Multiparticle cumulants of azimuthal angle correlations have been compelling tools to probe the properties of the quark-gluon plasma (QGP) created in the ultrarelativistic heavy-ion collisions and the search for the QGP in small collision systems at BNL's Relativistic Heavy Ion Collider (RHIC) and at CERN's Large Hadron Collider (LHC). However, only very few of them are available and have been studied in theoretical calculations and experimental measurements, while the rest are generally very interesting, but their direct implementation was not feasible. In this paper, we present a generic recursive algorithm for multiparticle cumulants, which enables the calculation of arbitrary order single and mixed harmonic multiparticle cumulants. Among them, the new 10-, 12-, 14-, and 16-particle cumulants of a single harmonic, named $c_n\left\{10\right\}, c_n\left\{12\right\}, c_n\left\{14\right\}$, and $c_n\left\{16\right\}$, and the corresponding $v_n$ coefficients, will be discussed for the first time. Our Monte Carlos studies show that these new multiparticle cumulants can be readily used along with updates to the generic framework of multiparticle correlations to a very high order. Finally, we propose a particular series of mixed harmonic multiparticle cumulants, which measures the general correlations between any moments of different flow coefficients. The predictions of these new observables are shown based on an initial-state model MC-Glauber, a toy Monte Carlo model, and the HIJING transport model for future comparisons between experimental data and theoretical model calculations. The study of these new multiparticle cumulants in heavy-ion collisions will significantly improve the understanding of the joint probability density function which involves both different harmonics of flow and also the symmetry planes. This will pave the way for more stringent constraints on the initial state and help to extract more precisely information on how the created hot and dense matter evolves. Meanwhile the efforts applied to small systems could be very helpful in the understanding of the origin of the observed collectivity at RHIC and the LHC.

中文翻译：

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高能核碰撞中方位相关多粒子累积量的通用算法

方位角相关性的多粒子累积量已成为探索超相对论重离子碰撞中产生的夸克-胶子等离子体（QGP）特性以及在BNL相对论重离子对撞机（RHIC）小型碰撞系统中寻找QGP的有力工具和欧洲核子研究组织的大型强子对撞机（LHC）。但是，只有很少一部分可用，并且已经在理论计算和实验测量中进行了研究，而其余的通常都很有趣，但是直接实现它们是不可行的。在本文中，我们提出了一种用于多粒子累积量的通用递归算法，该算法可以计算任意阶的单次和混合谐波多粒子累积量。其中，一次谐波的新的10、12、14和16粒子累积量命名为$C_{ñ}\left\{10\right\}， C_{ñ}\left\{12\right\}， C_{ñ}\left\{14\right\}$， 和 $C_{ñ}\left\{16\right\}$，以及相应的 $v_{ñ}$系数，将是第一次讨论。我们的蒙特卡洛斯研究表明，这些新的多粒子累积量可以很容易地与将多粒子关联的通用框架更新到很高的级别一起使用。最后，我们提出了一系列特殊的混合谐波多颗粒累积量，以测量不同流量系数的任何时刻之间的一般相关性。基于初始状态模型MC-Glauber，玩具蒙特卡洛模型和HIJING，显示了这些新可观察物的预测运输模型，以便将来在实验数据和理论模型计算之间进行比较。对重离子碰撞中这些新的多粒子累积量的研究将大大改善对联合概率密度函数的理解，该函数既涉及流动的不同谐波，也涉及对称平面。这将为对初始状态施加更严格的限制铺平道路，并有助于更精确地提取有关所产生的高温和高密度物质如何演化的信息。同时，应用于小型系统的工作可能对了解RHIC和LHC观测到的集体的起源非常有帮助。