Calculating the $K_L-K_S$ mass difference and $\epsilon_K$ to sub-percent accuracy

TL;DR

This paper proposes a comprehensive strategy combining perturbative and lattice QCD methods to calculate the $K_L-K_S$ mass difference and $ ext{Re}( ext{epsilon}_K)$ with sub-percent precision, accounting for all three quark contributions.

Contribution

It introduces a detailed approach to accurately compute $K_L-K_S$ mixing parameters, including all quark contributions, to improve precision in flavor physics.

Findings

Outline of a combined perturbative and lattice methodology

Identification of quark contributions to mixing parameters

Achieving sub-percent accuracy in $K_L-K_S$ mass difference and $ ext{epsilon}_K$

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 $\epsilon_K$ to sub-percent accuracy, looking in detail at the contributions from each of the three CKM matrix element products $V_{id}^*V_{is}$ for $i=u, c$ and $t$ as described in Ref. [1]