K -> pi pi decays with domain wall fermions: Towards physical results

We are using domain wall fermions to study K --> pi pi matrix elements by m easuring K --> pi and K --> 0 matrix elements on the lattice and employing chiral perturbation theory to relate these to the desired physical result. The residual chiral symmetry breaking of domain wall fermions with a finite extent in the fifth dimension impacts these measurements. Using the Ward-T akahashi identities, we investigate residual chiral symmetry breaking effec ts for divergent quantities and study pathologies of the quenched approxima tion for small quark mass. We then discuss the DeltaS = 1 operator O-2, whe re chiral symmetry is vital for the subtraction of unphysical effects.