Probing High-Energy Physics with High-Precision QED Measurements

I summarize our self-contained determinations of the lowest order hadronic contributions ^1,2 to the anomalous magnetic moments a_μτ of the muon and tau leptons, the running QED coupling α(M_Z) and the muonium hyperfine splitting ν. Using an average estimate of the light-by light scattering contribution: a_μ(LL) = 85(18) × 10^-11, we deduce: a^SM_μ = 116 591 861(78) × 10^-11, a^SM_τ = 117 759(7) × 10^-8, giving a^SM_μ - a^exp_μ = 162(170) × 10^-11. We also obtain: α^-1(M_Z) = 128.926(25) and the Fermi energy splitting: ν ^SM_F = 4 459 031 783(229) Hz. Lower bounds on some new physics are given, while ν ^SM_F leads e.g. to m_μ/m_e = 206.768 276(11) in remarkable agreement with the data.