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

The dynamics of the process $$ e^+e^- \rightarrow \pi ^+\pi ^-\pi ^0 $$ 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 $$\omega \pi ^0$$ . 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 $$\omega \pi ^0$$ 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 $$\omega (1650)\rightarrow \pi ^+\pi ^-\pi ^0$$ , whereas the $$\rho (770)\pi $$ mechanism dominates in the decay $$\omega (1420)\rightarrow \pi ^+\pi ^-\pi ^0$$ .