Abstract
This paper reports the evaluation of the tenth-order QED contribution to the lepton 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 gencode. 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 is . There is also a small mass-dependent contribution to the electron due to the muon loop: . The contribution of the tau-lepton loop is . The sum of all these contributions to the electron is . The same set of diagrams enables us to evaluate the contributions to the muon from the electron loop, muon loop, and tau-lepton loop. They add up to .
- Received 18 October 2011
DOI:https://doi.org/10.1103/PhysRevD.85.033007
© 2012 American Physical Society