Study of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ using initial state radiation with BABAR

Abstract

The process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ is studied at a center-of-mass energy near the ${\rm Y}(4S)$ resonance using a data sample of 469 fb${}^{-1}$ collected with the BABAR detector at the PEP-II collider. We have performed a precise measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ cross section in the center-of-mass energy range from 0.62 to 3.5 GeV. In the energy regions of the $\omega$ and $\varphi$ resonances, the cross section is measured with a systematic uncertainty of 1.3\%. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ cross section from threshold to 2.0 GeV is $(45.86\pm 0.14\pm 0.58)\times 10^{-10}$. From the fit to the measured $3\pi$ mass spectrum we have determined the resonance parameters $Γ(ω\to e^+e^-){\cal B}(ω\to π^+π^-π^0)=(0.5698\pm0.0031\pm0.0082) \mbox{ keV}$, $Γ(ϕ\to e^+e^-){\cal B}(ϕ\to π^+π^-π^0)=(0.1841\pm0.0021\pm0.0080) \mbox{ keV}$, and $\mathcal{B}(\rho \to 3\pi )=(0.88\pm 0.23\pm 0.30)\times 10^{-4}$. The significance of the $\rho \to 3\pi$ signal is greater than $6\sigma$. For the $J/\psi$ resonance we have measured the product ${Γ(J/ψ\to e^+e^-){\cal B}(J/ψ\to 3π)}=(0.1248\pm0.0019\pm0.0026)\mbox{ keV}$.

35 pages, 28 figures, corrected cross section in Table IV