TTP09-01 The supersymmetric Higgs sector and B-anti-B mixing for large tan beta

We match the Higgs sector of the most general flavour breaking and CP violating minimal supersymmetric standard model (MSSM) onto a generic two-Higgs-doublet model, paying special attention to the definition of $\tan\beta$ in the effective theory. In particular no $\tan\beta$-enhanced loop corrections appear in the relation to $\tan\beta$ defined in the $\overline{\textrm{DR}}$ scheme in the MSSM. The corrections to the Higgs-mediated flavour-changing amplitudes which result from this matching are especially relevant for the $B_d$ and $B_s$ mass differences $\dm_{d,s}$ for minimal flavour violation, where the superficially leading contribution vanishes. We give a symmetry argument to explain this cancellation and perform a systematic study of all Higgs-mediated effects, including Higgs loops. The corrections to $\dm_s$ are at most 7\% for $\mu>0$ and $M_A < 600\gev$ if constraints from other observables are taken into account. For $\mu<0$ they can be larger, but are always less than about 20\%. Contrary to recent claims we do not find numerically large contributions here, nor do we find any $\tan\beta$-enhanced contributions from loop corrections to the Higgs potential in $B^+ \to \tau^+ \nu$ or $B \to X_s \gamma$. We further update supersymmetric loop corrections to the Yukawa couplings, where we include all possible CP-violating phases and correct errors in the literature. The possible presence of CP-violating phases generated by Higgs exchange diagrams is briefly discussed as well. Finally we provide improved values for the bag factors $P^{\rm VLL}_1$, $P^{\rm

 LR}_2$, and $P^{\rm SLL}_1$ at the electroweak scale.