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arXiv 1807.10075nucl-th
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有限温度下赝标量{ \boldm $ q\bar q $ }束缚态的Dyson-Schwinger-Bethe-Salpeter方法

Pseudo-scalar {\boldm $ q\bar q $} bound states at finite temperatures within a Dyson-Schwinger--Bethe-Salpeter approach

S. M. Dorkin, L. P. Kaptari, B. Kämpfer

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39 pages, 6 figures
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摘要：

在非零温度下采用Dyson-Schwinger-Bethe-Salpeter方程。截断指的是一个彩虹阶梯近似增强的相互作用内核，这有利于一个特殊的温度依赖性。在低温下，$T \to 0$，我们从戴森-施温格（间隙）方程中恢复了夸克传播子，该方程提供了例如质量函数$B$、夸克重整化波函数$A$和双夸克凝聚$\la q \bar q \ra$，它们平滑地插值到$T = 0$结果，尽管在热浴中O（4）对称性破缺和离散松原频率。除了松原频率差进入相互作用内核，经常德拜屏蔽质量项时，扩展到非零温度的$T = 0$内核。然而，在更高的温度下，我们不得不在纵向相互作用核的红外部分降低德拜质量，以保持双夸克凝聚体的熔化在与晶格QCD结果一致的范围内。利用该夸克传播子的前几百个费米子松原频率，我们评估的Bethe-Salpeter顶点函数的赝标量$ q \bar q$通道的最低玻色子松原频率，并找到一个竞争的$ q \bar q$束缚态和准自由的两个夸克态在$T = {\cal O}$（100 MeV）。低于预期的QCD退禁闭温度的赝标介子离解的这一指示要求改进的方法，这是基于调整到$T = 0$的介子谱的相互作用。

英文摘要：

The combined Dyson-Schwinger--Bethe-Salpeter equations are employed at non-zero temperature. The truncations refer to a rainbow-ladder approximation augmented with an interaction kernel which facilitates a special temperature dependence. At low temperatures, $T \to 0$, we recover a quark propagator from the Dyson-Schwinger (gap) equation which delivers, e.g. mass functions $B$, quark renormalization wave function $A$, and two-quark condensate $\la q \bar q \ra$ smoothly interpolating to the $T = 0$ results, despite the broken O(4) symmetry in the heat bath and discrete Matsubara frequencies. Besides the Matsubara frequency difference entering the interaction kernel, often a Debye screening mass term is introduced when extending the $T = 0$ kernel to non-zero temperatures. At larger temperatures, however, we are forced to drop this Debye mass in the infra-red part of the longitudinal interaction kernel to keep the melting of the two-quark condensate in a range consistent with lattice QCD results. Utilizing that quark propagator for the first few hundred fermion Matsubara frequencies we evaluate the Bethe-Salpeter vertex function in the pseudo-scalar $ q \bar q$ channel for the lowest boson Matsubara frequencies and find a competition of $ q \bar q$ bound states and quasi-free two-quark states at $T = {\cal O}$ (100 MeV). This indication of pseudo-scalar meson dissociation below the anticipated QCD deconfinement temperature calls for an improvement of the approach, which is based on an interaction adjusted to the meson spectrum at $T = 0$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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