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

Abstract

We analyze the rare kaon decays K L→π 0ν ν ̄ , K +→π +ν ν ̄ , K L → π 0 e + e − and K L → 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(K L→π 0ν ν ̄ )≲1.2×10 −10 , BR(K +→π +ν ν ̄ )≲1.7×10 −10 , BR( K L → π 0 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 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( K L → π 0 e + e −) dir can also be expected.