Im$A_0$, Im$A_2$, and $\epsilon^\prime$ from quenched lattice QCD

Abstract

We present results for the imaginary parts of the I=0 and 2 $K\to\pi\pi$ decay amplitudes, Im$A_{0,2}$, and the ratio of CP violation parameters, $\epsilon^\prime/\epsilon$. Our calculation is done in the quenched approximation at $a^{-1}\approx 2$ GeV, lattice size $16^3\times 32$, using domain wall fermions with $L_s=16$. We study the three flavor case (charm is not an active flavor) and find $\epsilon^\prime/\epsilon$ is small and slightly negative.