Calculating $\Delta m_K$ with lattice QCD

TL;DR

This paper reports a lattice QCD calculation of the K meson mass difference, achieving a small statistical error but discussing potential systematic uncertainties from lattice size effects.

Contribution

It provides a detailed lattice QCD computation of elta m_K with physical quark masses on a large lattice, addressing systematic errors from smaller lattice studies.

Findings

Statistical error of 9% in elta m_K calculation

Systematic errors from lattice size are significant

Methodology for estimating systematic uncertainties

Abstract

We have completed a lattice QCD calculation of $\Delta m_K$, the mass difference between the long- and short-lived K mesons. The calculation was performed on a $64^3 \times 128$ lattice using 152 configurations with physical quark masses and an inverse lattice spacing of $1/a=2.36$ GeV. While the statistical error approaches a relatively small size of 9%, several sources of systematic errors may have more significant effects. In this paper we will address studies performed on smaller lattices to estimate the systematic errors in our result.