Resummed effective Lagrangian for Higgs-mediated flavor-changing neutral current interactions in theCP-violating MSSM

We derive the general resummed effective Lagrangian for Higgs-mediated flavor-changing neutral-current (FCNC) interactions in the minimal supersymmetric standard model, 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 $\mathrm{CP}$ 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 $\Delta M_{K,B},$ ${\epsilon }_K,$ ${\epsilon }^{\prime }/\epsilon ,$ $\mathcal{B}{(B}_{d,s}\to {\mathcal{l}}^{+}{\mathcal{l}}^{-})$ and their associated leptonic $\mathrm{CP}$ 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.