Abstract
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 $A_{0}$. Due to 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 over-complete 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 non-trivial 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 non-zero 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, 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 ${\cal M}_D$ and the temperature dependence of the ratio ${\cal M}_D/T$ shows a very similar behavior as that found in lattice simulations.
Highlights
At high temperatures, the properties of the quark-gluon plasma (QGP) created during ultrarelativistic heavy-ion collisions can be computed in the hard-thermal-loop (HTL) resummed perturbation theory
The challenge appears in the intermediate region, termed as “semi-QGP,” where neither of the above-mentioned theoretical tools is reliable since the effects of nonperturbative physics play an important role
Based on the above analysis, the following conclusion can be drawn for general SUðNÞ, that is, introducing a small but nonzero background field merely amounts to modifications on the perturbative Debye mass mD and the corresponding HQ potential is always deeper than the perturbative screened potential characterized by mD, which suggests a weaker screening and, a more tightly bounded quarkonium state in a holonomous plasma
Summary
The properties of the quark-gluon plasma (QGP) created during ultrarelativistic heavy-ion collisions can be computed in the hard-thermal-loop (HTL) resummed perturbation theory. In order to drive the transition to confinement, nonperturbative terms, which generate complete eigenvalue repulsion in the confining phase, have to be included Constructed in such a way, matrix models have been widely studied in recent years, for pure gauge theories, and for quantum chromodynamics (QCD) with dynamical quarks [9,10,11,12,13]. In a holonomous plasma, the explicit form of the resummed gluon propagator with Ac0l ≠ 0 adopted in the foresaid works relies on certain approximations; for example, one needs to assume an infinitely large number of the colors or neglect an anomalous term ∼T3 in the perturbative gluon self-energy that appears only with nonvanishing holonomy. Some details about the calculations performed in this work are provided in three appendixes
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