Photon-Photon Scattering Contribution to the Sixth-Order Magnetic Moments of the Muon and Electron

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±1.1) ${\left(\frac{\alpha }{\pi }\right)}^3$ 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±0.04) ${\left(\frac{\alpha }{\pi }\right)}^3$. The theoretical errors represent the accuracy of the required seven-dimensional numerical integrations.