For the vertex corrections to the partial decay rate Γ(Z → bb) involving the top quark only the leading terms of order αα s in the 1/M t expansion are known. In this work we compute the missing next-to-leading corrections. Thus at O(αα s ) the complete corrections to the decay of the Z boson into bottom quarks are at hand.

Corrections of O(α 2 s ) to the decay of the top quark into a W boson and a bottom quark are calculated. The method is based on an expansion of the top quark propagator for small external momentum, q, as compared to the top quark mass, M t . The physical point q 2 = M 2 t is reached through Padé approximations. The described method allows to take effects induced by a finite W boson mass into account. The numerical relevance of the result is discussed. Important cross-checks against recent results for the decay rate b → ulν and the two-loop QED corrections to µ-decay are performed.

We present results for the three-loop top quark contributions to the ρ parameter in the limit of large top quark mass. The simultaneous dependence on the mass of the Higgs boson M H and the mass of the top quark m t is obtained from expansions in the range of M H around m t and in the limit M H ≫ m t . In combination with the previous result for M H = 0 the dependence of the ρ parameter on the leading Yukawa contributions, i.e. on m t and M H , is well under control for all mass values of practical importance. The effects lead to a shift in the W mass in the order of 5 MeV and are relevant for precision measurements at TESLA.

We present analytical results for the leading contributions of the top quark to the electroweak ρ parameter at order G 3 F M 6 t and G 2 F M 4 t α s . The Higgs boson and the gauge bosons are taken to be massless in this limit. The correction of order G 3 F M 6 t is found to be sizeable in comparison to the the leading two-loop O(G 2 F M 4 t ) correction, however it is much smaller than the subleading O(G 2 F M 2 t M 2 Z ) correction.

We present numerical results for the two loop QCD corrections to the ghost gluon vertex, the quark gluon vertex, and the triple gluon vertex in the massless limit at the symmetric point. We restrict ourselves to the tensor structures existing in the tree level. The corrections are used to examine different coupling constant definitions in momentum subtraction schemes and the corresponding three-loop β functions.