HAL QCD方法在强子-强子相互作用中有效性的模型分析
Model analysis on the effectiveness of the HAL QCD method for hadron-hadron interactions
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中文总结 AI 辅助
本文通过推导公式，结合弹性散射简单模型及$\bar{K}N$散射分析，检验HAL QCD方法在强子-强子相互作用中的有效性，明确其定域势可定量再现散射相移并指示束缚态，还探讨了$\bar{K}N$势奇异行为的成因。
中文摘要 AI 辅助
HAL QCD方法是从格点QCD模拟数据中直接提取强子-强子相互作用的有力工具之一。本文旨在通过推导一个公式来检验HAL QCD方法的有效性，该公式可从有效模型内的强子-强子散射振幅计算HAL QCD方法中的物理量，如所谓的R关联子和HAL QCD定域势。在该框架下，我们可通过散射振幅判断按当前公式计算的HAL QCD定域势是否再现原始强子-强子相互作用的性质，其中散射振幅是以原始强子-强子相互作用为输入的利珀曼-施温格方程的解。在弹性散射的简单模型分析中，我们表明当原始相互作用主要是定域的时，HAL QCD定域能量势可定量再现强子-强子散射的相移，并正确指示束缚态的存在/不存在及其结合能约为MeV。时空的格点离散化仅对结果产生微小修正。此外，我们考虑了裸到$\bar{K}N$跃迁振幅中的$\bar{K}N$势，该势在最近格点QCD模拟数据的HAL QCD结果中表现出原点附近的奇异行为，并通过我们对$\bar{K}N$散射的模型分析讨论了HAL QCD方法中此类奇异行为的成因。
英文摘要
The HAL QCD method has been one of the powerful tools to extract hadron-hadron interactions directly from lattice QCD simulation data. In this paper, we aim at examining the effectiveness of the HAL QCD method by deriving a formula to calculate quantities in the HAL QCD method, such as the so-called R-correlators and HAL QCD local potentials, from the hadron-hadron scattering amplitudes within effective models. In this framework, we can judge whether the HAL QCD local potential, evaluated in the present formula, reproduces the properties of the original hadron-hadron interaction or not via the scattering amplitude, which is a solution of the Lippmann--Schwinger equation with the original hadron-hadron interaction as an input. In an analysis within a simple model of elastic scattering, we show that, when the original interaction is predominantly local, the HAL QCD local potentials quantitatively reproduce phase shifts of the hadron-hadron scatterings and correctly indicate the existence/absence of the bound state with its binding energy $\sim$ MeV. Lattice discretization of spacetime modifies the results only slightly. Furthermore, we consider the $\bar{K} N$ potential in a bare to $\bar{K} N$ transition amplitude, which shows singular behavior around the origin in the recent HAL QCD results of the lattice QCD simulation data, and discuss the cause of such singular behavior in the HAL QCD method through our model analysis of the $\bar{K} N$ scattering.
