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Register a new userResummed Gluon Propagator and Debye Screening Effect in a Holonomous Plasma
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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.
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Due to the rapid longitudinal expansion of the quark-gluon plasma created in heavy-ion collisions, large local-rest-frame momentum-space anisotropies are generated during the systems evolution. These momentum-space anisotropies complicate the modeling of heavy-quarkonium dynamics in the quark-gluon plasma due to the fact that the resulting inter-quark potentials are spatially anisotropic, requiring real-time solution of the 3D Schrodinger equation. Herein, we introduce a method for reducing anisotropic heavy-quark potentials to isotropic ones by introducing an effective screening mass that depends on the quantum numbers $l$ and $m$ of a given state. We demonstrate that, using the resulting effective Debye screening masses, one can solve a 1D Schrodinger equation and reproduce the full 3D results for the energies and binding energies of low-lying heavy-quarkonium bound states to relatively high accuracy. The resulting effective isotropic potential models could provide an efficient method for including momentum-anisotropy effects in open quantum system simulations of heavy-quarkonium dynamics in the quark-gluon plasma.
At a nonzero temperature T, a constant field $overline{A}_0 sim T/g$ generates nontrivial eigenvalues of the thermal Wilson line. We discuss contributions to the free energy of such a holonomous plasma when the coupling constant, $g$, is weak. We review the computation to $sim g^2$ by several alternate methods, and show that gauge invariant sources, which are nonlinear in the gauge potential $A_0$, generate novel contributions to the gluon self energy at $sim g^2$. These ensure the gluon self energy remains transverse to $sim g^2$, and are essential in computing contributions to the free energy at $sim g^3$ for small holonomy, $overline{A}_0 sim T$. We show that the contribution $sim g^3$ from off-diagonal gluons is discontinuous as the holonomy vanishes. The contribution from diagonal gluons is continuous as the holonomy vanishes, but sharply constrains the possible sources which generate nonzero holonomy, and must involve an infinite number of Polyakov loops.
We compute the gluon polarization tensor in a thermo-magnetic environment in the strong magnetic field limit at zero and high temperature. The magnetic field effects are introduced using Schwingers proper time method. Thermal effects are computed in the HTL approximation. At zero temperature, we reproduce the well-known result whereby for a non-vanishing quark mass, the polarization tensor reduces to the parallel structure and its coefficient develops an imaginary part corresponding to the threshold for quark-antiquark pair production. This coefficient is infrared finite and simplifies considerably when the quark mass vanishes. Keeping always the field strength as the largest energy scale, in the high temperature regime we analyze two complementary hierarchies of scales: $q^2ll m_f^2ll T^2$ and $m_f^2ll q^2ll T^2$. In the latter, we show that the polarization tensor is infrared finite as $m_f$ goes to zero. In the former, we discuss the thermal corrections to the magnetic Debye mass.
Quark-gluon plasma produced at the early stage of ultrarelativistic heavy ion collisions is unstable, if weakly coupled, due to the anisotropy of its momentum distribution. Chromomagnetic fields are spontaneously generated and can reach magnitudes much exceeding typical values of the fields in equilibrated plasma. We consider a high energy test parton traversing an unstable plasma that is populated with strong fields. We study the momentum broadening parameter $hat q$ which determines the radiative energy loss of the test parton. We develop a formalism which gives $hat q$ as the solution of an initial value problem, and we focus on extremely oblate plasmas which are physically relevant for relativistic heavy ion collisions. The parameter $hat q$ is found to be strongly dependent on time. For short times it is of the order of the equilibrium value, but at later times $hat q$ grows exponentially due to the interaction of the test parton with unstable modes and becomes much bigger than the value in equilibrium. The momentum broadening is also strongly directionally dependent and is largest when the test parton velocity is transverse to the beam axis. Consequences of our findings for the phenomenology of jet quenching in relativistic heavy ion collisions are briefly discussed.
In the deconfined regime of a non-Abelian gauge theory at nonzero temperature, previously it was argued that if a (gauge invariant) source is added to generate nonzero holonomy, that this source must be linear for small holonomy. The simplest example of this is the second Bernoulli polynomial. However, then there is a conundrum in computing the free energy to $sim g^3$ in the coupling constant $g$, as part of the free energy is discontinuous as the holonomy vanishes. In this paper we investigate two ways of generating the second Bernoulli polynomial dynamically: as a mass derivative of an auxiliary field, and from two dimensional ghosts embedded isotropically in four dimensions. Computing the holonomous hard thermal loop (HHTL) in the gluon self-energy, we find that the limit of small holonomy is only well behaved for two dimensional ghosts, with a free energy which to $sim g^3$ is continuous as the holonomy vanishes.
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