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

Understand

The quark-connected leading-order hadronic contributions to the running of the electromagnetic fine structure constant, $\alpha_{\rm QED}$, and the weak mixing angle, $\theta_W$, are determined by a four-flavour lattice QCD computation with twisted mass fermions.

• Full agreement of the results with a phenomenological analysis is observed with an even comparable statistical uncertainty.
• We show that the uncertainty of the lattice calculation is dominated by systematic effects which then leads to significantly larger errors than obtained by the phenomenological analysis.