Estimating $\chi_\mathrm{top}$ Lattice Artifacts from Flowed SU(2) Calorons

Abstract

Lattice computations of the high-temperature topological susceptibility of QCD receive lattice-spacing corrections and suffer from systematics arising from the type and depth of gradient flow. We study the lattice spacing corrections to $\chi_\mathrm{top}$ semi-analytically by exploring the behavior of discretized Harrington-Shepard calorons under the action of different forms of gradient flow. From our study we conclude that $N_\tau = 6$ is definitely too small of a time extent to study the theory at temperatures of order $4~T_\mathrm{c}$ and we explore how the amount of gradient flow influences the continuum extrapolation.