Bounds on the unitarity triangle, sin 2β and K → πνν̄ decays in models with minimal flavor violation

We present a general discussion of the unitarity triangle from ε_K, ΔM_d,s and K → πνν̄ in models with minimal flavor violation (MFV), allowing for arbitrary signs of the generalized Inami-Lim functions F_tt and X relevant for (ε_K,ΔM_d,s) and K → πνν̄, respectively. In the models in which F_tt has a sign opposite to the one in the standard model, i.e. F_tt<0, the data for (ε_K,ΔM_d,s) imply an absolute lower bound on the B_d → ψK_S CP asymmetry a_ψKS of 0.69, which is substantially stronger than 0.42 arising in the case of F_tt>0. An important finding of this paper is the observation that forgiven Br(K⁺ → π⁺νν̄) and a_ψKS only two values for Br (K_L → π⁰νν̄), 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(K_L → π⁰νν̄) as functions of Br(K⁺ → π⁺νν̄). Using the present experimental upper bounds on Br(K⁺ → π⁺νν̄) and |V_ub/V_cb|, we obtain the absolute upper bound Br(K_L → π⁰νν̄)<7.1×10^-10 (90% C.L.).