Three-loop QED Vacuum Polarization and the Four--loop Muon Anomalous Magnetic Moment

الأصل · EN

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 Padé 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.