Kaon Weak Matrix Elements in 2+1 flavor DWF QCD

K → π and K → 0 weak matrix elements of ∆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 → ππ matrix elements that enter in the quantitative value for the ∆I = 1/2 rule and ε ′/ε . Two light dynamical sea quark masses have been used, along with six valence quark masses, with the lightest valence quark mass ≈ 1/10 the physical strange quark mass. We report our results for lattice matrix elements in the SU(3)L × 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 ∆S = 1 weak operators, using the Rome-Southampton method.