$\rho-\omega-$Interference in $J/\psi-$Decays and $\rho\to \pi^+\pi^-\pi^0$ Decay

Abstract

We study $\rho-\omega-$interference by analyzing $J/\psi\to \pi^+\pi^-\pi^0\pi^0$. PDG-2002 data on $J/\psi$ decays into $PP$ and $PV$ ($P$ denotes pseudoscalar mesons; $V$, vector mesons) are used to fit a generic model which describes the $J/\psi$ decays. From the fits, we obtain anomalously large branching ratio $Br(\rho^0\to \pi^+\pi^-\pi^0)\sim 10^{-3}-10^{-2}$. A theoretical analysis for it is also provided, and the prediction is in good agreement with the anomalously large $Br(\rho^0\to \pi^+\pi^-\pi^0)$. By the fit, we also get the $\eta-\eta'-$mixing angle $\theta=-19.68^o\pm 1.49^o$ and the constituent quark mass ratio $m_u/m_s\sim 0.6$ which are all reasonable.