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

TL;DR

This paper investigates how lattice spacing and gradient flow affect the measurement of topological susceptibility in high-temperature QCD, using semi-analytical methods on discretized calorons to improve continuum extrapolation accuracy.

Contribution

It provides a semi-analytical analysis of lattice artifacts in topological susceptibility calculations, highlighting the impact of gradient flow and lattice parameters.

Findings

N_tau=6 is too small for reliable high-temperature studies

Gradient flow significantly influences continuum extrapolation

Discretized calorons reveal lattice-spacing corrections in susceptibility measurements

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.