We derive the QCD corrections to the electroweak gauge boson vacuum polarization functions at high and zero momentum transfer in the case of arbitrary internal quark masses. We then discuss in this general case (i) the connection between the $O\left(\alpha {\alpha }_s\right)$ calculations of the vector boson self-energies using dimensional regularization and the one performed via a dispersive approach and (ii) the QCD corrections to the $\rho$ parameter for a heavy quark isodoublet.

• Received 24 August 1993

DOI:https://doi.org/10.1103/PhysRevD.49.4705