标题： 统一算法在超相对论核碰撞中方位角和横动量的多粒子关联 显示英文标题

标题： A unified algorithm for multi-particle correlations between azimuthal angle and transverse momentum in ultra-relativistic nuclear collisions

摘要： 多粒子在方位角和平均横动量之间的关联是探测重离子碰撞初始状态下大小和形状关联的强大工具。这些关联也被用于研究核结构，包括在能量前沿潜在的核形状相变。然而，它们的实现非常复杂，先前的研究大多局限于低阶关联，例如修正的皮尔逊相关系数，$\rho(v_{\rm n}^{2}, [p_{\rm T}])$。本文提出了一种统一框架，采用递归算法，能够在保持计算效率的同时有效地评估任意阶关联。该框架使用了广泛采用的输运模型进行演示，包括AMPT和HIJING。提出的用于方位角和横动量之间多粒子关联的统一算法提供了一种系统且高效的方法来进行多粒子关联分析。其在相对论重离子对撞机和大型强子对撞机实验中的应用促进了在超高能下的核结构探索。 显示英文摘要

摘要： Multi-particle correlations between azimuthal angle and mean transverse momentum are a powerful tool for probing size and shape correlations in the initial conditions of heavy-ion collisions. These correlations have also been employed to investigate nuclear structure, including potential nuclear shape phase transitions at the energy frontier. However, their implementation is highly nontrivial, and prior studies have been mostly limited to lower-order correlations, such as the modified Pearson correlation coefficient, $\rho(v_{\rm n}^{2}, [p_{\rm T}])$. This paper presents a unified framework that employs a recursive algorithm, enabling the efficient evaluation of arbitrary-order correlations while maintaining computational efficiency. This framework is demonstrated using widely adopted transport models, including AMPT and HIJING. The proposed unified algorithm for multi-particle correlations between azimuthal angle and transverse momentum provides a systematic and efficient approach for multi-particle correlation analyses. Its application in experiments at the Relativistic Heavy Ion Collider and the Large Hadron Collider facilitates the exploration of nuclear structure at ultra-relativistic energies.