Rare Kaon Decays Beyond the Standard Model

The rare kaon decays K_L -> pi^0 nu {bar nu}, K^+ -> pi^+ nu {bar nu}, K_L -> pi^0 e^+ e^- and K_L -> pi^0 mu^+ mu^- are theoretically very clean and, being strongly CKM suppressed, highly sensitive to New Physics (NP). Recent Flavour Physics analyses show that they represent unique probes for revealing NP effects and to provide information on the NP flavour structure. After a brief discussion of the main properties that make rare K decays so promising and of the basic ideas of the most interesting NP models, we review the results of recent phenomenological analyses both within and beyond the framework of Minimal Flavour Violation (MFV), where the sources of flavour violation are the same as in the Standard Model. Within MFV we present the expectations found for rare K decays from a model-independent analysis and in three MFV models: the Littlest Higgs (LH) model, the (extra-dimension) Appelquist-Cheng-Dobrescu model and the Minimal Supersymmetric Standard Model (MSSM) with MFV. Beyond MFV, we discuss the results recently found within the MSSM (without MFV), the LH model with T-parity (LHT) and the 3-3-1 (Z') model. While in MFV models only small ( pi^0 nu {bar nu}, K^+ -> pi^+ nu {bar nu}, K_L -> pi^0 e^+ e^- and K_L -> pi^0 mu^+ mu^-, beyond MFV, in particular in the MSSM and in the LHT model, large (up to an order of magnitude) enhancements w.r.t. the SM turn out to be possible