Over the last years, machine learning (ML) methods have been successfully applied to a wealth of problems in high-energy physics. For instance, in a previous work we have reported that using ML techniques one can extract the multiparton interactions (MPI) activity from minimum-bias pp data. Using the available large hadron collider data on transverse momentum spectra as a function of multiplicity, we reported the average number of MPI (⟨N _mpi⟩) for minimum-bias pp collisions at and 13 TeV. In this work, we apply the same analysis to a new set of data. We report that ⟨N _mpi⟩ amounts to 3.98 1.01 for minimum-bias pp collisions at TeV. These complementary results suggest a modest center-of-mass energy dependence of ⟨N _mpi⟩. The study is further extended aimed at extracting the multiplicity dependence of ⟨N _mpi⟩ for the three center-of-mass energies. We show that our results qualitatively agree with existing ALICE measurements sensitive to MPI. Namely, ⟨N _mpi⟩ increases approximately linearly with the charged-particle multiplicity. But, it deviates from the linear dependence at large charged-particle multiplicities. The deviation from the linear trend can be explained in terms of a bias towards harder processes given the multiplicity selection at mid-pseudorapidity. The results reported in this paper provide additional evidence of the presence of MPI in pp collisions, and they can be useful for a better understanding of the heavy-ion-like behavior observed in pp data.

在过去的几年中，机器学习 (ML) 方法已成功应用于高能物理学中的大量问题。例如，在之前的一项工作中，我们报告说使用 ML 技术可以从最小偏差 pp 数据中提取多部分交互 (MPI) 活动。使用横向动量谱上可用的大型强子对撞机数据作为多重性的函数，我们报告了在13 TeV 和 13 TeV 时最小偏置 pp 碰撞的平均 MPI (⟨ N _mpi ⟩) 数。在这项工作中，我们将相同的分析应用于一组新数据。我们报告说，对于TeV 的最小偏差 pp 碰撞，⟨ N _mpi ⟩ 等于 3.98 1.01 。这些互补的结果表明 ⟨ N的质心能量依赖性适中 _mpi ⟩. 该研究进一步扩展，旨在提取 ⟨ N _mpi ⟩ 对三个质心能量的多重依赖性。我们表明，我们的结果定性地与现有的对 MPI 敏感的 ALICE 测量一致。即， ⟨ N _mpi⟩ 随带电粒子的多重性近似线性增加。但是，它偏离了大量带电粒子的线性相关性。与线性趋势的偏差可以解释为偏向于更难的过程，因为在中等伪随机性时选择了多重性。本文报告的结果为 pp 碰撞中存在 MPI 提供了额外的证据，它们可用于更好地理解 pp 数据中观察到的类重离子行为。