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

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