Resummed Effective Lagrangian for Higgs-Mediated FCNC Interactions in the CP-Violating MSSM

We derive the general resummed effective Lagrangian for Higgs-mediated flavour-changing neutral-current (FCNC) interactions in the Minimal Supersymmetric Standard Model (MSSM), without resorting to particular assumptions that rely on the squark-mass or the quark-Yukawa structure of the theory. In our derivation we also include the possibility of explicit CP violation through the Cabibbo--Kobayashi--Maskawa mixing matrix and soft supersymmetry-breaking mass terms. The advantages of our resummed FCNC effective Lagrangian are explicitly demonstrated within the context of phenomenologically motivated scenarios. We obtain new testable predictions in the large $\tan\beta$ regime of the theory for CP-conserving and CP-violating observables related to the $K$- and $B$-meson systems, such as $\Delta M_{K,B}$, $\epsilon_K$, $\epsilon'/\epsilon$, ${\cal B}(B_{d,s} \to \ell^+\ell^-)$ and their associated leptonic CP asymmetries. Finally, based on our resummed FCNC effective Lagrangian, we can identify configurations in the soft supersymmetry-breaking parameter space, for which a kind of a Glashow--Iliopoulos--Maiani-cancellation mechanism becomes operative and hence all Higgs-mediated, $\tan\beta$-enhanced effects on $K$- and $B$-meson FCNC observables vanish.