Tenth-Order Electron Anomalous Magnetic Moment --- Contribution of Diagrams without Closed Lepton Loops

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This paper presents a detailed account of evaluation of the electron anomalous magnetic moment aₑ which arises from the 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)(α/π)⁵, which replaces the very preliminary value reported in 2012. Combining it with other 6318 tenth-order diagrams published previously we obtain 7.795(336)(α/π)⁵ as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to aₑ(theory)=1 159 652 181.643(25)(23)(16)(763) × 10⁻¹², where first three uncertainties are from the eighth-order term, tenth-order term, and hadronic and elecroweak terms. The fourth and largest uncertainty is from α⁻¹=137.035 999 049(90), the fine-structure constant derived from the rubidium recoil measurement. Thus, aₑ(experiment) - aₑ(theory)= -0.91(0.82) × 10⁻¹². Assuming the validity of the standard model, we obtain the fine-structure constant α⁻¹(aₑ)=137.035 999 1570(29)(27)(18)(331), where uncertainties are from the eighth-order term, tenth-order term, hadronic and electroweak terms, and the measurement of aₑ. This is the most precise value of αavailable at present and provides a stringent constraint on possible theories beyond the standard model.