Revised Value of the Eighth-Order Contribution to the Electron $g-2$

The contribution to the eighth-order anomalous magnetic moment ($g-2$) of the electron from a set of diagrams without closed lepton loops is recalculated using a new FORTRAN code generated by an automatic code generator. Comparing the contributions of individual diagrams of old and new calculations, we find an inconsistency in the old treatment of IR subtraction terms in two diagrams. Correcting this error leads to the revised value $-1.9144(35)(\alpha /\pi {)}^4$ for the eighth-order term. This theoretical change induces the shift of the inverse of the fine structure constant by $-6.41180(73)\times {10}^{-7}$.

Figure 1

Eighth-order group V diagrams. 47 self-energy-like diagrams of $M_{01}-M_{47}$ represent 518 vertex diagrams.