On $K\toππ$ Decays in Quenched and Unquenched Chiral Perturbation Theory

Details On $K\toππ$ Decays in Quenched and Unquenched Chiral Perturbation Theory On $K\toππ$ Decays in Quenched and Unquenched Chiral Perturbation Theory

1999-09-09

arxiv.org/abs/hep-lat/9909069v1

Nucl.Phys.Proc.Suppl. 83 (2000) 250-252

Physics

High Energy Physics

High Energy Physics - Lattice

LATTICE99(Matrix Elements), LaTeX(espcrc2.sty), 3p, 1 ps figure

Scientific paper

We calculate the logarithmic corrections to the matrix elements for $K^+\to\pi^+$ and $K\to$vacuum (which are used on the lattice to determine $K\to\pi\pi$ amplitudes), in one-loop quenched and unquenched Chiral Perturbation Theory. We find that these corrections can be large. We also discuss, and present some results for, the direct determination of $K\to\pi\pi$ amplitudes. In particular, we address effects from choosing $m_s=m_d$ and vanishing external spatial momenta, finite volume and quenching. In the quenched octet case, we find enhanced finite-volume contributions which may make numerical estimates of this matrix element unreliable for large volumes.

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