Tenth-order lepton g−2 : Contribution from diagrams containing sixth-order light-by-light-scattering subdiagram internally

This paper reports the result of our evaluation of the tenth-order QED correction to the lepton g-2 from Feynman diagrams which have sixth-order light-by-light-scattering subdiagrams, none of whose vertices couple to the external magnetic field. The gauge-invariant set of these diagrams, called Set II(e), consists of 180 vertex diagrams. In the case of the electron g-2 (aₑ), where the light-by-light subdiagram consists of the electron loop, the contribution to aₑ is found to be -1.344 9 (10)(α/π)⁵. The contribution of the muon loop to aₑ is -0.000 465 (4)(α/π)⁵. The contribution of the tau-lepton loop is about two orders of magnitudes smaller than that of the muon loop and hence negligible. The sum of all of these contributions to aₑ is -1.345 (1)(α/π)⁵. We have also evaluated the contribution of Set II(e) to the muon g-2 (a_μ). The contribution to a_μ from the electron loop is 3.265 (12)(α/π)⁵, while the contribution of the tau-lepton loop is -0.038 06 (13)(α/π)⁵. The total contribution to a_μ, which is the sum of these two contributions and the mass-independent part of aₑ, is 1.882 (13)(α/π)⁵.