On the asymptotic ${\cal O}(\alpha \alpha_S)$ behavior of the electroweak gauge bosons vacuum polarization functions for arbitrary quark masses

Abstract

We derive the QCD corrections to the electroweak gauge bosons 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 $O(\alpha \alpha_S)$ calculations of the vector bosons 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.