K → πνν1-: A model-independent analysis and supersymmetry Original Research Article

We present a model-independent analysis of new-physics contributions to the rare decays K+ → π+νν1- and KL → π0νν1-. We parameterize the effects of new physics in these decays by two parameters: rK and the phase θK, with rK = 1 and θK = 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 → ψKS and B → π+π− as well as the ratio ||Vub/Vcb|| have to be also considered. This analysis offers simultaneously some insight in a possible violation of a “golden relation” between K → πνν1- decays and the CP asymmetry in B → ψKs 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 θK = 0, the measurements of Br(K+ → π+νν1-) and Br(KL → π0νν1-) 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 −25° < θK < 25°. Consequently, in these models the violation of the “golden relation” is possible and values for Br(K+ → π+νν1-) and Br(KL → π0νν1-) departing from the Standard Model expectations by factors 2–3 cannot be excluded. Simultaneously, the extraction of the “true” angle β from K → πνν1- 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.