K ->pi nu(nu)over-bar: a model-independent analysis and supersymmetry

We present a model-independent analysis of new-physics contributions to the rare decays K+ --> pi(+)upsilon(upsilon)over-bar and K-L --> pi(0)upsilon(upsilon)over-bar. We parameterize the effects of new physics in these decays by two parameters: r(K) and the phase theta(K), with r(K) = 1 and theta(K) = 0 in the Standard Model. We show how these parameters can be extracted from future data together with the relevant CKM parameters, in particular the angle beta of the unitarity triangle. To this end CP asymmetries in B --> psi K-S and B --> pi(+)pi(-) as well as the ratio [V-ub/V-cb] have to be also considered. This analysis offers simultaneously some insight in a possible violation of a "golden relation" between K --> pi upsilon(upsilon)over-bar decays and the CP asymmetry in B --> psi K-S in the Standard Model pointed out some time ago. We illustrate these ideas by considering a general class of supersymmetric models. We find that in the "constrained" MSSM, in which theta(K) = 0, the measurements of Br(K+) --> pi(+)upsilon(upsilon)over-bar) and Br(K-L) --> pi(0)upsilon(upsilon)over-bar) directly determine the angle beta. Moreover, the "golden relation" remains unaffected. On the other hand, in general SUSY models with unbroken R parity the present experimental constraints still allow for substantial deviations from r(K) = 1 and theta(K) = 0. Typically 0.5 < r(K) < 1.3 and -25 degrees < theta(K) < 25 degrees. Consequently, in these models the violation of the "golden relation" is possible and values for Br(K+) --> pi(+)upsilon(upsilon)over-bar) and Br(K-L) --> pi(0)upsilon(upsilon)over-bar) departing from the Standard Model expectations by factors 2-3 cannot be excluded. Simultaneously, the extraction of the "true" angle beta from K --> pi upsilon(upsilon)over-bar is not possible without additional information from other decays. Our conclusions differ in certain aspects from the ones reached in previous analyses. In particular, we stress the possible importance of left-right flavour-violating mass insertions that were not considered before. (C) 1998 Elsevier Science B.V.