$\cal O}(\alpha_s^2)$ corrections to top quark production at $e^+e^-$ colliders

Abstract.

In this article we evaluate mass corrections up to ${\cal O}((m^2/q^2)^6)$ to the three-loop polarization function induced by an axial-vector current. Special emphasis is put on the evaluation of the singlet diagram which is absent in the vector case. As a physical application ${\cal O}(\alpha_s^2)$ corrections to the production of top quarks at future $e^+e^-$ colliders are considered. It is demonstrated that for center of mass energies $\sqrt{s}\gsim500$ GeV the inclusion of the first seven terms into the cross section leads to a reliable description.