Built on

M. Luscher, Two particle states on a torus and their relation to the scattering matrix
Original
1991
Earlier work this paper cites.
S. Herrlich and U. Nierste, Enhancement of the K(L) - K(S) mass difference by short distance QCD corrections beyond leading logarithms
1994
Earlier work this paper cites.

Similar

L. Lellouch and M. Luscher, Weak transition matrix elements from finite-volume correlation functions
2001
Cited alongside, same era.
G. Isidori, G. Martinelli and P. Turchetti, Rare kaon decays on the lattice
2006
Cited alongside, same era.

Then

A. J. Buras, D. Guadagnoli and G. Isidori, On ϵ K \epsilon_{K} beyond lowest order in the Operator Product Expansion
Original
2010
Closest in time.

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2010

Long-distance contributions to weak amplitudes

Christ, Norman H.

Understand

The calculation of the long-distance contribution to the $K^0-\bar{K}^0$ mass matrix is divided into three parts: First, the calculation of the matrix element between kaon states of the product of two space-time integrated, $\Delta S=1$, four-quark weak operators.

Second an RI/MOM subtraction to remove the short distance part of this matrix element in a fashion consistent with the calculation of the physical short distance part.
Third an application of the Lellouch-Luscher method, generalized to second order in the weak interactions, to control finite volume errors.
Such an approach promises to permit accurate lattice calculation of the $K_L$-$K_S$ mass difference and the long-distance contributions to $\epsilon_K$.