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

TL;DR

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, which leads to a(e) = 1,159,652,181.

Abstract

This paper presents the complete QED contribution to the electron g-2 up to the tenth order. With the help of the automatic code generator, we have evaluated all 12672 diagrams of the tenth-order diagrams and obtained 9.16 (58)(α/π)^5. We have also improved the eighth-order contribution obtaining -1.9097(20)(α/π)^4, which includes the mass-dependent contributions. These results lead to a_e(theory)=1 159 652 181.78 (77) \times 10^{-12}. The improved value of the fine-structure constant α^{-1} = 137.035 999 174 (35) [0.25 ppb] is also derived from the theory and measurement of a_e.

Figures (2)

• Figure 1: Typical vertex diagrams representing 13 gauge-invariant subsets contributing to the eighth-order lepton $g\!-\!2$.
• Figure 2: Typical self-energy-like diagrams representing 32 gauge-invariant subsets contributing to the tenth-order lepton $g\!-\!2$. Solid lines represent lepton lines propagating in a weak magnetic field.