New Value of theα3Electron Anomalous Magnetic Moment

Highly accurate numerical evaluation of the sixth-order term of the electron anomalous magnetic moment $a_e$ has detected an error in the analytic value of a fourth-order infrared-divergent integral, which is needed to obtain the best estimate of the ${\alpha }^3$ term as a combination of analytic values of 67 Feynman diagrams and numerical values of 5 diagrams for which no analytic results are known. Correction of this error leads to a small but significant revision of the ${\alpha }^3$ term. As a consequence the fine structure constant $\alpha$ determined from theory and experiment of $a_e$ is reduced by $55\times {10}^{-9\mathrm{}}$.