Perturbative contributions to Δα(5) (MZ2)

We compute a theoretically driven prediction for the hadronic contribution to the electromagnetic running coupling at the Z scale using lattice QCD and state-of-the-art perturbative QCD. We obtain Delta alpha((5) )(M-Z(2)) = [279.5 +/- 0.9 +/- 0.59] x 10(-4 )(Mainz Collaboration)Delta alpha((5) )(M-Z(2)) = [278.42 +/- 0.22 +/- 0.59] x 10(-4 )(BMW Collaboration),where the first error is the quoted lattice uncertainty. The second is due to perturbative QCD, and is dominated by the parametric uncertainty on alpha(<^>)(s), which is based on a rather conservative error. Using instead the PDG average, we find a total error on Delta alpha((5) )(M-Z(2)) of 0.4 x 10(-4). Furthermore, with a particular emphasis on the charm quark contributions, we also update Delta alpha((5) )(M-Z(2)) when low-energy cross-section data is used as an input, obtaining Delta alpha((5) )(M-Z(2)) = [276.29 +/- 0.38 +/- 0.62] x 10(-4). The difference between lattice QCD and cross-section-driven results reflects the known tension between both methods in the computation of the anomalous magnetic moment of the muon. Our results are expressed in a way that will allow straight