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

Details On the Determination of Nonleptonic Kaon Decays from $K\toπ$ Matrix Elements On the Determination of Nonleptonic Kaon Decays from $K\toπ$ Matrix Elements

2000-06-29

arxiv.org/abs/hep-lat/0006029v1

JHEP 0008 (2000) 023

Physics

High Energy Physics

High Energy Physics - Lattice

29 pages, 7 figures

Scientific paper

10.1088/1126-6708/2000/08/023

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 $\eta'$ meson in some detail, and we give numerical examples of the size of chiral logarithms.

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