The QED vacuum polarization function at four loops and the anomalous magnetic moment at five loops

The anomalous magnetic moment of the muon is one of the most fundamental observables. It has been measured experimentally with a very high precision and on theory side the contributions from perturbative QED have been calculated up to five-loop level by numerical methods. Contributions to the muon anomalous magnetic moment from certain diagram classes are also accessible by alternative methods. In this paper we present the evaluation of contributions to the QED corrections due to insertions of the vacuum polarization function at five-loop level.