Casimir scaling of SU(3) static potentials

TL;DR

This study computes static potentials in SU(3) gauge theory across multiple representations, confirming Casimir scaling with high precision and excluding significant violations up to 1 fm separation.

Contribution

It provides the first non-perturbative lattice verification of Casimir scaling in SU(3) static potentials with high accuracy.

Findings

Casimir scaling holds within 5% up to 1 fm

Non-perturbative anisotropic lattice simulations used

Potential violations of Casimir scaling are minimal

Abstract

Potentials between static colour sources in eight different representations are computed in four dimensional SU(3) gauge theory. The simulations have been performed with the Wilson action on anisotropic lattices where the renormalised anisotropies have been determined non-perturbatively. After an extrapolation to the continuum limit we are able to exclude any violations of the Casimir scaling hypothesis that exceed 5% for source separations of up to 1 fm.