Abstract
We have calculated the three-photon exchange contribution to the sixth-order anomalous magnetic moment of the leptons. Our result for the electron-loop contribution to the muon moment (18.4\ifmmode\pm\else\textpm\fi{}1.1) ${(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})}^{3}$ brings the theoretical prediction into agreement with the CERN measurements within the 1-standard-deviation experimental accuracy. The result for the electron-loop contribution to the electron moment is (0.36\ifmmode\pm\else\textpm\fi{}0.04) ${(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})}^{3}$. The theoretical errors represent the accuracy of the required seven-dimensional numerical integrations.
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