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Next--to--Leading Order QCD corrections for the $B^0 \bar{B^0}$--mixing with an extended Higgs sector

We present a calculation of the B0-B0--mixing including Next--to--Leading Order (NLO) QCD corrections within the Two Higgs Doublet Model (2HDM). The QCD corrections at NLO are contained in the factor denoted by eta_2 which modifies the result obtained at the lowest order of perturbation theory. In the Standard Model case, we confirm the results for eta_2 obtained by Buras, Jamin and Weisz. The factor eta_2 is gauge and renormalization prescription invariant and it does not depend on the infrared behaviour of the theory, which constitutes an important test of the calculations. The NLO--calculations within the 2HDM enhance the LO--result up to 18%, which affects the correlation between M_H and V_{td}.