Im$A_0$, Im$A_2$, and ${ϵ}^{\prime }$ 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, ${ϵ}^{\prime }/ϵ$. 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 ${ϵ}^{\prime }/ϵ$ is small and slightly negative.

Comments: Three pages, latex, includes four eps figures. Contribution to the proceedings of the XIXth International Symposium on Lattice Field Theory, Berlin (hadronic matrix elements)