Non-singlet Corrections of O(α 2 S G F M

The partial decay rate of the Z boson into bottom quarks constitutes an important decay channel. This is mainly due to the virtual presence of the top quark in the loop diagrams giving rise to correction factors which are quadratic in the top quark mass. At one-and two-loop order it turned out that the leading term in the heavy-top expansion leads to very good approximations to the exact result. In this work the non-singlet diagrams at O(α 2 s G F M 2 t) are considered. The impressive experimental precision mainly at the Large Electron Positron collider (LEP) at CERN, the Stanford Linear Collider (SLC) and the FERMILAB Tevatron in Chicago has made it mandatory to evaluate higher order quantum corrections to the processes observed in the experiments [1]. The strategy to combine experimental information with theoretical computations has successfully been applied to the search for the top quark several years ago. Nowadays the same concept is used in order to pin down the mass of the Higgs boson, the only not yet discovered particle of the Standard Model of elementary particle physics. An important observable is the decay of the Z boson into bottom. QCD corrections are known up to O(α 3 s) (for a comprehensive review see [2]). The electroweak one-loop corrections are known since quite some time [3]. They have the interesting feature that the top quark appears virtually in the loop diagrams. Recently also the full corrections of O(αα s) were completed [4, 5, 6]. The diagrams involving a top quark are considered in [6] where the first five terms in the expansion for a heavy top quark mass, M t , is computed. It was demonstrated that these terms approximate the exact result quite well. Actually it turned out that both at O(α) and O(αα s) a large cancellation between the sub-leading terms takes place and effectively only the leading term proportional to G F M 2 t [7] remains. This is a strong motivation to look at the next order in the strong coupling constant and evaluate the leading terms. To the corrections enhanced by the top quark mass only those contributions have to be considered where a scalar particle, namely the Higgs boson, H,