Gradient Flow Analysis on MILC HISQ Ensembles

TL;DR

This paper presents a preliminary determination of lattice scales using gradient-flow techniques on MILC HISQ ensembles, involving multiple lattice spacings and quark mass values, with continuum and physical mass extrapolations.

Contribution

The study introduces a combined continuum chiral perturbation theory and Taylor series approach for scale setting on MILC HISQ ensembles, including mistuning corrections and preliminary results for scale parameters.

Findings

Preliminary scale determinations: √t0 = 0.1422(7) fm, w0 = 0.1732(10) fm

Continuum extrapolation of scale parameters and meson masses

Analysis of the mass dependence of w0 in the continuum

Abstract

We report on a preliminary scale determination with gradient-flow techniques on the $N_f = 2 + 1 + 1$ HISQ ensembles generated by the MILC collaboration. The ensembles include four lattice spacings, ranging from 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales $\sqrt{t_0}/a$ and $w_0/a$ are computed using Symanzik flow and the cloverleaf definition of $\langle E \rangle$ on each ensemble. Then both scales and the meson masses $aM_\pi$ and $aM_K$ are adjusted for mistunings in the charm mass. Using a combination of continuum chiral perturbation theory and a Taylor series ansatz in the lattice spacing, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. Our preliminary results are $\sqrt{t_0} = 0.1422(7)$fm and $w_0 = 0.1732(10)$fm. We also find the continuum mass-dependence of $w_0$.