On the determination of nonleptonic kaon decays from K→π matrix elements

The coupling constants of the order $p^2$ low-energy weak effectivelagrangian can be determined from the $K\to\pi$ and $K\to 0$ weak matrixelements, choosing degenerate quark masses for the first of these. However, fortypical 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 includedin future analyses. Here we provide the complete $O(p^4)$ expressions for thesematrix elements obtained from Chiral Perturbation Theory, valid for partiallyquenched QCD with $N$ degenerate sea quarks. Quenched QCD corresponds to thespecial 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.Comment: 29 pages, 7 figure