  We present a calculation of the low energy constants describing the real and
imaginary parts of the $K \to \pi \pi$ decay amplitudes $A_0$ and $A_2$.
Leading and next leading order chiral perturbation theory is used and its
applicability assessed. A combination of statistical and systematic errors
limits the precision of the results. The apparent limitations of chiral
perturbation theory raise doubts about the accuracy of a possible extrapolation
to physical $K \to \pi \pi$ kinematics.

High Energy Physics - Lattice