A New Precise Measurement of the $e^+e^-\toπ^+π^-(γ)$ Cross Section with the Initial-State Radiation Method at BaBar

Abstract

We measure the $e^+e^-\toπ^+π^-(γ)$ cross section from threshold to 1.4 GeV using 460 fb$^{-1}$ of BaBar initial-state radiation data. The result is obtained from the $π^+π^-/μ^+μ^-$ ratio, reducing systematic uncertainties that are in common. Unlike the previous 2009 BaBar analysis, the pion and muon contributions are separated statistically through their angular distributions. The compatibility with the previous BaBar result is quantified including statistical and systematic correlations. The new measurement is also compared with other two-pion results as a function of energy and in terms of its hadronic vacuum polarization (HVP) contribution to the muon magnetic anomaly. The leading-order HVP contribution of the two-pion channel in the energy range of 0.3$-$1.4 GeV is $a_μ^{ππ}=525.9\pm 3.5_\mathrm{stat}\pm3.8_\mathrm{syst}$ and $517.8\pm 2.4_\mathrm{stat}\pm3.3_\mathrm{syst}$ in units of $10^{-10}$ for the new 2026 and combined 2009 and 2026 BaBar measurements, respectively.