Long-distance contributions to weak amplitudes

Abstract

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 ${ϵ}_K$.

Comments: Contribution to the 28th International Symposium on Lattice Field Theory, Lattice 2010, June 14-19, 2010, Villasimius, Italy, 7 pages, 3 figures