Long distance part of $epsilon_K$ from lattice QCD

We demonstrate the lattice QCD calculation of the long distance contribution to $epsilon_K$. Due to the singular, short-distance structure of $epsilon_K$, we must perform a short-distance subtraction and introduce a corresponding low-energy constant determined from perturbation theory, which we calculate at Next Leading Order (NLO). We perform the calculation on a $24^3 times 64$ lattice with a pion mass of 329 MeV. This work is a complete calculation, which includes all connected and disconnected diagrams.