SU(3) analysis of four-quark operators: K → ππ and vacuum matrix elements

A bstract Hadronic matrix elements of local four-quark operators play a central role in non-leptonic kaon decays, while vacuum involving the same kind appear inclusive dispersion relations, such as those relevant τ -decay analyses. Using an SU(3) L ⊗ R decomposition operators, we derive generic relations between these elements, extending well-known results that link observables two different sectors. Two phenomenological applications are presented. First, determine electroweak-penguin contribution to CP-violating ratio ε ′ /ε , using measured hadronic spectral functions decay. Second, fit our dynamical parameters most recent lattice data on K → ππ elements. The comparison this numerical with from previous analytical approaches provides interesting anatomy ∆ I = $$ \frac{1}{2} 12 enhancement, confirming old suggestions about its underlying origin.