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 \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 $\omega (1650)\to\pi^+\pi^-\pi^0$, whereas the
$\rho(770)\pi$ mechanism dominates in the decay
$\omega(1420)\to\pi^+\pi^-\pi^0$.

Authors

SND Collaboration, M. N. Achasov, A. Yu. Barnyakov, A. A. Baykov, K. I. Beloborodov, A. V. Berdyugin, D. E. Berkaev, A. G. Bogdanchikov, A. A. Botov, T. V. Dimova, V. P. Druzhinin, V. B. Golubev, A. N. Kirpotin, L. V. Kardapoltsev, A. S. Kasaev, A. G. Kharlamov, I. A. Koop, A. A. Korol, D. P. Kovrizhin, A. S. Kupich