On the definition and interpretation of a static quark anti-quark potential in the colour-adjoint channel

Abstract

We study possibilities to define a static quark anti-quark pair in a colour-adjoint orientation based on Wilson loops with generator insertions, using both lattice QCD and leading order perturbation theory in various gauges. Non-perturbatively, the only way to obtain non-zero results while maintaining positivity of the Hamiltonian is by some form of temporal gauge. In this case the correlator is equivalent to a gauge invariant correlation function of a static quark anti-quark pair and a static adjoint quark, the resulting three-point potential is attractive. Saturating open colour indices with colour magnetic fields instead also leads to a gauge invariant correlator. However this object is found to couple to the singlet sector only. There appears to be no lattice observable that reproduces the repulsive adjoint potential predicted by perturbation theory in Lorenz or Coulomb gauges.

26 pages, 4 figures

References in corpus (7)

• Static quark-antiquark pairs at finite temperature
• Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks
• Determination of alpha_s from the QCD static energy
• The Polyakov Loop and its Relation to Static Quark Potentials and Free Energies
• The static-light meson spectrum from twisted mass lattice QCD
• Colour octet potential to three loops
• q \bar q-potential

Cited by in corpus (10)

• Heavy Quarkonium in Extreme Conditions
• Hybrid static potential flux tubes from SU(2) and SU(3) lattice gauge theory
• Measuring the Topological Susceptibility in a Fixed Sector
• Medium evolution of a static quark-antiquark pair in the large $N_c$ limit
• Interpreting Numerical Measurements in Fixed Topological Sectors
• Interaction potential between heavy $Q\bar{Q}$ in color octet configuration in QGP
• Lattice study of hybrid static potentials
• Structure of hybrid static potential flux tubes in SU(2) lattice Yang-Mills theory
• On the color structure of Yang-Mills theory with static sources in a periodic box
• $q\bar{q}$-potential: a critical reappraisal