Eighth-order magnetic moment of the electron. V. Diagrams containing no vacuum-polarization loop

Abstract

We have evaluated the eighth-order contribution to the anomalous magnetic moment of the electron arising from the 518 vertex diagrams which have no closed electron loops. Our result is $-1.934\mathrm{}\left(137\right)\mathrm{} {\left(\frac{\alpha }{\pi }\right)}^4$. The theoretical error represents the estimated accuracy (90% confidence limit) of the required numerical integration. Combining this with the updated results of the previous four papers in this series, we find the complete eighth-order QED contribution to be $-1.434\mathrm{}\left(138\right)\mathrm{} {\left(\frac{\alpha }{\pi }\right)}^4$. If one uses, for ${\alpha }^{-1\mathrm{}}$, the value 137.035 997 9(32) obtained from the quantized Hall effect, this leads to the most accurate theoretical value available at present for the magnetic moment anomaly of the electron, $a_e^{\mathrm{th}}=1159652140\mathrm{}\left(28\right)\mathrm{}\times {10}^{-12\mathrm{}}$, which is within 1.7 standard deviations of the experimental values for the electron and positron: $a_{e^{-}}^{\mathrm{expt}}=1159652188.4\mathrm{}\left(4.3\right)\mathrm{}\times {10}^{-12\mathrm{}}$, $a_{e^{+}}^{\mathrm{expt}}=1159652187.9\mathrm{}\left(4.3\right)\mathrm{}\times {10}^{-12\mathrm{}}$.