$K_L-K_S$ mass difference from Lattice QCD

We will report on the first full calculation of the $K_L-K_S$ mass difference in lattice QCD. The calculation is performed on a 2+1 flavor, domain wall fermion, $24^3\times 64$ ensemble with a 329 MeV pion mass and a 575 MeV kaon mass. Both double penguin diagrams and disconnected diagrams are included in this calculation. The calculation is made finite through the GIM mechanism by introducing a 949 MeV valence charm quark. While the double penguin diagrams contribute a very small fraction to the mass difference, there is a large cancellation between disconnected diagrams and other types of diagrams. We obtain the mass difference $\Delta M_K$=$3.30(34)\times 10^{-12}$ MeV for these unphysical kinematics.