$K \to πν\bar ν$: A Model Independent Analysis and Supersymmetry

Abstract

We present a model independent analysis of new-physics contributions to the decays K^+ \to π^+ ν\bar νand K_L \to π^0 ν\bar ν. We parameterize the effects of new physics in these decays by two parameters: r_K and θ_K, with r_K=1 and θ_K=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 \to πν\bar νdecays and the CP asymmetry in B \to ψK_S 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 θ_K=0, the measurements of Br(K^+ \to π^+ ν\bar ν) and Br(K_L \to π^0 ν\bar 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 r_K=1 and θ_K=0. Typically 0.5 < r_K < 1.3 and -25^0 < θ_K < 25^0. Consequently, in these models the violation of the "golden relation" is possible and values for Br(K^+ \to π^+ ν\bar ν) and Br(K_L \to π^0 ν\bar 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.