SU(3) analysis of four-quark operators: $K\to\pi\pi$ and vacuum matrix elements
Résumé
Hadronic matrix elements of local four-quark operators play a central role in non-leptonic kaon decays, while vacuum matrix elements involving the same kind of operators appear in inclusive dispersion relations, such as those relevant in τ-decay analyses. Using an SU(3)$_{L}$ ⊗ SU(3)$_{R}$ decomposition of the operators, we derive generic relations between these matrix elements, extending well-known results that link observables in the two different sectors. Two relevant phenomenological applications are presented. First, we determine the electroweak-penguin contribution to the kaon CP-violating ratio ε′/ε, using the measured hadronic spectral functions in τ decay. Second, we fit our SU(3) dynamical parameters to the most recent lattice data on K → ππ matrix elements. The comparison of this numerical fit with results from previous analytical approaches provides an interesting anatomy of the ∆I = $ \frac{1}{2} $ enhancement, confirming old suggestions about its underlying dynamical origin.
Mots clés
Chiral Lagrangians
CP violation
Effective Field Theories
Kaon Physics
K: hadronic decay
effective field theory
quark: four-fermion interaction
symmetry: chiral
perturbation theory: chiral
flavor: SU(3)
CP: violation
operator product expansion
spectral representation
dispersion relation
lattice
numerical calculations
K --> pi pi