Precision Measurement of the Hadronic Contribution to the Muon Anomalous Magnetic Moment

We report on a precision measurement of the cross section for the reaction $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ in the mass range $0.30<M_{\pi \pi }<1.00$ GeV with the initial state radiation (ISR) method, using 817 pb${}^{-1}$ of data at $e^{+}{e}^{-}$ center-of-mass energies near 3.77 GeV and 586 pb${}^{-1}$ of data at $e^{+}{e}^{-}$ center-of-mass energies near 4.17 GeV, collected with the CLEO-c detector at the CESR $e^{+}{e}^{-}$ collider at Cornell University. The integrated cross sections in the range $0.30<M_{\pi \pi }<1.00$ GeV for the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ are determined with a statistical uncertainty of $0.7\mathrm{\%}$ and a systematic uncertainty of $1.5\mathrm{\%}$. The leading-order hadronic contribution to the muon anomalous magnetic moment calculated using these measured $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ cross sections in the range $M_{\pi \pi }=0.30$ to 1.00 GeV is calculated to be $(500.4\pm 3.6(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 7.5(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}))\times {10}^{-10}$.