Resummed gluon propagator and Debye screening effect in a holonomous plasma

Based on the Dyson-Schwinger equation, we compute the resummed gluon propagator in a holonomous plasma that is described by introducing a constant background field for the vector potential A(0). Because of the transversality of the holonomous hard thermal loop in gluon self-energy, the resummed propagator has a similar Lorentz structure as that in the perturbative quark-gluon plasma where the holonomy vanishes. As for the color structures, since diagonal gluons are mixed in the overcomplete double-line basis, only the propagators for off-diagonal gluons can be obtained unambiguously. On the other hand, multiplied by a projection operator, the propagators for diagonal gluons, which exhibit a highly nontrivial dependence on the background field, are uniquely determined after summing over the color indices. As an application of these results, we consider the Debye screening effect on the in-medium binding of quarkonium states by analyzing the static limit of the resummed gluon propagator. In general, introducing nonzero holonomy merely amounts to modifications on the perturbative screening mass m(D) and the resulting heavy-quark potential, which remains the standard Debye screened form, is always deeper than the screened potential in the perturbative quark-gluon plasma. Therefore, a weaker screening and, thus, a more tightly bounded quarkonium state can be expected in a holonomous plasma. In addition, both the diagonal and off-diagonal gluons become distinguishable by their modified screening masses M-D, and the temperature dependence of the ratio M-D/T shows a very similar behavior as that found in lattice simulations.