Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops

Abstract

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 $(336)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$, which replaces the very preliminary value reported in 2012. Combining it with 6318 previously published tenth-order diagrams, we obtain 7.795 $(336)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$ as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to ${a}_{e}(\text{theory})=1\text{ }159\text{ }652\text{ }181.643\text{ }(25)(23)(16)(763)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}12}$, where the first three uncertainties are from the eighth-order, tenth-order, and hadronic and elecroweak terms. The fourth and largest uncertainty is from ${\ensuremath{\alpha}}^{\ensuremath{-}1}=137.035\text{ }999\text{ }049\text{ }(90)$, the fine-structure constant derived from the rubidium recoil measurement. Thus, ${a}_{e}(\text{experiment})\ensuremath{-}{a}_{e}(\text{theory})=\ensuremath{-}0.91\text{ }(0.82)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}12}$. Assuming the validity of the standard model, we obtain the fine-structure constant ${\ensuremath{\alpha}}^{\ensuremath{-}1}({a}_{e})=\phantom{\rule{0ex}{0ex}}137.035\text{ }999\text{ }1570\text{ }(29)(27)(18)(331)$, 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 $\ensuremath{\alpha}$ available at present and provides a stringent constraint on possible theories beyond the standard model.