QCD static force in gradient flow

TL;DR

This paper reviews a next-to-leading order study of the QCD static force using gradient flow, highlighting potential improvements in convergence for lattice QCD calculations and exploring properties across flow times.

Contribution

It introduces a next-to-leading order analysis of the QCD static force with gradient flow, addressing convergence issues in lattice computations.

Findings

Gradient flow improves convergence of static force calculations.

Static force free from $O( ext{Lambda}_{ ext{QCD}})$ renormalon.

Properties of static force analyzed for various flow times.

Abstract

We review our recent study on the QCD static force using gradient flow at next-to-leading order in the strong coupling. The QCD static force has the advantage of being free of the $O(\Lambda_{\text{QCD}})$ renormalon appearing in the static potential but suffers from poor convergence in the lattice QCD computations. It is expected that the gradient flow formalism can improve the convergence. Based on our next-to-leading-order calculations, we explore the properties of the static force for arbitrary flow time $t$, as well as in the limit $t\rightarrow 0$, which may be useful for lattice QCD simulations.