On the determination of non-leptonic kaon decays from K -> pi matrix elements

The coupling constants of the order p(2) low-energy weak effective lagrangi an can be determined from the K --> pi and K --> 0 weak matrix elements, ch oosing 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 partia lly quenched QCD with N degenerate sea quarks. Quenched QCD corresponds to the special case N = 0. We also discuss the role of the eta' meson in some detail, and we give numerical examples of the size of chiral logarithms.