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In order to improve the theoretical prediction of the electron anomalous magnetic moment a₄ we have carried out a new numerical evaluation of the 389 integrals of Set V, which represent 6, 354 Feynman vertex diagrams without lepton 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 incorrect assignment of integration variables. The correction of this error causes a shift of -1. 26 to the Set V contribution, and hence to the tenth-order universal (i. e. , mass-independent) term A₁^ (10). The previous evaluation of all other 388 integrals is free from errors and consistent with the new evaluation. Combining the new and the old (excluding X024) calculations statistically, we obtain 7. 606 (192) (/) ^5 as the best estimate of the Set V contribution. Including the contribution of the diagrams with fermion loops, the improved tenth-order universal term becomes A₁^ (10) =6. 675 (192). Adding hadronic and electroweak contributions leads to the theoretical prediction a₄ (theory) =1159652182. 032 (720) 10^-12. From this and the best measurement of a₄, we obtain the inverse fine-structure constant ^-1 (a₄) =137. 0359991491 (331). The theoretical prediction of the muon anomalous magnetic moment is also affected by the update of QED contribution and the new value of, but the shift is much smaller than the theoretical uncertainty.
Aoyama et al. (Thu,) studied this question.