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In this paper we compute the four-loop corrections to the QED photonself-energy Pi(Q^2) in the two limits of q=0 and Q^2->infinity. These resultsare used to explicitly construct the conversion relations between the QEDcharge renormalized in on-shell(OS) and MSbar scheme. Using these relations andresults of Baikov et al. [1] we construct the momentum dependent part ofPi(Q^2,m,alpha) at large Q^2 at five loops in both MSbar and OS schemes. As adirect consequence we arrive at the full result for the QED beta-function inthe OS scheme at five loops. These results are applied, in turn, toanalytically evaluate a class of asymptotic contributions to the muon anomalyat five and six loops.

nuclear physics b

The relation between the QED charge renormalized in MSbar and on-shell  schemes at four loops, the QED on-shell beta-function at five loops and  asymptotic contributions to the muon anomaly at five and six loops