Study of dynamics of the process $e^+e^-\to π^+π^-π^0$ in the energy range 1.15--2.00 GeV
The dynamics of the process $ e^+e^- \to π^+π^-π^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 $π^+π^-$ mass spectrum are analyzed in a model including the intermediate states $ρ(770)π$, $ρ(1450)π$, and $ωπ^0$. As a result, the energy dependences of the $ρ(770)π$ and $ρ(1450)π$ cross sections and the relative phases between the $ρ(770)π$ amplitude and the $ρ(1450)π$ and $ωπ^0$ amplitudes are obtained. The $ρ(1450)π$ cross section has a peak in the energy region of the $ω(1650)$ resonance (1.55-1.75 GeV). In this energy range the contributions of the $ρ(770)π$ and $ρ(1450)π$ states are of the same order of magnitude. No resonance structure near 1.65 GeV is observed in the $ρ(770)π$ cross section. We conclude that the intermediate state $ρ(1450)π$ gives a significant contribution to the decay of $ω(1650)\toπ^+π^-π^0$, whereas the $ρ(770)π$ mechanism dominates in the decay $ω(1420)\toπ^+π^-π^0$.