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

TL;DR

This study investigates the dynamics of the $e^+e^- o \pi^+\pi^-\pi^0$ process between 1.15 and 2.00 GeV, analyzing intermediate states and cross sections to understand resonance contributions and decay mechanisms.

Contribution

It provides the first detailed analysis of the energy dependence of intermediate states and their phases in the $e^+e^- o \pi^+\pi^-\pi^0$ process within this energy range.

Findings

The $ ho(1450)\pi$ cross section peaks near the $\omega(1650)$ resonance.

Both $ ho(770)\pi$ and $ ho(1450)\pi$ contribute significantly around 1.55-1.75 GeV.

No resonance observed near 1.65 GeV in the $ ho(770)\pi$ cross section.

Abstract

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 $\omega(1420)\to\pi^+\pi^-\pi^0$.