Kaon Weak Matrix Elements in 2+1 flavor DWF QCD

$K\to \pi$ and $K\to 0$ weak matrix elements of $\mathrm{\Delta }S=1$ operators have been measured in 2+1 flavor domain wall fermion (DWF) QCD on (3 fm)${}^3$ lattices with $a^{-1}=1.73(3)$ GeV. As is well known, using these matrix elements and chiral perturbation theory allows a determination of the $K \to \pi \pi$matrixelementsthatenterinthequantitativevalueforthe$\Delta I = 1/2$ruleand$\epsilon^\prime/\epsilon$. Two light dynamical sea quark masses have been used, along with six valence quark masses, with the lightest valence quark mass $\approx 1\mathrm{/}10$ the physical strange quark mass. We report our results for lattice matrix elements in the $SU(3{)}_L\times SU(3{)}_R$ (27,1), (8,1), and (8,8) representations, paying particular attention to the statistical errors achieved after measurements on 75 configurations. We also report on our calculation of the non-perturbative renormalization coefficients for these $\mathrm{\Delta }S=1$ weak operators, using the Rome-Southampton method.