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

Abstract

We analyze the rare kaon decays K L → π 0 νν, K + → π + νν, 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(, 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.

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