One-loop Electro-Weak Corrections to Three-jet Observables of b-quarks in e+e- Annihilations

We compute the full one-loop EW contributions of O(\alpha_S alpha_EM^3) entering the electron-positron into two b-quarks and one gluon cross section at the Z peak and LC energies. We include both factorisable and non-factorisable virtual corrections, photon bremsstrahlung but not the real emission of W^\pm and Z bosons. Their importance for the measurement of alpha_S from jet rates and shape variables is explained qualitatively and illustrated quantitatively. Their impact on the forward-backward asymmetry is also analysed.