On the determination of non-leptonic kaon decays from K → π matrix elements

The coupling constants of the order p^2 low-energy weak effective lagrangian can be determined from the K → π and K → 0 weak matrix elements, choosing degenerate quark masses for the first of these. However, for typical values of quark masses in Lattice QCD computations, next-to-leading O(p^4) corrections are too large to be ignored, and will need to be included in future analyses. Here we provide the complete O(p^4) expressions for these matrix elements obtained from Chiral Perturbation Theory, valid for partially quenched QCD with N degenerate sea quarks. Quenched QCD corresponds to the special case N = 0. We also discuss the role of the η' meson in some detail, and we give numerical examples of the size of chiral logarithms.