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, a mu(had), (NNLO) = 1.24 +/- 0.01 x 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. (C) 2014 The Authors. Published by Elsevier B. V.