Upper bounds on K ->pi nu(nu)over-bar and K-L ->pi(0)e(+)e(-) from epsilon'/epsilon and K-L ->mu(+)mu(-)

We analyze rare kaon decays in models in which the dominant new effect is a n enhanced (s) over bar dZ vertex Z(ds). We point out that in spite of larg e theoretical uncertainties the CP-violating ratio epsilon'/epsilon provide s at present the strongest constraint on Im Zds Assuming 0 less than or equ al 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)o ver 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 th an 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>) les s than or equal to 2.3 x 10(-10). In this context we derive an analytic upp er 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 impo rtant new contributions. In this case larger values of the branching ratios in question cannot be excluded. (C) 1999 Elsevier Science B.V.