On the definition and interpretation of a static quark-antiquark potential in the color-adjoint channel

Abstract

We study possibilities to define a static quark-antiquark pair in a color-adjoint orientation based on Wilson loops with generator insertions, using both lattice QCD and leading-order perturbation theory in various gauges. Nonperturbatively, the only way to obtain nonzero results while maintaining positivity of the Hamiltonian is by using either temporal gauge or Coulomb gauge with some additional constraint on the temporal links removing the residual gauge symmetry. In this case the correlator is equivalent to a gauge invariant correlation function of a static quark-antiquark pair and a static adjoint quark; the resulting three-point potential is attractive. Saturating open color indices with color magnetic fields instead also leads to a gauge invariant correlator. However, this object is found to couple to the singlet sector only and results in a hybrid potential. None of the considered lattice observables reproduces the repulsive adjoint potential predicted by perturbation theory in Lorenz or Coulomb gauges.