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

Abstract

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, $a_{\mu }^{\mathrm{had},\mathrm{NNLO}}=1.24\pm 0.01\times 10^{-10}$, has the same order of magnitude as the current uncertainty of the leading order hadronic contribution and should thus be included in future analyses.

Comments: 9 pages,v2: note on NLO hadronic light-by-light contribution added, matches published version, Physics Letters B 734 (2014) 144-147