Simple chromatic properties of gradient flow

TL;DR

This paper investigates how the gradient flow parameter $t_0$ behaves across different numbers of colors and fermion configurations, revealing linear scaling and large $N_c$ consistency in lattice simulations.

Contribution

It demonstrates the linear scaling of the flow parameter $t_0$ with the number of colors and its behavior in dynamical fermion simulations, providing insights for lattice QCD.

Findings

The fiducial point for the flow parameter must scale nearly linearly with $N_c$.

Dependence of $t_0$ on pseudoscalar meson mass flattens as $N_c$ increases.

Results are consistent with large $N_c$ theoretical expectations.

Abstract

It has become customary to use a smoothing algorithm called "gradient flow" to fix the lattice spacing in a simulation, through a parameter called $t_0$. It is shown that in order to keep the length $t_0$ fixed with respect to mesonic or gluonic observables as the number of colors $N_c$ is varied, the fiducial point for the flow parameter must be scaled nearly linearly in $N_c$. In simulations with dynamical fermions, the dependence of $t_0$ on the pseudoscalar meson mass flattens as the number of colors rises, in a way which is consistent with large $N_c$ expectations.