Measurement of the $e^+e^-\toπ^+π^-π^0$ cross section from 0.7 GeV to 3.0 GeV via initial-state radiation

The cross section of the process $e^+e^-\toπ^+π^-π^0$ is measured with a precision of 1.6% to 25% in the energy range between $0.7$ and 3.0 GeV using the Initial State Radiation method. A data set with an integrated luminosity of $2.93$fb$^{-1}$ taken at the center-of-mass energy of $\sqrt{s}=3.773$GeV with the BESIII detector at the BEPCII collider is used. The product branching fractions for $ω$, $φ$, $ω(1420)$, and $ω(1650)$ are measured to be $\mathcal{B}(ω\to e^+e^-) \times \mathcal{B}(ω\to π^+π^-π^0)=(6.94\pm0.08\pm0.16) \times 10^{-5}$, $\mathcal{B}(φ\to e^+e^-) \times \mathcal{B}(φ\toπ^+π^-π^0) = (4.20\pm0.08\pm0.19) \times 10^{-5}$, $\mathcal{B}(ω(1420)\to e^+e^-) \times \mathcal{B}(ω(1420) \to π^+π^-π^0) = (0.84\pm0.09\pm0.09) \times 10^{-6}$, and $\mathcal{B}(ω(1650) \to e^+e^) \times \mathcal{B}(ω(1650)\to π^+π^-π^0) = (1.14\pm0.15\pm0.15)\times10^{-6}$, respectively. The branching fraction $\mathcal{B}(J/ψ\to π^+π^-π^0)$ is measured to be $(2.188 \pm 0.024 \pm 0.024 \pm0.040 (Γ_{ee}^{J/ψ}))\%$, where $Γ_{ee}^{J/ψ}$ is the dileptonic width of $J/ψ$. The first errors are of statistical, the second and third ones of systematic nature.