Heavy lepton contribution to the anomalous magnetic moment of the muon and the electron at four loops in QED

We present results for the QED contribution from a heavy lepton loop to the anomalous magnetic moment of the muon and the electron. Exploiting the strong hierarchy between the tau, muon and electron masses (mτ >>mμ >>me), we use the method of asymptotic expansion which leads to on-shell and vacuum integrals up to three and four loops, respectively. Analytic results are presented up to four loops for the muon anomalous moment involving virtual τ-lepton loops and for the electron magnetic moment involving τ- and μ-lepton loops.