Final state interactions in ... formula ... decays: ... formula ... rule vs. ... formula ...

摘要

Dispersive effects from strong ππ rescattering in the final state interaction (FSI) of weak K → ππ decays are revisited with the goal to have a global view on their relative importance for the ΔI = 1/2 rule and the ratio ε^′/ε in the standard model (SM). We point out that this goal cannot be reached within a pure effective (meson) field approach like chiral perturbation theory in which the dominant current–current operators governing the ΔI = 1/2 rule and the dominant density–density (four-quark) operators governing ε^′/ε cannot be disentangled from each other. But in the context of a dual QCD approach, which includes both long-distance dynamics and the UV completion, that is, QCD at short-distance scales, such a distinction is possible. We find then that beyond the strict large N limit, N being the number of colours, FSIs are likely to be important for the ΔI = 1/2 rule but much less relevant for ε^′/ε. The latter finding diminishes significantly hopes that improved calculations of ε^′/ε would bring its SM prediction to agree with the experimental data, opening thereby an arena for important new physics contributions to this ratio.