论文标题
在伯特 - 钙板方程框架中估算梅森质量的扰动方法超出其主要相互作用
Perturbative method to estimate meson masses in the framework of Bethe-Salpeter equation beyond its dominant interaction
论文作者
论文摘要
我们提出了一种新的方法，以计算戴森·辛金格方程和伯特 - 盐方程的框架中的介子质量，一旦确定了它们的主要相互作用。该方法基于基质的扰动理论，该理论广泛用于量子力学。将其他相互作用以外的相互作用作为扰动，我们得出了夸克传播器的一阶校正。然后，对BSE实施扰动，然后给出一阶的质量校正。我们用众所周知的彩虹式截断（RL）截断来体现这种方法，并使用简单模型（即Munczek-Nemirovsky〜（MN）模型）超越RL，通过研究Pion和$ρ$ Mesons质量转移。结果与通过将BSE超出RL的BSE完全求解而获得的结果非常吻合。因此，我们的扰动方法可用于在BSES复杂化的情况下对超出主导者的相互作用变得复杂的情况进行半定量估计。
We propose a novel method to calculate the meson mass in the framework of Dyson-Schwinger equation and Bethe-Salpeter equation, once their dominant interactions are identified. The method is based on the perturbation theory of matrix, which is widely used in quantum mechanics. Taking interactions other than the dominant ones as perturbations, we derive the first order correction of quark propagator. Implementing the perturbation on BSE, the mass correction at first order is then given. We exemplify this method with the well known Rainbow-Ladder (RL) truncation, and go beyond the RL using a simple model, i.e., the Munczek-Nemirovsky~(MN) model, by studying the pion and $ρ$ mesons mass shift. The results are all in good agreement with those obtained by fully solving the BSE beyond RL. Our perturbative method therefore can be used to give a semi-quantitative estimate of meson mass correction in cases when the BSEs are complicated by interactions that go beyond the dominant one.
