On the consistency between the observed amount ofCPviolation in theKandBdsystems 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 $B_d$ systems. We find that $CP$ violation in the $B_d$ system, measured most precisely through $(\sin 2\beta {)}_{J/\psi K_s}$, implies $|{ϵ}_K^{\mathrm{SM}}|=1.78(25)\times {10}^{-3}$ for the parameter ${ϵ}_K$, measuring indirect $CP$ violation in the $K$ system, to be compared with the experimental value $|{ϵ}_K^{\exp }|=2.23(1)\times {10}^{-3}$. To bring this prediction to $1\sigma$ 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.