Precise determination of the lattice spacing in full lattice QCD

TL;DR

This paper compares three methods for accurately determining the lattice spacing in full lattice QCD, providing precise values for parameters like $r_1$, $r_0$, and $ ext{m}_{ ext{$oldsymbol{ exteta}_s$}}$, aiding ensemble comparisons and tuning.

Contribution

It introduces and compares three methods for lattice spacing determination in lattice QCD, offering precise continuum limit values for key parameters and discussing the use of $ ext{m}_{ ext{$oldsymbol{ exteta}_s$}}$ for tuning.

Findings

Combined methods yield $r_1=0.3133(23)(3)$ fm in the continuum limit.

Derived $r_0=0.4661(38)$ fm from $r_1$ and MILC ratios.

Provided values for $m_{ ext{$oldsymbol{ exteta}_s$}}$ and $f_{ ext{$oldsymbol{ exteta}_s$}}$ for tuning and scale setting.

Abstract

We compare three different methods to determine the lattice spacing in lattice QCD and give results from calculations on the MILC ensembles of configurations that include the effect of $u$, $d$ and $s$ sea quarks. It is useful, for ensemble to ensemble comparison, to express the results as giving a physical value for $r_1$, a parameter from the heavy quark potential. Combining the three methods gives a value for $r_1$ in the continuum limit of 0.3133(23)(3) fm. Using the MILC values for $r_0/r_1$, this corresponds to a value for the $r_0$ parameter of 0.4661(38) fm. We also discuss how to use the $\eta_s$ for determining the lattice spacing and tuning the $s$-quark mass accurately, by giving values for $m_{\eta_s}$ (0.6858(40) GeV) and $f_{\eta_s}$ (0.1815(10) GeV).