Lattice QCD Calculation of the K+ → π+ π 0 decay amplitude with the Wilson Quark action

We present our results for the K⁺ → π⁺ π ⁰ decay amplitude with the Wilson quark action in the quenched approximation at β = 6.1. The amplitude is extracted from the ratio of K → ππ 3-point function divided either by K and π meson 2-point functions or by K meson 2-point function and I = 2 ππ 4-point function, which yield results in good agreement. Finite size effects are examined with calculations made on 24 ³ × 64 and 32 ³ × 64 lattices. We convert the lattice amplitude into the continuum value employing a recent one-loop calculation of chiral perturbation theory by Golterman and Leung. The result is consistent with the experimental value if extrapolated to the chiral limit. Various uncertainties inherent in the present methods for calculating the decay amplitude are discussed.