πνν Decays in Models with Minimal Flavour Violation

We present a general discussion of the unitarity triangle from εK , ∆Md,s and K → πνν in models with minimal flavour violation (MFV), allowing for arbitrary signs of the generalized Inami–Lim functions Ftt and X relevant for (εK ,∆Md,s) and K → πνν, respectively. In the models in which Ftt has a sign opposite to the one in the Standard Model, i.e. Ftt < 0, the data for (εK ,∆Md,s) imply an absolute lower bound on the Bd → ψKS CP asymmetry aψKS of 0.69, which is substantially stronger than 0.42 arising in the case of Ftt > 0. An important finding of this paper is the observation that for given Br(K → πνν) and aψKS only two values for Br(KL → πνν), corresponding to the two signs of X, are possible in the full class of MFV models, independently of any new parameters arising in these models. This provides a powerful test for this class of models. Moreover, we derive absolute lower and upper bounds on Br(KL → πνν) as functions of Br(K → πνν). Using the present experimental upper bounds on Br(K → πνν) and |Vub/Vcb|, we obtain the absolute upper bound Br(KL → πνν) < 7.1 · 10 (90% C.L.). ∗ E-mail: [email protected] † E-mail: [email protected]