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

TL;DR

This paper reports lattice QCD calculations of decay amplitudes and CP violation ratios in kaon decays, providing insights into the size and sign of direct CP violation within the quenched approximation.

Contribution

First lattice QCD calculation of Im$A_0$, Im$A_2$, and $ ext{Re}(rac{ ext{CP violation parameters}}{})$ in the quenched approximation using domain wall fermions.

Findings

$ ext{Re}(rac{ ext{CP violation}}{})$ is small and slightly negative

Results are obtained at lattice spacing $a^{-1} oughly 2$ GeV

Study uses three-flavor quenched approximation with domain wall fermions.

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.