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, $a_\mu^{\rm had,NNLO} = 1.24 \pm 0.01 \times 10^{-10}$, has the same order of magnitude as the current uncertainty of the leading order hadronic contribution and should thus be included in future analyses.
Highlights
The anomalous magnetic moment of the electron and the muon are measured with high precision and at the same time accurately predicted including high-order quantum corrections
Rather we present for the first time next-tonext-to-leading order (NNLO) hadronic predictions
We classify the NNLO contributions in analogy to next-to-leading order (NLO) according to the number of hadronic insertions and closed electron loops
Summary
The anomalous magnetic moment of the electron and the muon are measured with high precision and at the same time accurately predicted including high-order quantum corrections (see, e.g., Refs. [1,2,3,4] for reviews on this topic). The anomalous magnetic moment of the electron and the muon are measured with high precision and at the same time accurately predicted including high-order quantum corrections Notable recent achievements in this context are the five-loop QED corrections obtained in Refs. In the case of the muon the largest input to the uncertainty comes from hadronic contributions which to a large extent rely on experimental measurements of the cross section σ(e+e− → hadrons). In this paper we compute the next-tonext-to-leading order (NNLO) hadronic corrections to the anomalous magnetic moment of the electron and the muon. Note that we do not consider the light-by-light contribution where the external photon couples to the hadronic loop We briefly mention some technical details of our calculation and discuss the NLO contribution.
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