Higgs – mediated K → πνν in the MSSM at large tan β

We analyze the impact of Higgs-mediated amplitudes on the rare decays KL → πνν and K → πνν in the MSSM with large tan β and general flavour mixing. We point out that, going beyond the minimal flavour violation hypothesis, Z-penguin amplitudes generated by charged-Higgs exchange can induce sizable modifications of K → πνν rates. Interestingly, these effects scale as tan β at the amplitude level. For large values of tanβ, this mechanism allows deviations from the SM expectations even for tiny (CKM-type) off-diagonal mixing terms in the right-handed squark sector. I. The strong suppression within the Standard Model (SM) and the high sensitivity to physics beyond the SM of the two K → πνν rates, signal the unique possibilities offered by these rare processes in probing the underlying mechanism of flavour mixing (see e.g. Refs. [1,2]). This statement has been reinforced by the recent theoretical progress in the evaluation of NNLO [3] and power-suppressed [4] contributions to K → πνν. These allow to obtain predictions for the corresponding branching ratio of high accuracy (∼ 6%), not far from exceptional level of precision (∼ 2%) already reached in the KL → πνν case [2, 5]. The non-standard contributions to K → πνν decays appearing in the minimal supersymmetric extensions of the SM (MSSM) with generic sources of flavour mixing have been widely discussed in the literature [6–9]. However, all previous analysis are focused on scenarios with tanβ = O(1). In this case, taking into account the existing constraints from other flavour-changing neutral current (FCNC) observables, the only amplitudes which allow sizable deviations from the SM are those generated by chargino/up-squark loops. In particular, large effects are generated only if the left-right mixing of the up squarks has a flavour structure substantially different from the so-called Minimal Flavour Violation (MFV) hypothesis [10]. In this paper we point out the existence of a completely different mechanism which could allows sizable modifications of K → πνν amplitudes: the charged-Higgs/top-quark