The Tenth-Order QED Contribution to the Lepton g-2: Evaluation of Dominant ${\alpha }^5$ Terms of Muon g-2

Abstract

The QED contribution to the anomalous magnetic moments of electron and muon are known very precisely up to the order ${\alpha }^4$. However, the knowledge of ${\alpha }^5$ term will also be required when the precision of measurement improves further. This paper reports the first systematic attempt to evaluate the ${\alpha }^5$ term. Feynman diagrams contributing to this term can be classified into six gauge-invariant sets which can be subdivided further into 32 gauge-invariant subsets. Thus far we have numerically evaluated all integrals of 17 gauge-invariant subsets which contain light-by-light-scattering subdiagrams and/or vacuum-polarization subdiagrams. They cover most of leading terms of muon $g-2$ and lead to a preliminary result 663(20) $(\alpha /\pi {)}^5$, which is 8.5 times more precise than the old estimate.

arXiv comment47 pages, 8 figures.A_2^{(10)} is increased to 663(20)

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