This paper presents a detailed account of the evaluation of the electron anomalous magnetic moment $a_e$ which arises from a gauge-invariant set, called Set V, consisting of 6354 tenth-order Feynman diagrams without closed lepton loops. The latest value of the sum of Set V diagrams evaluated by the Monte?Carlo integration routine VEGAS is 8.726 $(336)(\alpha /\pi {)}^5$, which replaces the very preliminary value reported in 2012. Combining it with 6318 previously published tenth-order diagrams, we obtain 7.795 $(336)(\alpha /\pi {)}^5$ as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to $a_e(\text{theory})=1159652181.643(25)(23)(16)(763)\times 10^{?12}$, where the first three uncertainties are from the eighth-order, tenth-order, and hadronic and elecroweak terms. The fourth and largest uncertainty is from ${\alpha }^{?1}=137.035999049(90)$, the fine-structure constant derived from the rubidium recoil measurement. Thus, $a_e(\text{experiment})?a_e(\text{theory})=?0.91(0.82)\times 10^{?12}$. Assuming the validity of the standard model, we obtain the fine-structure constant ${\alpha }^{?1}(a_e)=137.0359991570(29)(27)(18)(331)$, where uncertainties are from the eighth-order, tenth-order, and hadronic and electroweak terms, and the measurement of $a_e$. This is the most precise value of $\alpha$ available at present and provides a stringent constraint on possible theories beyond the standard model.

• Received 29 December 2014

DOI: https://doi.org/10.1103/PhysRevD.91.033006