# Kaon matrix elements and CP violation from quenched lattice QCD: The 3-flavor case

## Abstract

We report the results of a calculation of the [Formula Presented] matrix elements relevant for the [Formula Presented] rule and [Formula Presented] in quenched lattice QCD using domain wall fermions at a fixed lattice spacing [Formula Presented] Working in the three-quark effective theory, where only the u, d, and s quarks enter and which is known perturbatively to next-to-leading order, we calculate the lattice [Formula Presented] and [Formula Presented] matrix elements of dimension six, four-fermion operators. Through lowest order chiral perturbation theory these yield [Formula Presented] matrix elements, which we then normalize to continuum values through a nonperturbative renormalization technique. For the ratio of isospin amplitudes [Formula Presented] we find a value of [Formula Presented] (statistical error only) compared to the experimental value of 22.2, with individual isospin amplitudes 10%–20% below the experimental values. For [Formula Presented] using known central values for standard model parameters, we calculate [Formula Presented] (statistical error only) compared to the current experimental average of [Formula Presented] Because we find a large cancellation between the [Formula Presented] and [Formula Presented] contributions to [Formula Presented] the result may be very sensitive to the approximations employed. Among these are the use of quenched QCD, lowest order chiral perturbation theory, and continuum perturbation theory below 1.3 GeV. We also calculate the kaon B parameter [Formula Presented] and find [Formula Presented] Although currently unable to give a reliable systematic error, we have control over statistical errors and more simulations will yield information about the effects of the approximations on this first-principles determination of these important quantities. © 2003 The American Physical Society.