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

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