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

Abstract

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.

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