Tenth-Order QED Contribution to the Electrong−2and an Improved Value of the Fine Structure Constant

Abstract

This Letter presents the complete QED contribution to the electron $g-2$ up to the tenth order. With the help of the automatic code generator, we evaluate all 12 672 diagrams of the tenth-order diagrams and obtain $9.16(58)(\alpha /\pi {)}^5$. We also improve the eighth-order contribution obtaining $-1.9097(20)(\alpha /\pi {)}^4$, which includes the mass-dependent contributions. These results lead to $a_e(\mathrm{\text{theory}})=1159652181.78(77)\times {10}^{-12}$. The improved value of the fine-structure constant ${\alpha }^{-1}=137.035999173(35)$ [0.25 ppb] is also derived from the theory and measurement of $a_e$.