Tenth-order QED contribution to the lepton g-2: Evaluation of dominant α5 terms of muon g-2

The QED contribution to the anomalous magnetic moments of electron and muon are known very precisely up to the order α4. However, the knowledge of the α5 term will also be required when the precision of measurement improves further. This paper reports the first systematic attempt to evaluate the α5 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) (α/π)5, which is 8.5 times more precise than the old estimate