Computing the long-distance contribution to the kaon mixing parameter \epsilon_K

TL;DR

This paper discusses the calculation of the long-distance contribution to the CP violation parameter _K in kaon mixing, extending lattice QCD techniques to improve the precision of theoretical predictions.

Contribution

It generalizes recent lattice methods to compute the long-distance contribution to _K, which was previously estimated but not directly calculated.

Findings

Long-distance contribution to _K is estimated at about 5%.

Lattice techniques are adapted for this specific long-distance calculation.

Enhanced understanding of CP violation in kaon mixing.

Abstract

The largest contribution to the CP violating K_L-K_S mixing parameter \epsilon_K comes from second order weak interactions at short distances and can be accurately determined by a combination of electroweak perturbation theory and the calculation of the parameter B_K from lattice QCD. However, there is an additional long distance contribution to \epsilon_K which is estimated to be of order 5%. Here recently introduced lattice techniques for computing the long-distance component of the K_L-K_S mass difference are generalized to this long-distance contribution to \epsilon_K.