Abstract
The process \(e^{+}e^{-}\to\pi^{+}\pi^{-}\pi^{0}\) was studied in the energy range between 1.075 and 1.975 GeV on the basis of data characterized by an integrated luminosity of about 70 pb \({}^{-1}\) that were accumulated in an experiment with the Spherical Neutral Detector (SND) at the VEPP-2000 \(e^{+}e^{-}\) collider. The respective Dalitz distributions were analyzed within a model that includes \(\rho(770)\pi\) , \(\rho(1450)\pi\) , and \(\omega\pi^{0}\) intermediate states. As a result, the energy dependences of the total cross section for the process \(e^{+}e^{-}\to\pi^{+}\pi^{-}\pi^{0}\) and the cross sections for the \(\rho(770)\pi\) and \(\rho(1450)\pi\) intermediate states were measured along with the phase shift of the \(\rho(770)\pi\) amplitude with respect to the \(\rho(1450)\pi\) and \(\omega\pi^{0}\) amplitudes. For the first time, a simultaneous approximation of the cross sections for the processes \(e^{+}e^{-}\to\rho(770)\pi\) and \(\rho(1450)\pi\) and the relative phase of the respective final states was performed on the basis of the vector-meson dominance model. The contributions of the \(\omega\) , \(\phi\) , \(\omega(1420)\) , and \(\omega(1650)\) resonances were taken into account. The approximation showed that the decay \(\omega(1650)\to\pi^{+}\pi^{-}\pi^{0}\) proceeds predominantly through the \(\rho(1450)\pi\) intermediate state, while the decay \(\omega(1420)\to\pi^{+}\pi^{-}\pi^{0}\) receives a dominant contribution from the \(\rho(770)\pi\) mechanism. The results of this study refined the results of earlier measurements with the SND setup.
