O(α 2 ) Corrections to Top Quark Production at e + e − Colliders

In this article we evaluate mass corrections up to 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 O(� 2 ) corrections to the production of top quarks at future e + e colliders is considered. It is demonstrated that for center of mass energies √ s ∼ 500 GeV the inclusion of the first seven terms into the cross section leads to