On the consistency between the observed amount of CP violation in the K- and B$_d$-systems within minimal flavor violation

We reappraise the question whether the Standard Model, and Minimal Flavor Violating (MFV) models at large, can simultaneously describe the observed CP violation in the K- and Bd-systems. We find that CP violation in the Bd-system, measured most precisely through (sin 2 beta)_{J/psi Ks}, implies |epsilon_K^{SM}| = 1.78(25) x 10^{-3} for the parameter epsilon_K, measuring indirect CP violation in the K-system, to be compared with the experimental value |epsilon_K^{exp}| = 2.23(1) x 10^{-3}. To bring this prediction to 1 sigma agreement with experiment, we explore then the simplest new-physics possibility not involving new phases, namely that of MFV scenarios with no new effective operators besides the Standard Model ones. We emphasize the crucial input and/or measurements to be improved in order to probe this case. In particular we point out that this tension could be removed in this framework, with interesting signatures, e.g. correlated suppression patterns for rare K decay branching ratios. On the other hand, MFV contributions from new operators appear, in the calculable case of the MSSM, to worsen the situation. We finally explore some well-motivated new-physics scenarios beyond MFV, like those involving generic new contributions in Z-penguins.