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arXiv 1012.5372nucl-thhep-phnucl-ex
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介子$q\bar q$束缚态的Schwinger-Dyson和Bethe-Salpeter方程的联合解

A Combined Solution of the Schwinger-Dyson and Bethe-Salpeter Equations for Mesons as $q\bar q$ Bound States

S. M. Dorkin, T. Hilger, B. Kaempfer, L. P. Kaptari

摘要:

重赝标介子的质量谱被描述为夸克-反夸克束缚系统,被认为是在Bethe-Salpeter形式主义与动量依赖的质量的成分。这种依赖性是通过在彩虹梯近似下求解夸克传播子的Schwinger-Dyson方程得到的。这样的近似是已知的,以提供一个快速收敛的数值方法和最轻的介子的准确结果。然而,随着介子质量的增加,该方法变得不太稳定,必须特别注意解决相应方程的数值方法的细节。我们专注于赝标部门,并表明我们的数值方案相当准确地描述了$π$,$K$,$D$,$D_s$和$η_c$基态。也考虑了激发态。我们的计算与FAIR未来的物理计划直接相关。

英文摘要:

The mass spectrum of heavy pseudoscalar mesons, described as quark-antiquark bound systems, is considered within the Bethe-Salpeter formalism with momentum dependent masses of the constituents. This dependence is found by solving the Schwinger-Dyson equation for quark propagators in rainbow-ladder approximation. Such an approximation is known to provide both a fast convergence of numerical methods and accurate results for lightest mesons. However, as the meson mass increases, the method becomes less stable and special attention must be devoted to details of numerical means of solving the corresponding equations. We focus on the pseudoscalar sector and show that our numerical scheme describes fairly accurately the $π$, $K$, $D$, $D_s$ and $η_c$ ground states. Excited states are considered as well. Our calculations are directly related to the future physics programme at FAIR.

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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