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

Abstract

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 $\Delta M_{K,B}$, ${\epsilon }_K$, ${\epsilon }^{\prime }/\epsilon$, $\mathcal{B}(B_{d,s}\to {\ell }^{+}{\ell }^{-})$ 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.

40 pages, version as to appear in Physical Review D

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