K → πν ν: A Model Independent Analysis and Supersymmetry

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We present a model independent analysis of new-physics contributions to the decays K+ → π+ ν νand Kₗ → π⁰ ν ν. We parameterize the effects of new physics in these decays by two parameters: rₖ and θₖ, with rₖ=1 and θₖ=0 in the Standard Model (SM). We show how these parameters can be extracted from future data. This analysis offers some insight in a possible violation of a "golden relation" between K → πν νdecays and the CP asymmetry in B → ψKₛ in the SM 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 θₖ=0, the measurements of Br(K+ → π+ ν ν) and Br(Kₗ → π⁰ ν ν) directly determine the angle β. 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 rₖ=1 and θₖ=0. Typically 0.5 < rₖ < 1.3 and -25⁰ < θₖ < 25⁰. Consequently, in these models the violation of the "golden relation" is possible and values for Br(K+ → π+ ν ν) and Br(Kₗ → π⁰ ν ν) departing from the SM expectations by factors 2-3 cannot be excluded. 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.