Abstract

This paper reports the tenth-order contributions to the $g\ensuremath{-}2$ of the electron ${a}_{e}$ and those of the muon ${a}_{\ensuremath{\mu}}$ from the gauge-invariant Set II(c), which consists of 36 Feynman diagrams, and Set II(d), which consists of 180 Feynman diagrams. Both sets are obtained by insertion of sixth-order vacuum-polarization diagrams in the fourth-order anomalous magnetic moment. The mass-independent contributions from Set II(c) and Set II(d) are $\ensuremath{-}0.116\text{ }489\text{ }(32)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$ and $\ensuremath{-}0.243\text{ }00\text{ }(29)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$, respectively. The leading contributions to ${a}_{\ensuremath{\mu}}$, which involve electron loops only, are $\ensuremath{-}3.888\text{ }27\text{ }(90)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$ and $0.4972\text{ }(65)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$ for Set II(c) and Set II(d), respectively. The total contributions of the electron, muon, and tau-lepton loops to ${a}_{e}$ are $\ensuremath{-}0.116\text{ }874\text{ }(32)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$ for the Set II(c), and $\ensuremath{-}0.243\text{ }10\text{ }(29)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$ for the Set II(d), respectively. The contributions of the electron, muon, and tau-lepton loop to ${a}_{\ensuremath{\mu}}$ are $\ensuremath{-}5.5594\text{ }(11)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$ for the Set II(c) and $0.2465\text{ }(65)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$ for the Set II(d), respectively.

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