Calculation of $Ktopipi$ decay amplitudes from $Ktopi$ matrix elements in quenched domain-wall QCD

We present a calculation of the $Ktopipi$ decay amplitudes from the $Ktopi$ matrix elements using leading order relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD with the domain-wall fermion action and the renormalization group improved gluon action. Our results show that the I=2 amplitude is reasonably consistent with experiment whereas the I=0 amplitude is sizably smaller. Consequently the $Delta I=1/2$ enhancement is only half of the experimental value, and $epsilon/epsilon$ is negative.