AI 中文总结
研究复单态扩展标准模型中暗物质湮灭热平均截面的次领头阶 QCD 和电弱修正，推导修正遗迹密度，讨论影响与不确定性，通过改变重整化方案估计，结果有现象学影响，已在新代码实现，迈出相关计算第一步。
AI 中文摘要
在本文中，我们给出了在具有一个暗物质候选者的复单态扩展标准模型（CxSM）框架下，对暗物质湮灭热平均截面的次领头阶（NLO）QCD 和电弱修正的计算。我们推导了相应的 NLO QCD 和电弱修正的遗迹密度，并讨论了修正的影响以及由于缺失高阶修正而剩余的理论不确定性。这是通过对单态真空期望值 $v_S$ 和希格斯混合角 $\alpha$ 的重整化方案的变化来估计的。对于大部分扫描的参数点，发现 QCD 和电弱修正具有典型大小，剩余理论不确定性在百分之几的水平。发现的较大修正可归因于在用于重整化的衰变通道中出现大质量间隙时 $v_S$ 的大抵消项。这些修正具有现象学影响。存在一些在领头阶（LO）允许但在包含遗迹密度的 NLO 修正后被排除的参数点，反之亦然。我们的修正已在基于 LO 代码 RelExt 的新代码 RelExt@NLO 中实现，该代码已公开可用。这项工作标志着朝着计算由离散 $\mathbb{Z}_2$ 对称性稳定的暗物质候选者模型中的 QCD 和电弱修正遗迹密度迈出了第一步。
英文摘要
In this work, we present the calculation of the next-to-leading order (NLO) QCD and electroweak corrections to the thermally averaged cross section of Dark Matter (DM) annihilation in the framework of the complex singlet extended Standard Model (CxSM) with one DM candidate. We derive the corresponding NLO QCD and electroweak corrected relic density and discuss the impact of the corrections as well as the remaining theoretical uncertainty due to missing higher-order corrections. This is estimated through a variation of the renormalization schemes for the singlet vacuum expectation value $v_S$ and the Higgs mixing angle $α$. For the bulk of the scanned parameter points, the QCD and electroweak corrections are found to be of typical size with the remaining theoretical uncertainty ranging at the percent level. The larger corrections that are found, can be attributed to a large counterterm for $v_S$ emerging in the case of large mass gaps in the decay channel used for the renormalization. The corrections are of phenomenological impact. There are parameter points that are allowed at leading order (LO), but are excluded after including the NLO corrections to the relic density, and vice versa. Our corrections have been implemented in the new code RelExt@NLO based on the LO code RelExt, which has been made publicly available. This work marks a first step towards the calculation of the QCD and electroweak corrected relic densities in models with DM candidates stabilized by a discrete $\mathbb{Z}_2$ symmetry.
Comments26 pages, 7 figures
