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In order to improve the theoretical prediction of the electron anomalousmagnetic moment $a_e$ we have carried out a new numerical evaluation of the 389integrals of Set V, which represent 6,354 Feynman vertex diagrams withoutlepton loops. During this work, we found that one of the integrals, called$X024$, was given a wrong value in the previous calculation due to an incorrectassignment of integration variables. The correction of this error causes ashift of $-1.25$ to the Set~V contribution, and hence to the tenth-orderuniversal (i.e., mass-independent) term $ A_1^{(10)}$. The previous evaluationof all other 388 integrals is free from errors and consistent with the newevaluation. Combining the new and the old (excluding $X024$) calculationsstatistically, we obtain $7.606~(192) (\alpha/\pi)^5$ as the best estimate ofthe Set V contribution. Including the contribution of the diagrams with fermionloops, the improved tenth-order universal term becomes$A_1^{(10)}=6.678~(192)$. Adding hadronic and electroweak contributions leadsto the theoretical prediction $a_e (\text{theory})=1~159~652~182.032~(720)\times 10^{-12}$. From this and the best measurement of$a_e$, we obtain the inverse fine-structure constant $\alpha^{-1}(a_e) =137.035~999~1491~(331)$. The theoretical prediction of the muon anomalousmagnetic moment is also affected by the update of QED contribution and the newvalue of $\alpha$, but the shift is much smaller than the theoreticaluncertainty.

Revised and Improved Value of the QED Tenth-Order Electron Anomalous Magnetic Moment