Tenth-order QED lepton anomalous magnetic moment: Eighth-order vertices containing a second-order vacuum polarization

This paper reports the evaluation of the tenth-order QED contribution to the lepton g-2 from the gauge-invariant set of 2072 Feynman diagrams, called Set IV, which are obtained by inserting a second-order lepton vacuum-polarization loop into 518 eighth-order vertex diagrams of four-photon exchange type. The numerical evaluation is carried out by the adaptive-iterative Monte Carlo integration routine vegas using the fortran codes written by the automatic code-generating algorithm gencodeN. Some of the numerical results are confirmed by comparison with the values of corresponding integrals that have been obtained previously by a different method. The result for the mass-independent contribution of the Set IV to the electron g-2 is -7.7296(48)(α/π)⁵. There is also a small mass-dependent contribution to the electron g-2 due to the muon loop: -0.01136(7)(α/π)⁵. The contribution of the tau-lepton loop is -0.0000937(104)(α/π)⁵. The sum of all these contributions to the electron g-2 is -7.7407(49)(α/π)⁵. The same set of diagrams enables us to evaluate the contributions to the muon g-2 from the electron loop, muon loop, and tau-lepton loop. They add up to -46.95(17)(α/π)⁵.