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

We analyze the rare kaon decays K-L --> pi(0)v (v) over bar, K+ --> pi(+) v (v) over bar, K-L --> pi(0)e(+)e(-) and K-L --> mu(+)mu(-) in conjunction with the CP-violating ratio epsilon'/epsilon in a general class of supersym metric models in which Z- and magnetic-penguin contributions can be substan tially larger than in the Standard Model. We point out that radiative effec ts relate the double left-right mass insertion to the single left-left one, and that the phenomenological constraints on the latter reflect into a str ingent bound on the supersymmetric contribution to the Z penguin. Using the bound, and those coming from recent data on epsilon(+)/epsilon(-), we find BR(K-L --> pi(0)v (v) over bar) less than or equal to 1.2 x 10(-10), BR(K --> pi+v (v) over bar) less than or equal to 1.7 x 10(-10), BR(K-L --> pi( 0)epsilon(+)epsilon(-))(dir) less than or similar to 2.0 x 10(-11), assumin g the usual determination of the CKM parameters and neglecting the possibil ity of cancellations among different supersymmetric effects in epsilon(+)ep silon(-). Larger values are possible, in principle, but rather unlikely. We stress the importance of a measurement of these three branching ratios, to gether with improved data and improved theory of a epsilon'/epsilon, in ord er to shed light on the realization of various supersymmetric scenarios. We reemphasize that the most natural enhancement of epsilon'/epsilon, within supersymmetric models, comes from chromomagnetic penguins and show that in this case sizable enhancements of BR(K-L --> pi(0)e(+) e(-))(dir) can also be expected. (C) 2000 Elsevier Science B.V. All rights reserved.