Kaon Weak Matrix Elements in 2+1 flavor DWF QCD

Abstract

$K \to π$ and $K \to 0$ weak matrix elements of $ΔS = 1$ 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 $K \to ππ$ matrix elements that enter in the quantitative value for the $ΔI = 1/2$ rule and $ε^\prime/ε$. Two light dynamical sea quark masses have been used, along with six valence quark masses, with the lightest valence quark mass $\approx 1/10$ 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 $ΔS=1$ weak operators, using the Rome-Southampton method.