K → ππ decays with domain wall fermions: towards physical results

We are using domain wall fermions to study K → ππ matrix elements by measuring K → π 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-Takahashi identities, we investigate residual chiral symmetry breaking effects for divergent quantities and study pathologies of the quenched approximation for small quark mass. We then discuss the ΔS = 1 operator O2, where chiral symmetry is vital for the subtraction of unphysical effects