$K\toππ$ Decays with Domain Wall Fermions: Lattice Matrix Elements

Abstract

We present a lattice calculation of the $K\toπ$ and $K\to 0$ matrix elements of the $ΔS=1$ effective weak Hamiltonian which can be used to determine $ε^\prime/ε$ and the $ΔI=1/2$ rule for $K$ decays in the Standard Model. The matrix elements for $K\toππ$ decays are related to $K\toπ$ and $K\to 0$ using lowest order chiral perturbation theory. We also present results for the kaon $B$ parameter, $B_K$. Our quenched domain wall fermion simulation was done at $β=6.0$ ($a^{-1}\approx 2$ GeV), lattice size $16^3\times 32\times 16$, and domain wall height $M_5=1.8$.