We suggest a framework based on the rainbow approximation to the Dyson-Schwinger and Bethe-Salpeter equations with effective parameters adjusted to lattice QCD data to calculate the masses of the ground and excited states of pseudo-scalar glueballs. The structure of the truncated Bethe-Salpeter equation with the gluon and ghost propagators as solutions of the truncated Dyson-Schwinger equations is analysed in Landau gauge. Both, the Bete-Salpeter and Dyson-Schwinger equations, are solved numerically within the same rainbow-ladder truncation with the same effective parameters which ensure consistency of the approach. We found that with a set of parameters, which provides a good description of the lattice data within the Dyson-Schwinger approach, the solutions of the Bethe Salpeter equation for the pseudo-scalar glueballs exhibit a rich mass spectrum which also includes the ground and excited states predicted by lattice calculations. The obtained mass spectrum contains also several intermediate excitations beyond the lattice approaches. The partial Bethe-Salpeter amplitudes of the pseudo-scalar glueballs are presented as well.

中文翻译：

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具有彩虹梯形截断的 Bethe-Salpeter 方法的伪标量胶球的质谱

我们提出了一个基于 Dyson-Schwinger 和 Bethe-Salpeter 方程的彩虹近似的框架，其中有效参数调整到晶格 QCD 数据，以计算伪标量胶球的基态和激发态的质量。在朗道规范中分析了截断 Bethe-Salpeter 方程的结构，其中胶子和鬼传播子作为截断 Dyson-Schwinger 方程的解。Bete-Salpeter 和 Dyson-Schwinger 方程都在相同的彩虹梯形截断中以相同的有效参数进行数值求解，以确保方法的一致性。我们发现，通过一组参数，可以很好地描述 Dyson-Schwinger 方法中的晶格数据，伪标量胶球的 Bethe Salpeter 方程的解表现出丰富的质谱，其中还包括通过晶格计算预测的基态和激发态。获得的质谱还包含几个超出晶格方法的中间激发。还给出了伪标量胶球的部分 Bethe-Salpeter 振幅。