The leading hadronic contribution to the running of the Weinberg angle using covariant coordinate-space methods

We present a preliminary study of the leading hadronic contribution to the running of the Weinberg angle θW. The running is extracted from the correlation function of the electromagnetic current with the vector part of the weak neutral current using both the standard time-momentum representation method and the Lorentz-covariant coordinate-space method recently introduced by Meyer. Both connected and disconnected contributions have been computed on Nf = 2 + 1 non-perturbatively O(a)-improved Wilson fermions configurations from the Coordinated Lattice Simulations initiative. Similar covariant coordinate-space methods can be used to compute the leading hadronic contribution to the anomalous magnetic moment of the muon (g − 2)µ and to the running of the QED coupling α.