Improved analytic theory of the muon anomalous magnetic moment

We consider the recent results of Kinoshita in which he improves the accuracy of the theoretical value for the anomalous magnetic moment of the muon. This is needed now that a new, more accurate experiment has been approved at Brookhaven National Laboratory. Kinoshita's results are completely numerical. Here we perform an independent check of his results in fourth and sixth order by analytical means, using expansions in the small mass ratios which occur in the computation. Our result for the fourth-order contribution is aμ(4)-ae(4)=5 904 475.1(3)x10-12. This is to be compared with Kinoshita's result aμ(4)-ae(4)=5 904 485x10-12. For the sixth-order vacuum-polarization contribution we obtain (aμ(6)-ae(6))(vacuum polarization)=24 064.8(6)x10-12. Kinoshita's result is (aμ(6)-ae(6))(vacuum polarization)=24 069(6)x10-12