(g− 2)μand α(M²Z) re-evaluated using new precise data

We update our standard model predictions for g − 2 of the muon and for the hadronic contributions to the running of the QED coupling, Δα (5) had ( M 2 Z ). Particular emphasis is put on recent changes in the hadronic contributions from new data in the 2π channel and from the energy region just below 2 GeV. In particular, for the e + e − → π + π − contribution we include the recent 'radiative return' data from KLOE and BaBar. We also include the recent BaBar data on other exclusive channels. We make a detailed study of the effect of replacing the measurements of the inclusive cross section, σ(e + e − → hadrons), by the sum of the exclusive channels in the energy interval GeV, which includes a QCD sum-rule analysis of this energy region. Our favoured prediction for the muon anomalous magnetic moment is ( g − 2)/2 = (11 659 182.8 ± 4.9) × 10 −10 which is 3.3 σ below the present world-average measurement. We compare our g − 2 value with other recent calculations. Our prediction for the QED coupling, obtained via Δα (5) had ( M Z 2 ) = (276.26 ± 1.38) × 10 −4 , is α( M 2 Z ) −1 = 128.944 ± 0.019.