Abstract
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
$e^+e^-\to\mu^+\mu^-(\gamma)\gamma_{\rm ISR}$, 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 $(514.1 \pm 2.2({\rm stat})
\pm 3.1({\rm syst}))\times 10^{-10}$.