Upper bounds on K → πνν and KL → π0e+e− from ε′/ε and KL → μ+μ− Original Research Article

We analyze rare kaon decays in models in which the dominant new effect is an enhanced sdZ vertex Zds. We point out that in spite of large theoretical uncertainties the CP-violating ratio ε′/ε provides at present the strongest constraint on Im Zds. Assuming 0 ⩽ ε′/ε ⩽ 2 × 10−3 and Standard Model values for the CKM parameters we obtain the bounds BR(KL → π0νν) ⩽ 2.4 × 10−10 and BR(KL → π0e+e−) ⩽ 3.6 × 10−11 (which are substantially stronger than the bounds found recently by Colangelo and Isidori, using εK instead of ε′/ε). We illustrate how these bounds can be improved with the help of the forthcoming data on ε′/ε. Using the the bound on Re Zds from KL → μ+μ− we find BR(K+ → π+νν ⩽ 2.3 × 10−10. In this context we derive an analytic upper bound on BR(K+ → π+νν) as a function of BR(KL → π0νν) and the short distance contribution to BR(KL → μ+μ−). We also discuss new physics scenarios in which in addition to an enhanced sdZ vertex also neutral meson mixing receives important new contributions. In this case larger values of the branching ratios in question cannot be excluded.