The relation between the QED charge renormalized in MS? 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

摘要

In this paper we compute the four-loop corrections to the QED photon self-energy Π(Q~2) in the two limits of q=0 and Q~2→∞. These results are used to explicitly construct the conversion relations between the QED charge renormalized in on-shell (OS) and MS? scheme. Using these relations and results of Baikov et al. [1] we construct the momentum dependent part of Π(Q~2, m, α) at large Q~2 at five loops in both MS? 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.