Dalitz plot analyses of $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$, $J/\psi \to K^{+}{K}^{-}{\pi }^0$, and $J/\psi \to K_S^0{K}^{\pm }{\pi }^{\mp }$ produced via $e^{+}{e}^{-}$ annihilation with initial-state radiation

Abstract

We study the processes $e^{+}{e}^{-}\to {\gamma }_{\mathrm{ISR}}J/\psi$ where $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$, $J/\psi \to K^{+}{K}^{-}{\pi }^0$, and $J/\psi \to K_S^0{K}^{\pm }{\pi }^{\mp }$ using a data sample of 519 $f{b}^{-1}$ recorded with the BaBar detector operating at the SLAC PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at center-of-mass energies at and near the ${\rm Y}(nS)$ ($n=2,3,4$) resonances. We measure the ratio of branching fractions $R_1=\frac{B(J/\psi \to K^{+}{K}^{-}{\pi }^0)}{B(J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0)}$ and $R_2=\frac{B(J/\psi \to K_S^0{K}^{\pm }{\pi }^{\mp })}{B(J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0)}$. We perform Dalitz-plot analyses of the three $J/\psi$ decay modes and measure fractions for resonances contributing to the decays. We also analyze the $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay using the Veneziano model. We observe structures compatible with the presence of $\rho (1450)$ in all the three $J/\psi$ decay modes and measure the relative branching fraction: $R(\rho (1450))=\frac{B(\rho (1450)\to K^{+}{K}^{-})}{B(\rho (1450)\to {\pi }^{+}{\pi }^{-})}=0.307\pm 0.084(\mathrm{stat})\pm 0.082(\mathrm{sys})$.

22 pages, 17 postscript figures, to be published in Phys. Rev. D