On the Determination of Nonleptonic Kaon Decays from $K\to \pi$ Matrix Elements

Abstract

The coupling constants of the order $p^2$ low-energy weak effective lagrangian can be determined from the $K\to \pi$ and $K\to 0$ 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 ${\eta }^{\prime }$ meson in some detail, and we give numerical examples of the size of chiral logarithms.

29 pages, 7 figures

References in corpus (3)

• Weak transition matrix elements from finite-volume correlation functions
• Quenched Light Hadron Spectrum
• Physical Results from Unphysical Simulations

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