$K^{+}\toπ^{+}π^{0}$ Decay Amplitude with the Wilson Quark Action in Quenched Lattice QCD

Details $K^{+}\toπ^{+}π^{0}$ Decay Amplitude with the Wilson Quark Action in Quenched Lattice QCD $K^{+}\toπ^{+}π^{0}$ Decay Amplitude with the Wilson Quark Action in Quenched Lattice QCD

1997-11-21

arxiv.org/abs/hep-lat/9711046v2

Phys.Rev. D58 (1998) 054503

Physics

High Energy Physics

High Energy Physics - Lattice

LaTeX, 23 pages, 8 figures, uses revtex and epsf

Scientific paper

10.1103/PhysRevD.58.054503

We present a calculation for the $K^+\to\pi^+ \pi^0 $ decay amplitude using a quenched simulation of lattice QCD with the Wilson quark action at $\beta=6/g^2=6.1$. The decay amplitude is extracted from the ratio, the $K\to\pi\pi$ three-point function divided by either $K$ and $\pi$ meson two-point functions or $K$ meson two-point function and I=2 $\pi\pi$ four-point function; the two different methods yield consistent results. Finite size effects are examined with calculations made on $24^3\times 64$ and $32^3\times 64$ lattices, and are shown that they are explained by one-loop effects of chiral perturbation theory. The lattice amplitude is converted to the continuum value by employing a one-loop calculation of chiral perturbation theory, yielding a value in agreement with experiment if extrapolated to the chiral limit. We also report on the $K$ meson $B$ parameter $B_K$ obtained from the $K^+\to\pi^+\pi^0$ amplitude using chiral perturbation theory.

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