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We report a measurement of the e^+e^- ^+^-⁰ 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 (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^- ^+^-⁰ events, which involve a ⁰ 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 and 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_^3 = 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.
Collaboration et al. (Sun,) studied this question.