Implications of gradient flow on the static force

TL;DR

This paper explores how gradient flow techniques can be used to compute the static force in lattice gauge theory, enabling comparisons with perturbative calculations and potentially advancing the study of field correlators in effective theories.

Contribution

It introduces a method to compute the static force using gradient flow and Wilson loops, facilitating precise extraction of the b3b1_0 parameter and opening avenues for future correlator calculations.

Findings

Gradient flow provides a new way to compute the static force.

Comparison with perturbative calculations allows precise parameter extraction.

Potential for extending to correlators of chromoelectric and chromomagnetic fields.

Abstract

We use gradient flow to compute the static force based on a Wilson loop with a chromoelectric field insertion. The result can be compared on one hand to the static force from the numerical derivative of the lattice static energy, and on the other hand to the perturbative calculation, allowing a precise extraction of the $\Lambda_0$ parameter. This study may open the way to gradient flow calculations of correlators of chromoelectric and chromomagnetic fields, which typically arise in the nonrelativistic effective field theory factorization.