Precise Measurement of the e+ e- --> pi+ pi- (gamma) Cross Section with the Initial-State Radiation Method at BABAR

A precise measurement of the cross section of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}(\gamma )$ from threshold to an energy of 3GeV is obtained with the initial-state radiation (ISR) method using 232fb${}^{-1}$ of data collected with the BaBar detector at $e^{+}{e}^{-}$ center-of-mass energies near 10.6GeV. The ISR luminosity is determined from a study of the leptonic process $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}(\gamma ){\gamma }_{\mathrm{I}\mathrm{S}\mathrm{R}}$, which is found to agree with the next-to-leading-order QED prediction to within 1.1%. The cross section for the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}(\gamma )$ is obtained with a systematic uncertainty of 0.5% in the dominant $\rho$ resonance region. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured $\pi \pi$ cross section from threshold to 1.8GeV is $(514.1 \pm 2.2({\rm stat}) \pm 3.1({\rm syst}))\times 10^{-10}$.