Improved analysis ofJ/ψdecays into a vector meson and two pseudoscalars

Abstract

Recently, the BES collaboration has published an extensive partial-wave analysis of experimental data on $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\phi}{K}^{+}{K}^{\ensuremath{-}}$ and $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\omega}{K}^{+}{K}^{\ensuremath{-}}$. These new results are analyzed here, with full account of detection efficiencies, in the framework of a chiral unitary description with coupled-channel final state interactions between $\ensuremath{\pi}\ensuremath{\pi}$ and $K\overline{K}$ pairs. The emission of a dimeson pair is described in terms of the strange and nonstrange scalar form factors of the pion and the kaon, which include the final state interaction and are constrained by unitarity and by matching to the next-to-leading-order chiral expressions. This procedure allows for a calculation of the $S$-wave component of the dimeson spectrum including the ${f}_{0}(980)$ resonance, and for an estimation of the low-energy constants of Chiral Perturbation Theory, in particular, the large ${N}_{c}$ suppressed constants ${L}_{4}^{r}$ and ${L}_{6}^{r}$. The decays in question are also sensitive to physics associated with OZI violation in the ${0}^{++}$ channel. It is found that the $S$-wave contributions to $\ensuremath{\phi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, $\ensuremath{\phi}{K}^{+}{K}^{\ensuremath{-}}$ and $\ensuremath{\omega}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ given by the BES partial-wave analysis may be very well fitted up to a dimeson center-of-mass energy of $\ensuremath{\sim}1.2\text{ }\text{ }\mathrm{GeV}$, for a large and positive value of ${L}_{4}^{r}$ and a value of ${L}_{6}^{r}$ compatible with zero. An accurate determination of the amount of OZI violation in the $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay is achieved, and the $S$-wave contribution to $\ensuremath{\omega}{K}^{+}{K}^{\ensuremath{-}}$ near threshold is predicted.