Chiral perturbation theory, K to pi pi decays and 2+1 flavor domain wall QCD

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.