K+→π+π0 decay amplitude with the Wilson quark action in quenched lattice QCD

Abstract

We present a calculation for the K+→π+π0 decay amplitude using a quenched simulation of lattice QCD with the Wilson quark action at β=6/g2=6.1. The decay amplitude is extracted from the ratio, the K→ππ three-point function divided by either K and π meson two-point functions or K meson two-point function and I=2 ππ four-point function: the two different methods yield consistent results. Finite size effects are examined with calculations made on 243×64 and 323×64 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 BK obtained from the K+→π+π0 amplitude using chiral perturbation theory.