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arXiv 1110.2633hep-phhep-lathep-th
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QCD中的无质量束缚态激发和Schwinger机制

Massless bound-state excitations and the Schwinger mechanism in QCD

A. C. Aguilar, D. Ibáñez, V. Mathieu, J. Papavassiliou

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37 pages, 20 figures
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摘要：

一个有效胶子质量的规范不变生成过程是通过著名的施温格机制进行的，其关键动力学成分是纵向耦合无质量束缚态激发的非微扰形成。这些激发在理论的顶点引入了极点，以这样一种方式，在存在大质量胶子传播子的情况下保持斯拉夫诺夫-泰勒恒等式的完整性。在目前的工作中，我们首先集中在非微扰的三胶子顶点的修改所引起的包括无质量的两胶子束缚态的内核出现在其胶子展开。然后从Slavnov-Taylor恒等式和控制胶子传播子的Schwinger-Dyson方程得到了这些束缚态的基本组成块与胶子质量之间的某些一般关系。在一定的简化假设下，导出了确定上述束缚态波函数的齐次Bethe-Salpeter方程。然后，通过详细的分析和数值研究表明，这个方程承认非平凡的解决方案，表明QCD动力学确实支持这种无质量的束缚态的形成。这些解决方案，随后使用，结合上述关系，以确定动力学胶子质量的动量依赖性。最后，进一步的可能性和开放的问题进行了简要讨论。

英文摘要：

The gauge invariant generation of an effective gluon mass proceeds through the well-known Schwinger mechanism, whose key dynamical ingredient is the nonperturbative formation of longitudinally coupled massless bound-state excitations. These excitations introduce poles in the vertices of the theory, in such a way as to maintain the Slavnov-Taylor identities intact in the presence of massive gluon propagators. In the present work we first focus on the modifications induced to the nonperturbative three-gluon vertex by the inclusion of massless two-gluon bound-states into the kernels appearing in its skeleton-expansion. Certain general relations between the basic building blocks of these bound-states and the gluon mass are then obtained from the Slavnov-Taylor identities and the Schwinger-Dyson equation governing the gluon propagator. The homogeneous Bethe-Salpeter equation determining the wave-function of the aforementioned bound state is then derived, under certain simplifying assumptions. It is then shown, through a detailed analytical and numerical study, that this equation admits non-trivial solutions, indicating that the QCD dynamics support indeed the formation of such massless bound states. These solutions are subsequently used, in conjunction with the aforementioned relations, to determine the momentum-dependence of the dynamical gluon mass. Finally, further possibilities and open questions are briefly discussed.

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