Setting the scale for nHYP fermions with the L\"uscher-Weisz gauge action

TL;DR

This paper establishes a detailed parameterization for setting the scale in lattice QCD simulations using nHYP smeared fermions with the L"uscher-Weisz gauge action, improving accuracy and ease of tuning.

Contribution

It provides a comprehensive parameterization of lattice spacing and pion mass dependence on coupling parameters for $N_f=2$ QCD with this specific action, aiding future simulations.

Findings

Achieved percent-level statistical accuracy in lattice measurements.

Provided universal parameterizations for chiral extrapolation.

Quantified finite-volume effects as sub-percent.

Abstract

Lattice QCD calculations using gauge smearing for fermion kernels are computationally efficient. Hypercubic blocking (nHYP smearing) has been shown to reduce scaling errors. In this work we use an improved action for $N_f=2$ QCD, based on the L\"uscher-Weisz gauge action and clover-improved Wilson fermions with nHYP smeared gauge links. We perform a parameter scan in the region with lattice spacing between $0.066 \mathop{\hbox{fm}}$ and $0.115 \mathop{\hbox{fm}}$ and pion mass between $207 \mathop{\hbox{MeV}}$ and $834 \mathop{\hbox{MeV}}$. We determine the lattice spacing and pion mass as a function of the bare coupling parameters ($\beta$ and $\kappa$). The results are obtained from twenty-two ensembles on a $24^3\times 48$ lattice to percent level in statistical accuracy. The finite-volume effects for these ensemble are at the sub-percent level. From these measurements we produce easy-to-use parameterizations to help tune simulations with this action. The lattice spacing is fixed using a mass-independent procedure, by matching observables in the chiral limit. We also provide a parameterization for the chiral extrapolation which is universal and should hold for all discretizations of $N_f=2$ QCD.