Measurement of the e⁺e⁻ → π⁺π⁻π⁰ cross section in the energy range 0.62-3.50 GeV at Belle II

We report a measurement of the e⁺e⁻ → π⁺π⁻π⁰ cross section in the energy range from 0.62 to 3.50 GeV using an initial-state radiation technique. We use an e⁺e⁻ data sample corresponding to 191 fb⁻¹ of integrated luminosity, collected at a center-of-mass energy at or near the Υ(4S) resonance with the Belle II detector at the SuperKEKB collider. Signal yields are extracted by fitting the two-photon mass distribution in e⁺e⁻ → π⁺π⁻π⁰γ events, which involve a π⁰ → γγ decay and an energetic photon radiated from the initial state. Signal efficiency corrections with an accuracy of 1.6% are obtained from several control data samples. The uncertainty on the cross section at the ω and φ resonances is dominated by the systematic uncertainty of 2.2%. The resulting cross sections in the 0.62-1.80 GeV energy range yield a_μ3π = [48.91 ± 0.23~(stat) ± 1.07~(syst)] × 10⁻¹⁰ for the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. This result differs by $2.5$ standard deviations from the most precise current determination.