Abstract
Dispersive effects from strong pi pi rescattering in the final state interaction (FSI) of weak Krightarrow pi pi decays are revisited with the goal to have a global view on their relative importance for the Delta I=1/2 rule and the ratio varepsilon '/varepsilon 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 Delta I=1/2 rule and the dominant density–density (four-quark) operators governing varepsilon '/varepsilon 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 Delta I=1/2 rule but much less relevant for varepsilon '/varepsilon . The latter finding diminishes significantly hopes that improved calculations of varepsilon '/varepsilon would bring its SM prediction to agree with the experimental data, opening thereby an arena for important new physics contributions to this ratio.
Highlights
Among the most important observables in flavour physics are the ratio of K → π π isospin amplitudes Re A0/Re A2 and ε /ε
The question of 1/N -suppressed strong final state interaction (FSI) effects on such a hadronic matrix element may be raised at this point
Going beyond chiral perturbation theory (ChPT) (BChPT), one might advocate [12,13,14,15,16,17,18,19] that an overall dispersive factor R0 ≈ exp(1/N ) > 1 resulting from the all-order resummation of pion loops only should be applied to the weak decay amplitude in (9) and, in particular, to its indistinguishable penguin component
Summary
Among the most important observables in flavour physics are the ratio of K → π π isospin amplitudes Re A0/Re A2 and ε /ε. Re A2 dual QCD while the corresponding result from the RBC–UKQCD collaboration is [7]. The RBC–UKQCD lattice collaboration calculating the hadronic matrix elements of all operators but not including isospin breaking effects finds [7,8]. Using the hadronic matrix elements of QCD- and EWpenguin (V − A) ⊗ (V + A) operators from RBC–UKQCD lattice collaboration but extracting the matrix elements of penguin (V − A)⊗(V − A) operators from the CP-conserving K → π π amplitudes and including isospin breaking effects one finds [9].
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