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Motivated by recent progress of theory and experiment on the anomalousmagnetic moment of the electron, a_e, we update the hadronic contributions toa_e. Using our up-to-date compilation of e^+ e^- \to hadrons data, we find theleading 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 hadroniccontribution 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 theexperimental data and the uncertainty in the treatment of radiativecorrections, respectively. These values are compatible with earlier evaluationsby other groups, but have significantly improved uncertainties due to the moreprecise input data used. We also update the leading order hadronic contributionto 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 isconsistent with the most precise evaluation in the literature and reduces itserror by a factor of two.

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