Setting the scale for the CLS $2 + 1$ flavor ensembles

TL;DR

This paper determines the scale of CLS $2+1$ flavor lattice ensembles by measuring decay constants and the gradient flow scale $t_0$, correcting for quark mass mistunings to improve accuracy.

Contribution

It introduces a method to set the lattice scale for CLS $2+1$ flavor ensembles using decay constants and gradient flow, with corrections for quark mass mistunings.

Findings

Measured decay constants and $t_0$ scale for CLS ensembles.

Corrected for quark mass mistunings to improve scale setting.

Provided a precise scale calibration for $2+1$ flavor lattices.

Abstract

We present measurements of a combination of the decay constants of the light pseudoscalar mesons and the gradient flow scale $t_0$, which allow to set the scale of the lattices generated by CLS with $2 + 1$ flavors of non-perturbatively improved Wilson fermions. Mistunings of the quark masses are corrected for by measuring the derivatives of observables with respect to the bare quark masses.