Re $A_0$ and Re $A_2$ from Quenched Lattice QCD

Abstract

We have used domain wall fermions to calculate $K \to \pi$ and $K \to 0$ matrix elements which can be used to study the $\Delta I = 1/2$ rule for K decays in the Standard Model. Nonlinearities in the $\Delta I = 3/2$ matrix elements due to chiral logarithms are explored and the subtractions needed for the $\Delta I = 1/2$ matrix elements are discussed. Using renormalization factors calculated using non-perturbative renormalization then yields values for real $A_0$ and $A_2$. We present the details of our quenched $16^3 \times 32 \times 16$, $\beta = 6.0$, $M_5 = 1.8$ simulation, where a previous calculation showed that the finite $L_s$ chiral symmetry breaking effects are small ($m_{\rm res} \approx 4 \rm MeV$).