Three--loop contributions to massive QED vacuum polarization are evaluated by a combination of analytical and numerical techniques. The first three Taylor coefficients, at small q2, are obtained analytically, using d\/--dimensional recurrence relations. Combining these with analytical input at threshold, and at large q2, an accurate Pad\'e approximation is obtained, for all q2. Inserting this in the one--loop diagram for the muon anomalous magnetic moment, we find reasonable agreement with four--loop, single--electron--loop, muon--anomaly contributions, recently re--evaluated by Kinoshita, using 8--dimensional Monte--Carlo integration. We believe that our new method is at least two orders of magnitude more accurate than the Monte--Carlo approach, whose uncertainties appear to have been underestimated, by a factor of 6.
@article{arxiv.hep-ph/9504398,
title = {Three-loop QED Vacuum Polarization and the Four--loop Muon Anomalous Magnetic Moment},
author = {P. A. Baikov and D. J. Broadhurst},
journal= {arXiv preprint arXiv:hep-ph/9504398},
year = {2007}
}