Revised value of the eighth-order QED contribution to the anomalous magnetic moment of the electron

Abstract

We have carried out a new evaluation of the eighth-order contribution to the electron $g\ensuremath{-}2$ using FORTRAN codes generated by an automatic code generator gencode$N$. Comparison of the new result with the old one has revealed an inconsistency in the treatment of the infrared divergences in the latter. With this error corrected we now have two independent determinations of the eighth-order term. This leads to the revised value $1\text{ }159\text{ }652\text{ }182.79(7.71)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ of the electron $g\ensuremath{-}2$, where the uncertainty comes mostly from that of the best non-QED value of the fine structure constant $\ensuremath{\alpha}$. The new value of $\ensuremath{\alpha}$ derived from the revised theory and the latest experiment is ${\ensuremath{\alpha}}^{\ensuremath{-}1}=137.035\text{ }999\text{ }084(51)\text{ }[0.37\text{ }\text{ }\mathrm{ppb}]$, which is about 4.7 ppb smaller than the previous ${\ensuremath{\alpha}}^{\ensuremath{-}1}$.