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arXiv 1601.05441nucl-thhep-ph
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带隙和Bethe-Salpeter方程的保持对称截断

Symmetry preserving truncations of the gap and Bethe-Salpeter equations

Daniele Binosi, Lei Chang, Joannis Papavassiliou, Si-Xue Qin, Craig D. Roberts

备注：
6 pages, 8 figures
发表信息：
Phys. Rev. D 93, 096010 (2016)
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摘要：

Ward-Green-Takahashi（WGT）恒等式在强子物理学中起着至关重要的作用，例如在一体和二体问题的核之间施加严格的关系，这些关系必须在任何将介子作为束缚态的准确处理中保持。在这一点上，我们可以把修饰胶子-夸克顶点$Γ_μ^a$看作是基本的。我们使用一种新的表示$Γ_μ^a$，在胶子-夸克散射矩阵，开发一种方法能够阐明独特的夸克-反夸克Bethe-Salpeter内核，$K$，这是一个给定的夸克间隙方程的相容性。该方案的一个优点是它能够暴露和利用内核中的图形对称性。这一点在一项分析中得到了展示，该分析揭示了$K$中$H$-图的起源，$H$-图是两粒子不可约的贡献，生成为涉及三胶子顶点的双环图，不能被吸收为$Γ_μ^a$在贝特-萨尔皮特核中的修饰，也不能被表示为交叉盒图类的成员。因此，在一般情况下，通过简单地将胶子-夸克的两个顶点都用梯形截断来得到贝特-萨尔彼得核，就不能保持有效描述介子所必需的WGT恒等式;而且，添加任何数量的类似修饰的交叉盒图都不能改善这种情况。

英文摘要：

Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one- and two-body problems, which must be preserved in any veracious treatment of mesons as bound-states. In this connection, one may view the dressed gluon-quark vertex, $Γ_μ^a$, as fundamental. We use a novel representation of $Γ_μ^a$, in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quark-antiquark Bethe-Salpeter kernel, $K$, that is symmetry-consistent with a given quark gap equation. A strength of the scheme is its ability to expose and capitalise on graphic symmetries within the kernels. This is displayed in an analysis that reveals the origin of $H$-diagrams in $K$, which are two-particle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of $Γ_μ^a$ in a Bethe-Salpeter kernel nor expressed as a member of the class of crossed-box diagrams. Thus, there are no general circumstances under which the WGT identities essential for a valid description of mesons can be preserved by a Bethe-Salpeter kernel obtained simply by dressing both gluon-quark vertices in a ladder-like truncation; and, moreover, adding any number of similarly-dressed crossed-box diagrams cannot improve the situation.

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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