====== 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 ======
 
 
   <hidden 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.
 </hidden>
|**P. A. Baikov, K. G. Chetyrkin, J. H. K&uuml;hn and C. Sturm**  | 
|** Nucl. Phys. B867  182-202\ 2013 25 pages, 6 figures; v2: final published version **  |
| {{preprints:2012:ttp12-021.pdf|PDF}} {{preprints:2012:ttp12-021.ps|PostScript}} [[http://arxiv.org/abs/1207.2199|arXiv]]   |
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