Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order

We compute the next-to-next-to-leading order hadronic contribution to the muon anomalous magnetic moment originating from the photon vacuum polarization. The corresponding three-loop kernel functions are calculated using asymptotic expansion techniques which lead to analytic expressions. Our final result, ahad,NNLOμ=1.24±0.01×10−10 , has the same order of magnitude as the current uncertainty of the leading order hadronic contribution and should thus be included in future analyses.