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

Abstract

We present a lattice calculation of the $K\to \pi$ and $K\to 0$ matrix elements of the $\Delta S=1$ effective weak Hamiltonian which can be used to determine ${\epsilon }^{\prime }/\epsilon$ and the $\Delta I=1/2$ rule for $K$ decays in the Standard Model. The matrix elements for $K\to \pi \pi$ decays are related to $K\to \pi$ 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 $\beta =6.0$ ($a^{-1}\approx 2$ GeV), lattice size $16^3\times 32\times 16$, and domain wall height $M_5=1.8$.

Parallel talk contribution to Lattice 2000 proceedings (weak matrix elements

Cited by in corpus (6)

• Kaon Matrix Elements and CP-violation from Quenched Lattice QCD: (I) the 3-flavor case
• Kaon B parameter from quenched domain-wall QCD
• Calculation of Non-Leptonic Kaon Decay Amplitudes from $K\to \pi$ Matrix Elements in Quenched Domain-Wall QCD
• Analysis of the DeltaI=1/2 Rule and e'/e with Overlap Fermions
• Perturbative Matching of the staggered four-fermion operators for e'/e
• Matrix Elements of Light Quarks