# TTP12-021 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

TTP12-021 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

TTP12-021 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

In this paper we compute the four-loop corrections to the QED photon

self-energy $\Pi(Q^2)$ in the two limits of $q = 0$ and $Q^2 \to \infty$. These results are used to explicitly construct the conversion
relations between the QED charge renormalized in on-shell(OS) and $\MSbar$
scheme. Using these relations and results of Baikov et al. \cite{Baikov:2012zm} we
construct the momentum dependent part of $\Pi(Q^2,m,\alpha)$ at
large $Q^2$ at five loops in both $\MSbar$ and OS schemes.  As a direct
consequence we arrive at the full result for the QED $\beta$-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.
 P. A. Baikov, K. G. Chetyrkin, J. H. Kühn and C. Sturm Nucl. Phys. B867 182-202\ 2013 25 pages, 6 figures; v2: final published version PDF PostScript arXiv