完整等离子体中恢复的胶子散射和德拜屏蔽效应
Resummed Gluon Propagator and Debye Screening Effect in a Holonomous Plasma
摘要：
本文从Dyson-Schwinger方程出发，通过在矢量势$A_{0}$中引入一个恒定的背景场来描述完整等离子体，计算了完整等离子体中的非线性胶子传播子。由于胶子自能中完整性硬热环的横截性，该传播子具有与完整性消失的微扰夸克-胶子等离子体中相似的洛伦兹结构。在色结构方面，由于对角胶子是在过完备双线基中混合的，因此只能得到非对角胶子的传播子。另一方面，乘以投影算子，对角胶子的传播子，表现出高度非平凡的依赖于背景场，是唯一确定的求和后的颜色指数。作为这些结果的一个应用，我们通过分析量子化胶子传播子的静态极限，考虑了德拜屏蔽效应对夸克偶素态介质内束缚的影响。一般来说，引入非零完整性仅仅相当于对微扰屏蔽质量$m_D$的修改，并且由此产生的重夸克势仍然是标准的德拜屏蔽形式，总是比微扰夸克-胶子等离子体中的屏蔽势更深。因此，较弱的屏蔽，从而更紧密的夸克偶素状态可以预期在一个完整的等离子体。此外，对角胶子和非对角胶子都可以通过它们的修正屏蔽质量${\cal M}_D$来区分，并且比率${\cal M}_D/T$的温度依赖性显示出与晶格模拟中发现的非常相似的行为。
英文摘要：
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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