K → πvv̄: A model-independent analysis and supersymmetry

We present a model-independent analysis of new-physics contributions to the rare decays K⁺ → π⁺vv̄ and K_L → π⁰vv̄. We parameterize the effects of new physics in these decays by two parameters: r_K and the phase θ_K, with r_K = 1 and θ_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 β of the unitarity triangle. To this end CP asymmetries in B → ψK_S and B → π⁺π^- 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 → πvv̄ decays and the CP asymmetry in B → ψK_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 θ_K = 0, the measurements of Br(K⁺ → π⁺vv̄) and Br(K_L → π⁰vv̄) 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° < θ_K < 25°. Consequently, in these models the violation of the "golden relation" is possible and values for Br(K⁺ → π⁺vv̄) and Br(K_L → π⁰vv̄) departing from the Standard Model expectations by factors 2-3 cannot be excluded. Simultaneously, the extraction of the "true" angle β from K → πvv̄ 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.