Connections between ε′/ε and rare kaon decays in supersymmetry Original Research Article

We analyze the rare kaon decays KL→π0νν̄, K+→π+νν̄, KL→π0e+e− and 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. We point 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 this bound, and those coming from recent data on ε′/ε, we find BR(KL→π0νν̄)≲1.2×10−10, BR(K+→π+νν̄)≲1.7×10−10, BR(KL→π0e+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 principle, but rather unlikely. We stress 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. We reemphasize that the most natural enhancement of ε′/ε, within supersymmetric models, comes from chromomagnetic penguins and show that in this case sizable enhancements of BR(KL→π0e+e−)dir can also be expected.