We calculate for the first time the scattering cross section between lightest glueballs in $SU(2)$ pure Yang-Mills theory, which are good candidates of dark matter. In the first step, we evaluate the interglueball potential on lattice using the HAL QCD method, with several lattice spacings ($\beta = 2.1, 2.2, 2.3, 2.4$, and 2.5). The systematics associated with nonzero angular momentum effect is removed by subtracting the centrifugal force. The statistical accuracy is improved by employing the cluster-decomposition error reduction technique and by using all space-time symmetries. We then determine the low energy glueball effective Lagrangian and the scattering cross section at low energy, which is compared with the observational constraint on the dark matter self-scattering. We derive the lower bound on the scale parameter of the $SU(2)$ Yang-Mills theory, as $\Lambda>60$ MeV.

中文翻译：

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暗杨米尔斯理论中的暗物质散射截面和动力学

我们首次计算了 $SU(2)$ 纯杨-米尔斯理论中最轻胶球之间的散射截面，这是暗物质的良好候选者。在第一步中，我们使用 HAL QCD 方法评估晶格上的 interglueball 潜力，具有多个晶格间距（$\beta = 2.1、2.2、2.3、2.4$ 和 2.5）。通过减去离心力，消除了与非零角动量效应相关的系统性。通过采用聚类分解误差减少技术并使用所有时空对称性，可以提高统计精度。然后我们确定低能胶球有效拉格朗日函数和低能散射截面，与暗物质自散射的观测约束进行比较。