Weak mixing angle at low energies
  We determine the weak mixing angle in the MS-bar scheme at energy scales relevant for present and future low energy electroweak measurements. We relate the renormalization group evolution of the weak mixing angle to the corresponding evolution of the QED coupling and include higher-order terms in alpha_s and alpha that had not been treated in previous analyses. We also up-date the analysis of non-perturbative hadronic contributions and argue that the associated uncertainty is small compared to anticipated experimental errors. The resulting value of the low-energy weak mixing angle is sin^2 theta_W (0) = 0.23867 +- 0.00016. 
Jens Erler and Michael J. Ramsey-Musolf