Hadronic contributions to the anomalous magnetic moment of the electron and the hyperfine splitting of muonium

Motivated by recent progress of theory and experiment on the anomalous magnetic moment of the electron, a_e, we update the hadronic contributions to a_e. Using our up-to-date compilation of e^+ e^- \to hadrons data, we find the leading order hadronic contribution a_e^{had,LO,VP} = (1.866 \pm 0.010_{exp} \pm 0.005_{rad}) \cdot 10^{-12} and the next-to-leading order hadronic contribution a_e^{had,NLO,VP} = (- 0.2234 \pm 0.0012_{exp} \pm 0.0007_{rad}) \cdot 10^{-12}, where the first and second errors are from the error of the experimental data and the uncertainty in the treatment of radiative corrections, respectively. These values are compatible with earlier evaluations by other groups, but have significantly improved uncertainties due to the more precise input data used. We also update the leading order hadronic contribution to the ground state hyperfine splitting of muonium, obtaining \Delta \nu_{Mu}^{had,VP} = (232.68 \pm 1.25_{exp} \pm 0.72_{rad}) Hz. This value is consistent with the most precise evaluation in the literature and reduces its error by a factor of two.