On the consistency between the observed amount of CP violation in the K and Bd systems within minimal flavor violation

We reappraise the question of 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 2β)J/ψKs, implies |KSM|=1.78(25)×10-3 for the parameter K, measuring indirect CP violation in the K system, to be compared with the experimental value |Kexp|=2.23(1) ×10-3. To bring this prediction to 1σ agreement with experiment, we then explore 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 models, like those involving generic new contributions in Z penguins.