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Dispersive effects from strong $\pi\pi$ rescattering in the final state (FSI)of weak $K\to\pi\pi$ decays are revisited with the goal to have a global viewon their {\it relative} importance for the $\Delta I=1/2$ rule and the ratio$\varepsilon^\prime/\varepsilon$ in the Standard Model (SM). We point out thatthis goal cannot be reached within a pure effective (meson) field approach likechiral perturbation theory in which the dominant current-current operatorsgoverning the $\Delta I=1/2$ rule and the dominant density-density (four-quark)operators governing $\varepsilon^\prime/\varepsilon$ cannot be disentangledfrom each other. But in the context of a dual QCD approach, which includes bothlong distance dynamics and the UV completion, that is QCD at short distancescales, such a distinction is possible. We find then that beyond the strictlarge $N$ limit, $N$ being the number of colours, FSI are likely to beimportant for the $\Delta I=1/2$ rule but much less relevant for$\varepsilon^\prime/\varepsilon$. The latter finding diminishes significantlyhopes that improved calculations of $\varepsilon^\prime/\varepsilon$ wouldbring its SM prediction to agree with the experimental data, opening thereby anarena for important new physics contributions to this ratio.

Final State Interactions in $K\to\pi\pi$ Decays: $\Delta I=1/2$ Rule vs. $\varepsilon^\prime/\varepsilon$