Dalitz plot analyses of J /ψ →π+π-π0, J /ψ →k+K-π0, and J /ψ → Ks0 K±π∓ produced via e+e- annihilation with initial-state radiation

We study the processes e^+e^− → γISR J/ψ, where J/ψ → π^+π^−π^0, J/ψ → K^+K^−π^0, and J/ψ → K^0_SK^±π^∓ using a data sample of 519 fb^(−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 Υ(nS) (n=2,3,4) resonances. We measure the ratio of branching fractions R_1 = ^(B(J/ψ → K^+K^−π^0)) /_(B(J/ψ → π^+π^−π^0)) and R_2 = ^(B(J/ψ → K^0_SK^±π^∓))/_(B(J/ψ → π^+π^−π^0)). We perform Dalitz plot analyses of the three J/ψ decay modes and measure fractions for resonances contributing to the decays. We also analyze the J/ψ → π^+π^−π^0 decay using the Veneziano model. We observe structures compatible with the presence of ρ(1450) in all three J/ψ decay modes and measure the relative branching fraction: R(ρ(1450)) = ^(B(ρ(1450) → K^+K^−))/_(B(ρ(1450) → π^+π^−)) = 0.307±0.084(stat)±0.082(sys).