Revised and improved value of the QED tenth-order electron anomalous magnetic moment

Abstract

In order to improve the theoretical prediction of the electron anomalous magnetic moment ${a}_{e}$ 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 $\ensuremath{-}1.26$ to the Set V contribution, and hence to the tenth-order universal (i.e., mass-independent) term ${A}_{1}^{(10)}$. 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 $7.606(192)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$ 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 ${A}_{1}^{(10)}=6.675(192)$. Adding hadronic and electroweak contributions leads to the theoretical prediction ${a}_{e}(\text{theory})=1159652182.032(720)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$. From this and the best measurement of ${a}_{e}$, we obtain the inverse fine-structure constant ${\ensuremath{\alpha}}^{\ensuremath{-}1}({a}_{e})=137.0359991491(331)$. The theoretical prediction of the muon anomalous magnetic moment is also affected by the update of QED contribution and the new value of $\ensuremath{\alpha}$, but the shift is much smaller than the theoretical uncertainty.