K ! and " 0 =" in simplied new physics models

The decays K + ! + and KL! 0 , being the theoretically cleanest rare decays of mesons, are very sensitive probes of New Physics (NP). In view of the excellent prospects of reaching the Standard Model (SM) sensitivity for K + ! + by the NA62 experiment at CERN and for KL! 0 by the KOTO experiment at J-PARC, we study them in the simplest extensions of the SM in which stringent correlations between these two decays and other avour observables are present. We rst consider simple models with tree-level Z and Z 0 contributions in which either Minimal Flavour Violation (MFV) or a U(2) 3 symmetry is imposed on the quark avour-violating couplings. We then compare the