Revised ${\alpha }^4$ Term of Lepton $g-2$ from the Feynman Diagrams Containing an Internal Light-By-Light Scattering Subdiagram

The ${\alpha }^4$ contribution to the lepton $g-2$ from a gauge-invariant set of 18 Feynman diagrams containing a light-by-light scattering subdiagram internally has been reevaluated by a method independent of the previous approach. Comparison of two methods revealed a program error in the first version. Correcting this error, the contributions of these 18 diagrams become $-0.99072(10)(\alpha /\pi {)}^4$ and $-4.43243(58)(\alpha /\pi {)}^4$ for the electron and muon $g-2$, respectively. The correction is not large enough to affect the comparison between theory and experiment for the muon $g-2$, but it does alter the inferred value for the fine structure constant ${\alpha }^{-1}$ by 6 ppb.

Figure 1

Vertex diagrams containing a light-by-light scattering subdiagram internally. There are altogether 18 such diagrams.

Figure 2

Self-energy-like diagrams in which lepton lines propagate in the magnetic field. First-order terms in the weak magnetic field expansion correspond to the diagrams of Fig. 1.