Tenth-order QED contribution to the lepton anomalous magnetic moment: Sixth-order vertices containing an internal light-by-light-scattering subdiagram

This paper reports the tenth-order QED contribution to the lepton g-2 from the gauge-invariant set, called Set III(c), which consists of 390 Feynman vertex diagrams containing an internal fourth-order light-by-light-scattering subdiagram. The mass-independent contribution of Set III(c) to the electron g-2 (aₑ) is 4.9210 (103) in units of (α/π)⁵. The mass-dependent contributions to aₑ from diagrams containing a muon loop is 0.00370 (37) (α/π)⁵. The tau-lepton loop contribution is negligible at present. Altogether the contribution of Set III(c) to aₑ is 4.9247 (104) (α/π)⁵. We have also evaluated the contribution of the closed electron loop to the muon g-2 (a_μ). The result is 7.435 (134) (α/π)⁵. The contribution of the tau-lepton loop to a_μ is 0.1999 (28) (α/π)⁵. The total contribution of various leptonic loops (electron, muon, and tau-lepton) of Set III(c) to a_μ is 12.556 (135)(α/π)⁵.