On lattice extraction of $K \to ππ$ amplitudes to $O(p^{4})$ in Chiral Perturbation Theory

We show that lattice calculation of $K\to\pi\pi$ and $\epe$ amplitudes for (8,1) and (27,1) operators to $O(p^4)$ in chiral perturbation theory is feasible when one uses $K\to\pi\pi$ computations at the two unphysical kinematics allowed by the Maiani-Testa theorem, along with the usual (computable) two and three point functions, namely $K\to0$, $K\to\pi$ (with momentum) and $K-\bar K$.