Study of dynamics of the process $e^+e^-to pi^+pi^-pi^0$ in the energy range 1.15--2.00 GeV

The dynamics of the process $ e^+e^- to pi^+pi^-pi^0 $ is studied in the energy region from 1.15 to 2.00 GeV using data accumulated with the SND detector at the VEPP-2000 $e^+e^-$ collider. The Dalitz plot distribution and $pi^+pi^-$ mass spectrum are analyzed in a model including the intermediate states $rho(770)pi$, $rho(1450)pi$, and $omegapi^0$. As a result, the energy dependences of the $rho(770)pi$ and $rho(1450)pi$ cross sections and the relative phases between the $rho(770)pi$ amplitude and the $rho(1450)pi $ and $omegapi^0$ amplitudes are obtained. The $rho(1450)pi$ cross section has a peak in the energy region of the $omega(1650)$ resonance (1.55-1.75 GeV). In this energy range the contributions of the $rho(770)pi$ and $rho(1450)pi$ states are of the same order of magnitude. No resonance structure near 1.65 GeV is observed in the $rho(770)pi$ cross section. We conclude that the intermediate state $rho(1450)pi$ gives a significant contribution to the decay of $omega (1650)topi^+pi^-pi^0$, whereas the $rho(770)pi$ mechanism dominates in the decay $omega(1420)topi^+pi^-pi^0$.