Leading and next-to-leading QCD corrections to ε-parameter and B⁰B⁰ 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 η_2K and η_2B, relevant for the CP-violating ε-parameter and B⁰B⁰ 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(x_t) with x_t = m_t²/M_W² depends sensitively on the definition of the top quark mass and only the product η₂(x_t)S(x_t) (S(x_t) being the function resulting from the lowest order box diagram) is free from this dependence. For m_t = m_t(M_W) the corresponding η₂'s decrease strongly with m_t, whereas for m_t^* = m_t(m_t) they show only a weak m_t^*-dependence: 0.58 ≥ η_2K^* ≥ 0.56 and 0.88 ≥ η_2B^* ≥ 0.84 for 60 GeV ≤ m_t^* ≤ 300 GeV and Λ_MS = 200 MeV. A critical discussion of the existing literature on QCD calculations in the presence of a large m_t is presented.