标题： $SU(2)$粒子的比较晶格分析 显示英文标题

标题： A comparative lattice analysis of $SU(2)$ dark gluebal

摘要： 我们使用格点模拟研究$SU(2)$胶球作为暗物质候选者的质量与散射截面。 我们同时采用朴素和改进的$SU(2)$规范作用量，在$3+1$维空间中使用多个$\beta$值，并采用传统的蒙特卡洛方法以及基于机器学习技术的流模型来生成格点构型。 计算了具有$J^{PC}=0^{++}$的暗标量胶球质量和NBS波函数。 以耦合常数$\beta=2.2$为例，我们比较了从两种方法生成的构型计算得到的暗胶球质量。 虽然可以得到一致的结果，但两种方法表现出不同的优势。 使用龙格-库塔方法，我们提取了胶球相互作用势和两体散射截面。 根据观测约束，我们得到了作为暗物质候选者的标量胶球质量的下限。 显示英文摘要

摘要： We study the mass and scattering cross section of $SU(2)$ glueballs as dark matter candidates using lattice simulations. We employ both naive and improved $SU(2)$ gauge actions in $3+1$ dimensions with several $\beta$ values, and adopt both the traditional Monte Carlo method and the flow-based model based on machine learning techniques to generate lattice configurations. The mass of dark scalar glueball with $J^{PC}=0^{++}$ and the NBS wave function are calculated. Using a coupling constant of $\beta=2.2$ as an illustration, we compare the dark glueball mass calculated from the configurations generated from the two methods. While consistent results can be achieved, the two methods demonstrate distinct advantages. Using the Runge-Kutta method, we extract the glueball interaction potential and two-body scattering cross section. From the observational constraints, we obtain the lower bound of the mass of scalar glueball as candidates of dark matter.