name

Thomas Charles Blum

refid

12636

email

tblum@bnl.gov

title

$K \rightarrow \pi \pi$ decays with domain wall fermions: lattice matrix elements

collaboration

RBC Collaboration

abstract

We present results for lattice matrix elements of the operators of the
$\Delta S=1$ effective weak Hamiltonian which are required for the
$\Delta I=1/2$ rule and $\epsilon^\prime/\epsilon$. Using quenched QCD
with domain wall fermions, we calculate matrix elements between $K$
and $\pi$ states and $K$ and vacuum states and then use lowest order
chiral perturbation theory to relate these off-shell matrix elements to
the lattice on-shell $K \rightarrow \pi \pi $ amplitudes. Domain wall
fermions should lead to good chiral behavior for the matrix elements,
which is seen in our results and is crucial for the use of chiral
perturbation theory. Small violations of chiral symmetry that arise
from the use of a finite 5th dimension are discussed and shown to be
under control. The simulations are done at beta=5.85 and 6.0 with
lattice sizes 12^3x32x20 and 16^3x32x16, respectively, where the last
dimension denotes the size of the 5th dimension.

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