$ resonances are obtained. The obtained values of $\mathcal{B}(\omega \to e^{+}{e}^{-})\mathcal{B}(\omega \to 3\pi )$, mass and width of the $\omega$ meson, and $\mathcal{B}(\rho \to 3\pi )$ have accuracy better than the current world average values.