Long distance contribution to $K_{L}$-$K_{S}$ mass difference

TL;DR

This paper introduces a non-perturbative method to compute the long-distance contribution to the $K_{L}$-$K_{S}$ mass difference, utilizing lattice QCD with domain wall fermions and GIM mechanism to control divergences.

Contribution

The paper presents a novel lattice QCD approach that combines GIM mechanism and RI/MOM techniques to accurately determine long-distance effects in kaon mass differences.

Findings

Successfully eliminated quadratic divergences using GIM mechanism.

Implemented RI/MOM to replace short-distance effects with physical contributions.

Performed calculations on 2+1 flavor lattice configurations with controlled systematic effects.

Abstract

We present a method to non-perturbatively determine the long-distance contribution to the $K_{L}$-$K_{S}$ mass difference. The calculation is performed on 2+1 flavor, domain wall fermion, $16^3\times32$ configurations with a 421 MeV pion mass and a kaon mass of 559 MeV . We include only current-current operators and drop all disconnected diagrams in the calculation. The largest contribution comes from quadratically divergent, short distance lattice artifacts. This quadratic divergence is eliminated through the GIM mechanism by introducing a valence charm quark. The remaining short distance effects are then removed by using RI/MOM technique which allows their exact replacement by the physical short distance part.