The relation between the QED charge renormalized in image and on-shell schemes at four loops, the QED on-shell β-function at five loops and asymptotic contributions to the muon anomaly at five and six loops Original Research Article

In this paper we compute the four-loop corrections to the QED photon self-energy image in the two limits of image and image. These results are used to explicitly construct the conversion relations between the QED charge renormalized in on-shell (OS) and image scheme. Using these relations and results of Baikov et al. we construct the momentum dependent part of image at large image at five loops in both image and OS schemes. As a direct consequence we arrive at the full result for the QED β-function in the OS scheme at five loops. These results are applied, in turn, to analytically evaluate a class of asymptotic contributions to the muon anomaly at five and six loops.