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The quark-connected leading-order hadronic contributions to the running ofthe electromagnetic fine structure constant, $\alpha_{\rm QED}$, and the weakmixing angle, $\theta_W$, are determined by a four-flavour lattice QCDcomputation with twisted mass fermions. Full agreement of the results with aphenomenological analysis is observed with an even comparable statisticaluncertainty. We show that the uncertainty of the lattice calculation isdominated by systematic effects which then leads to significantly larger errorsthan obtained by the phenomenological analysis.

Leading hadronic contributions to the running of the electroweak coupling constants from lattice QCD