Calculating the $K_L-K_S$ mass difference and ${ϵ}_K$ to sub-percent accuracy

Abstract

The real and imaginary parts of the $K_L-K_S$ mixing matrix receive contributions from all three charge-2/3 quarks: up, charm and top. These give both short- and long-distance contributions which are accessible through a combination of perturbative and lattice methods. We will discuss a strategy to compute both the mass difference, $\Delta M_K$ and ${ϵ}_K$ to sub-percent accuracy, looking in detail at the contributions from each of the three CKM matrix element products $V_{id}^{\ast }{V}_{is}$ for $i=u,c$ and $t$ as described in Ref. [1]

Comments: Presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany, 7 pages and 5 figures