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

Understand

The process $e^+e^-\to \pi^+\pi^-\pi^0\gamma$ is studied at a center-of-mass energy near the $\Upsilon(4S)$ 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 $\phi$ 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 $(45.86 \pm 0.14 \pm 0.58)\times 10^{-10}$.