Calculating $\mathrm{\Delta }{m}_K$ with lattice QCD

We have completed a lattice QCD calculation of $\mathrm{\Delta }{m}_K$, 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 $1\mathrm{/}a=2.36$ 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.