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We update our standard model predictions for g − 2 of the muon and for the hadronic contributions to the running of the QED coupling, α (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 1.43 < √ s < 2 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 α (5) had M 2 Z = (276.26 ± 1.38) × 10 −4 , is α M 2 Z −1 = 128.944 ± 0.019.

This work presents a complete re-evaluation of the hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon, a had, VP µ and the hadronic contributions to the effective QED coupling at the mass of the Z boson, ∆α had (M 2 Z ), from the combination of e + e − → hadrons cross section data. Focus has been placed on the development of a new data combination method, which fully incorporates all correlated statistical and systematic uncertainties in a bias free approach. All available e + e − → hadrons cross section data have been analysed and included, where the new data compilation has yielded the full hadronic R-ratio and its covariance matrix in the energy range m π ≤ √ s ≤ 11.2 GeV. Using these combined data and perturbative QCD above that range results in estimates of the hadronic vacuum polarisation contributions to g − 2 of the muon of a had, LO VP µ = (693.26 ± 2.46) × 10 −10 and a had, NLO VP µ = (−9.82 ± 0.04) × 10 −10 . The new estimate for the Standard Model prediction is found to be a SM µ = (11 659 182.04±3.56)×10 −10 , which is 3.7σ below the current experimental measurement. The prediction for the five-flavour hadronic contribution to the QED coupling at the Z boson mass is ∆α (5) had (M 2 Z ) = (276.11±1.11)×10 −4 , resulting in α −1 (M 2 Z ) = 128.946±0.015. Detailed comparisons with results from similar related works are given. arXiv:1802.02995v2 [hep-ph] 13 Jul 2018 4 Conclusions and future prospects for the muon g − 2 39