Eighth-order magnetic moment of the electron. I. Second-order vertex containing second-, fourth-, and sixth-order vacuum polarization subdiagrams

Abstract

We have calculated the contribution to the eighth-order anomalous magnetic moment of the electron arising from 25 Feynman diagrams generated by inserting second-, fourth-, and sixth-order vacuum polarization loops in the photon line of the second-order vertex diagram. Our result is $0.0766\left(6\right)\mathrm{}{\left(\frac{\alpha }{\pi }\right)}^4$. The theoretical error represents the estimated accuracy (90% confidence limit) of the numerical integrations.