Long distance contribution to $K_{L}$-$K_{S}$ mass difference

Understand

We present a method to non-perturbatively determine the long-distance contribution to the $K_{L}$-$K_{S}$ mass difference.

• The calculation is performed on 2+1 flavor, domain wall fermion, $16^3\times32$ configurations with a 421 MeV pion mass and a kaon mass of 559 MeV .
• We include only current-current operators and drop all disconnected diagrams in the calculation.
• The largest contribution comes from quadratically divergent, short distance lattice artifacts.