Sixth-order magnetic moment of the electron

We have evaluated the contribution of 50 Feynman diagrams of three-photon-exchange type to the electron magnetic moment by two independent methods. The results are mutually consistent and are several times more accurate than previously reported calculations. If we combine the analytic result of Levine and Roskies for 10 diagrams and our numerical result for the remaining 40 diagrams, we obtain the best estimate available at present: $(0.922\mathrm{}\pm 0.024)\times {\left(\frac{\alpha }{\pi }\right)}^3$. Including the contribution from the remaining 22 diagrams calculated previously, the complete theoretical prediction for the electron anomaly up to the order ${\alpha }^3$ is $\frac{1}{2}\frac{\alpha }{\pi }-0.328\mathrm{}48{\left(\frac{\alpha }{\pi }\right)}^2+(1.195\mathrm{}\pm 0.026){\left(\frac{\alpha }{\pi }\right)}^3$, in fair agreement with the latest experimental result.