Dalitz plot analyses of J/ψ→π+π−π0 , J/ψ→K+K−π0 , and J/ψ→Ks0K±π∓ produced via e+e− annihilation with initial-state radiation

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

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