A New Precise Measurement of the $e^+e^-\to\pi^+\pi^-(\gamma)$ Cross Section with the Initial-State Radiation Method at BaBar
Abstract
We report precise results for the $e^+e^-\to \pi^+\pi^-(\gamma)$ cross section in the energy range between threshold and 1.4 GeV, relevant for the hadronic vacuum polarization contribution to the muon $g-2$ prediction. Using the full 460 fb$^{-1}$ of on- and off-$\Upsilon(4S)$ data, the cross section is derived from the ratio of $\pi^+\pi^-$ to $\mu^+\mu^-$ initial-state radiation (ISR) events, in which many systematic uncertainties cancel. The pion/muon separation does not rely on particle identification as in the 2009 BaBar analysis, but rather makes use of the well-known, different angular distributions in the two-particle center-of-mass system. The compatibility and correlation between the 2026 and 2009 measurements are discussed. The new measurement is also compared with other two-pion results. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the new 2026 and combined 2009 and 2026 BaBar measurements in the energy range of 0.3$-$1.4 GeV are $525.9\pm 3.5_\mathrm{stat}\pm3.8_\mathrm{syst}$ and $517.8\pm 2.4_\mathrm{stat}\pm3.3_\mathrm{syst}$ in units of $10^{-10}$, respectively.