Connections between ε'/ε and rare kaon decays in supersymmetry

We analyze the rare kaon decays KL→π0νν, K+→π+νν, KL→μ+μ- in conjunction with the CP violating ratio ε'/ε in a general class of supersymmetric models in which Z- and magnetic-penguin contributions can be substantially larger than in the Standard Model. It is pointed out that radiative effects relate the double left-right mass insertion to the single left-left one, and that the phenomenological constraints on the latter reflect into a stringent bound on the supersymmetric contribution to the Z penguin. Using 1.1 · 10-10, BR(K+→π+νν) ≤1.7 · 10-10, BR(KL→π0 e+ e-)dir ≤ 2.0 · 10-11, assuming the usual determination of the CKM parameters and neglecting the possibility of cancellations among different supersymmetric effects in ε'/ ε. Larger values are possible, in principles, but rather unlikely. It is stressed the importance of a measurement of these three branching ratios, together with improved data and improved theory of ε'/ε, in order to shed light on the realization of various supersymmetric scenarios. It is here reemphasized that the most natural enhancement of ε'/ε, within supersymmetric models, comes from chromomagnetic penguins and show that in in this case sizable enhancements of BR (KL →π0 e+ e-)dir