Casimir scaling of SU(3) static potentials

TL;DR

This paper non-perturbatively tests Casimir scaling of static SU(3) potentials by computing V_D(r) for eight representations on anisotropic lattices with a non-perturbatively determined renormalised anisotropy. Using smeared Wilson loops and continuum extrapolation, it demonstrates that after subtracting short-distance self-energies, the ratios V_D(r)/V_F(r) closely follow the Casimir factors d_D = C_D/C_F for r up to about 1 fm, with violations below 5%. The work carefully quantifies anisotropy, lattice spacing effects, and finite-size checks, and it discusses the implications for confinement models, ruling out several scenarios and highlighting the string-breaking regime at larger distances as a separate phenomenon. Overall, the results provide strong non-perturbative support for Casimir scaling in static SU(3) potentials within the explored distance range and set constraints on competing confinement mechanisms.

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.

Figures (10)

• Figure 1: Ground state overlaps for the case of the fundamental potential determined from Wilson loops in three different orientations at $\beta=6.2$, $\xi_0=3.25$.
• Figure 2: The three potentials $V_{\tau\sigma}$, $V_{\sigma\sigma}$ and $V_{\sigma\tau}$ in units of $a_{\sigma}$ at $\beta=6.2$, $\xi_0=3.25$.
• Figure 3: Differences between $\hat{V}_{\sigma\sigma}$ and $\xi\hat{V}_{\sigma\tau}$.
• Figure 4: The potentials for all measured representations, obtained at $\beta=6.2$. Note that we did not subtract any self energy pieces but just rescaled the raw lattice data in units of $r_0$.
• Figure 5: The potentials normalised to the fundamental potential at $\beta=5.8$, in comparison to the expectations from Casimir scaling (horizontal lines).