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Rainbow modified-ladder approximation and degenerate pion

机译：彩虹修改梯近似和退化磁场

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摘要

Correlation functions can be described by the corresponding equations, viz., the gap equation for the quark propagator and the inhomogeneous Bethe-Salpeter equation for the vector dressed-fermion-Abelian-gauge-boson vertex in which specific truncations have to be implemented. The general vector and axial-vector Ward-Green-Takahashi identities require these correlation functions to be interconnected; in consequence of this, truncations made must be controlled consistently. It turns out that, if the rainbow approximation is assumed in the gap equation, the scattering kernel in the Bethe-Salpeter equation can adopt the ladder approximation, which is one of the most basic attempts to truncate the scattering kernel. Additionally, a modified-ladder approximation is also found to be a possible symmetry-preserving truncation scheme. As an illustration of this approximation for application, a treatment of the pion is included. The pion mass and decay constant are found to be degenerate in ladder and modified-ladder approximations, even though the Bethe-Salpeter amplitudes are with apparent distinction. The justification for the modified-ladder approximation is examined with the help of the Gell-Mann-Oakes-Renner relation.
机译：相关函数可以由相应的等式，VIZ描述，夸克传播者的间隙方程和用于载体衣服 - 费米偏军 - 千钟 - 型 - 玻色子顶点的空隙传播器的间隙方程，其中必须实现特定截短的特定截短。一般的向量和轴向 - 载体病房 - 绿色高塔哈里特征需要互连这些相关函数;因此，必须一致地控制所做的截断。事实证明，如果在间隙方程中假设彩虹近似，则Bethe - Salpeter方程中的散射内核可以采用梯形图近似，这是截断散射内核的最基本尝试之一。另外，还发现修改梯形梯度是一种可能的对称保护截断方案。作为施加该近似的图示，包括π孔的处理。距离梯子和衰减恒定的磁场和衰减常数也在梯形和改进梯形梯度下变质，即使贝特 - Salpeter幅度具有表观区别。在Gell-Mann-Oakes-Renner关系的帮助下，检查了修改梯形近似的理由。

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