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SUSX-TH/01-022 Chargino Contributions to ε and ε ′

We analyze the chargino contributions to the K−K̄ mixing and ε in the mass insertion approximation and derive the corresponding bounds on the mass insertion parameters. We find that the chargino contributions can significantly enlarge the regions of the parameter space where CP violation can be fully supersymmetric. In principle, the observed values of ε and ε may be entirely due to the chargino – up-squark loops. A convenient way to parameterize SUSY contributions to the flavor changing processes is to employ the so called mass insertion approximation [1]. The advantage of this approach is that it allows to treat such contributions in a model independent way without resorting to specific assumptions about the SUSY flavor structures (a technical definition of this approximation will be given below). The gluino contributions to the kaon observables in the mass insertion approximation have been studied in detail [2]-[4], but the chargino contributions have not received similar attention. The latter have been considered either in the context of minimal flavor violation, that is in SUSY models with the flavor mixing given by the CKM matrix [5], [6] or as contributing to the K − K̄ mixing only [7]. In general, the flavor structure in the squark sector may be very complicated. In particular, flavor patterns in the up and down sectors can be entirely different, which may result in the dominance of the chargino contributions to the K and B observables. On the other hand, the neutralino contributions involve the same mass insertions as the gluino ones (i.e. down type mass insertions) and thus cannot qualitatively change the picture. In this Letter, we study the chargino contributions to the K − K̄ mixing and ε using the mass insertion approximation and derive the corresponding bounds on the mass insertion parameters. Let us first consider the K − K̄ mixing. The two observables of primary interest are the KL-KS mass difference and indirect CP violation in K → ππ decays: ∆MK = MKL − MKS , 1