A study of the charged-particle density (number density) in the transverse region of the dihadron correlations exploiting the existing pp and $\mathrm{p}\overline{\mathrm{p}}$ data from RHIC to LHC energies is reported. This region has contributions from the underlying event (UE) as well as from initial- and final-state radiation (ISR-FSR). Based on the data, a two-component model is built. This has the functional form $\propto s^{\alpha }+\beta \log (s)$, where the logarithmic ($\beta =0.140\pm 0.007$) and the power-law ($\alpha =0.270\pm 0.005$) terms describe the components more sensitive to the ISR-FSR and UE contributions, respectively. The model describes the data from RHIC to LHC energies; the extrapolation to higher energies indicates that at around $\sqrt{s}\approx 100\mathrm{TeV}$ the number density associated to UE will match that from ISR-FSR. Although this behavior is not predicted by pythia 8.244, the power-law behavior of the UE contribution is consistent with the energy dependence of the parameter that regulates multiparton interactions. Using simulations, KNO-like scaling properties of the multiplicity distributions in the regions sensitive to either UE or ISR-FSR are also discussed. The results presented here can be helpful to constrain QCD-inspired Monte Carlo models at the future circular collider energies, as well as to characterize the UE-based event classifiers which are currently used at the LHC.

中文翻译：

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从 RHIC 到 LHC 能量的潜在事件可观测值的能量依赖性

利用现有的 pp 和 $\mathrm{磷}\overline{\mathrm{磷}}$报告了从 RHIC 到 LHC 能量的数据。该区域有潜在事件 (UE) 以及初始和最终状态辐射 (ISR-FSR) 的贡献。基于这些数据，建立了一个二元模型。这有函数形式$\propto {秒}^{\alpha }+\beta \mathrm{日志}(秒)$, 其中对数 ($\beta =0.140\pm 0.007$) 和幂律 ($\alpha =0.270\pm 0.005$) 术语分别描述了对 ISR-FSR 和 UE 贡献更敏感的组件。该模型描述了从 RHIC 到 LHC 能量的数据；对更高能量的外推表明，在大约$\sqrt{秒}\approx 100\mathrm{伏特}$与 UE 关联的数密度将与来自 ISR-FSR 的数密度匹配。尽管pythia 8.244没有预测这种行为，但 UE 贡献的幂律行为与调节多部分交互的参数的能量依赖性一致。使用模拟，还讨论了对 UE 或 ISR-FSR 敏感的区域中多重分布的类似 KNO 的缩放特性。此处提供的结果有助于在未来的圆形对撞机能量下约束受 QCD 启发的蒙特卡罗模型，以及表征当前在 LHC 中使用的基于 UE 的事件分类器。