Leading and next-to-leading QCD corrections to ε-parameter and B0-anti B0 mixing in the presence of a heavy top quark

We present a complete calculation of leading and next-to-leading QCD corrections to the QCD factors η2K and anti η2B, relevant for the CP-violating ε-parameter and B0-anti B0 mixing in the presence of a heavy top quark. We demonstrate explicitly that the resulting η2's are gauge as well as renormalization prescription independent. We also show that they do not depend on the infrared structure of the theory. We emphasize that these results only follow after correct factorization of short and long distance contributions, which has not been done properly in many recent QCD analyses present in the literature. We stress however that η2(xt) with xt=mt2/MW2 depends sensitively on the definition of the top quark mass and only the product η2(xt)S(xt) (S(xt) being the function resulting from the lowest order box diagram) is free from this dependence. For mt=anti mt(MW) the corresponding η2's decrease strongly with mt, whereas for mt*=anti mt(mt) they show only a weak mt*-dependence: 0.58≥η2K*≥0.56 and 0.88≥ anti η2B* ≥ 0.84 for 60 GeV ≤ mt* ≤ 300 GeV and Λ MS=200 MeV. A critical discussion of the existing literature on QCD calculations in the presence of a large mt is presented. (orig.)