Precise Measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}(\gamma )$ 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 3 GeV is obtained with the initial state radiation (ISR) method using $232{\mathrm{fb}}^{-1}$ of data collected with the BABAR detector at $e^{+}{e}^{-}$ center-of-mass energies near 10.6 GeV. The ISR luminosity is determined from a study of the leptonic process $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma (\gamma )$. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the $\pi \pi$ cross section measured from threshold to 1.8 GeV is $\mathbf{(}514.1\pm 2.2(\mathrm{stat})\pm 3.1(\mathrm{syst})\mathbf{)}\times {10}^{-10}$.

Figure 1

(a) The ratio of the measured cross section for $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma (\gamma )$ to the NLO QED prediction. The band represents Eq. (2). (b) The measured cross section for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}(\gamma )$ from 0.3 to 3 GeV. (c) Enlarged view of the $\rho$ region in energy intervals of 2 MeV. The plotted errors are from the sum of the diagonal elements of the statistical and systematic covariance matrices.