Upper bounds on K→πν(ν)over-bar and KL→π0e+e- from ε′/ε and KL→μ+μ-

We analyze rare kaon decays in models in which the dominant new effect is an enhanced (s) over bar dZ vertex Z(ds). We point out that in spite of large theoretical uncertainties the CP-violating ratio epsilon'/epsilon provides at present the strongest constraint on Im Zds Assuming 0 less than or equal to epsilon'/epsilon less than or equal to 2 x 10(-3) and Standard Model values for the CKM parameters we obtain the bounds BR(K-L --> pi(0)nu<(nu)over bar>) less than or equal to 2.4 x 10(-10) and BR (K-L --> pi(0) e(+)e(-)) less than or equal to 3.6 x 10(-11) (which are substantially stronger than the bounds found recently by Colangelo and Isidori, using Ere instead of epsilon'/epsilon). We illustrate how these bounds can be improved with the help of the forthcoming data on epsilon'/epsilon. Using the bound on Re Z(ds) from K-L --> mu(+) mu(-) we find BR (K+ --> pi(+) nu<(nu)over bar>) less than or equal to 2.3 x 10(-10). In this context we derive an analytic upper bound on BR (K+ --> pi(+) nu<(nu)over bar>) as a function of BR (K-L --> pi(0)nu<(nu)over bar>) add the short distance contribution to BR (K-L --> mu(+) mu(-)). We also discuss new physics scenarios in which in addition to an enhanced (s) over bar dZ vertex also neutral meson mixing receives important new contributions. In this case larger values of the branching ratios in question cannot be excluded. (C) 1999 Elsevier Science B.V.