$K^{+}\to {\pi }^{+}{\pi }^0$ 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.

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

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• An exploratory lattice study of DI=3/2 K -> pi pi decays at next-to-leading order in the chiral expansion
• Lattice QCD at the end of 2003
• Matrix elements relevant for Delta I=1/2 rule and epsilon-prime from Lattice QCD with staggered fermions
• The generating functional for hadronic weak interactions and its quenched approximation
• The leading chiral electromagnetic correction to the nonleptonic Delta I = 3/2 amplitude in kaon decays
• $K\to \pi \pi$ matrix elements beyond the leading-order chiral expansion
• On Lattice Computations of K+ --> pi+ pi0 Decay at m_K =2m_pi
• $\Delta I=3/2$ and $\Delta I=1/2$ channels of $K\to \pi \pi$ decay at the physical point with periodic boundary conditions
• On-shell Delta I = 3/2 kaon weak matrix elements with non-zero total momentum
• Chiral Logarithms in $\Delta S=1$ Kaon Decay Amplitudes in General Effective Flavor Theories