Wilson flow with naive staggered quarks

TL;DR

This study uses Wilson flow to analyze scale setting in two-flavor staggered quark QCD, examining lattice spacing effects and improvements, with findings on scale ratios and uncertainties.

Contribution

It demonstrates the effectiveness of Wilson flow with naive staggered quarks for scale setting and assesses lattice spacing effects and improvements across a range of parameters.

Findings

Error in flow scale increases with inverse square of lattice spacing.

Tree level improvement reduces scale uncertainties.

The continuum limit of w_0/√t_0 is approximately 1.106.

Abstract

Scale setting for QCD with two flavours of staggered quarks is examined using Wilson flow over a factor of four change in both the lattice spacing and the pion mass. The statistics needed to keep the errors in the flow scale fixed is found to increase approximately as the inverse square of the lattice spacing. Tree level improvement of the scales t_0 and w_0 is found to be useful in most of the range of lattice spacings we explore. The scale uncertainty due to remaining lattice spacing effects is found to be about 3%. The ratio w_0/\sqrt{t_0} is N_f dependent and we find its continuum limit to be 1.106 \pm 0.007 (stat) \pm 0.005 (syst) for m_\pi w_0 \simeq 0.3.