作者机构：
School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China;[Zhiming Li; Yuanfang Wu] Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China;[Ye-Yin Zhao] School of Physics and Electronic Engineering, Sichuan University of Science and Engineering (SUSE), Zigong 643000, China;[Yunshan Cheng; Gang Wang] Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA;[Lizhu Chen] School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China<&wdkj&>Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
摘要：
Hyperorder cumulants C5/C1 and C6/C2 of net-baryon distributions are anticipated to offer crucial insights into the phase transition from quark-gluon plasma to hadronic matter in heavy-ion collisions. However, the accuracy of C5 and C6 is highly contingent on the fine shape of the distribution's tail, the detectable range of which could be essentially truncated by low statistics. In this paper, we use the fast Skellam-based simulations, as well as the ultrarelativistic quantum molecular dynamics model, to assess the impact of limited statistics on the measurements of C5/C1 and C6/C2 of net-proton distributions at lower energies available at the BNL Relativistic Heavy Ion Collider. Both ratios decrease from the unity baseline as we reduce statistics and could even turn negative without a pertinent physics mechanism. By incorporating statistics akin to experimental data, we can replicate the net-proton C5/C1 and C6/C2 values comparable to the corresponding measurements for Au+Au collisions at sNN=7.7 , 11.5, and 14.5 GeV. Our findings underscore a caveat to the interpretation of the observed beam energy dependence of hyperorder cumulants.
作者机构：
[Long, Fen; Liu, Kangning; Guo, Ranran; Wu, Yuanfang; Zhao, Jia; Li, Xiaobing; Li, Zhiming] Cent China Normal Univ, Key Lab Quark & Lepton Phys, MOE, Wuhan 430079, Peoples R China.;[Long, Fen; Liu, Kangning; Guo, Ranran; Wu, Yuanfang; Zhao, Jia; Li, Xiaobing; Li, Zhiming] Cent China Normal Univ, Inst Particle Phys, Wuhan 430079, Peoples R China.;[Zhou, Yu] Univ Calif Los Angeles, Los Angeles, CA 90095 USA.
关键词：
machine learning;phase transition;QCD critical point;three-dimensional Ising universality class
摘要：
Exploration of the QCD phase diagram and critical point is one of the main goals in current relativistic heavy-ion collisions. The QCD critical point is expected to belong to a three-dimensional (3D) Ising universality class. Machine learning techniques are found to be powerful in distinguishing different phases of matter and provide a new way to study the phase diagram. We investigate phase transitions in the 3D cubic Ising model using supervised learning methods. It is found that a 3D convolutional neural network can be trained to effectively predict physical quantities in different spin configurations. With a uniform neural network architecture, it can encode phases of matter and identify both second- and first-order phase transitions. The important features that discriminate different phases in the classification processes are investigated. These findings can help study and understand QCD phase transitions in relativistic heavy-ion collisions.
作者机构：
[吴元芳; 李笑冰; 许明梅; 钟昱明; 李治明] Institution of Particle Physics, Central China Normal University, Wuhan, 430079, China;[陈丽珠] School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, China;[潘雪] School of Electronic Engineering, Chengdu Technological University, Chengdu, 611730, China;[张凡] Wuhan Optical Valley Future School, Wuhan, 430078, China;[张雁华] Department of Physics and Electronic Engineering, Yuncheng University, Yuncheng, 044000, China
关键词：
相对论重离子碰撞;QCD相变;非临界涨落;有限系统尺度;非平衡
摘要：
为了从相对论重离子碰撞实验确定量子色动力学（Quantum Chromo-dynamics,QCD）所预言的相变临界点和相边界，必须考虑实验数据中非临界涨落、有限系统尺度、有限演化时间的影响。本文综述了这三方面工作的主要内容、结果和意义。对于非临界涨落，主要讨论了由于有限事件数对观察量测量的影响，估计了在相对论重离子对撞机（Relativistic Heavy-Ion Collider,RHIC）能量扫描区，精确测量高阶守恒荷高阶矩所需要的事件数。提出用泊松分布描述有限末态粒子数所致的统计涨落，将统计涨落和实验结果比较，发现统计涨落贡献为主，必须扣除泊松主导的统计涨落。提出混合事件方法，定义动力学累积矩为原始样本的累积矩减去混合样本的累积矩，利用多相输运模型（A Multiphase Transport Model,AMPT）的default模型重建了一个与之相对应的混合事件样本，结果表明：动力学累积矩确实能很好地扣除泊松样的统计涨落，尤其是中心度bin宽度和探测器效率的影响。对于有限系统尺度的影响，利用三维三态Potts模型研究了各种有限系统尺度下，它的磁化强度的高阶感应率在一级相变、临界点，以及平滑过渡区域的行为。发现在固定外场，穿越相边界的时候，从二阶到六阶磁化率都会出现非单调行为，或符号的变化，而且在三个相变区域，非单调行为类似。因此，仅从非单调行为不能区分不同级数的相变。进一步研究了磁化率的有限尺度标度行为，它们的标度指数在不同级数相变中是不一样的，可以区分不同级数的相变。根据观测量的有限尺度标度性，给出了用固定点确定临界参数的定量方法，并将该方法应用到三维三态Potts模型模拟产生的数据分析，展示了方法的精确有效性。对于非平衡演化的影响，采用Metropolis算法模拟了三维Ising模型在临界点附近从非平衡到平衡的演化过程。发现其序参量在演变过程中以指数形式趋近其平衡值，这与动力学朗之万方程给出的结果相同。临界温度下的平均弛豫时间随系统尺度的z次幂发散，表明它能很好地表示动力学方程中的弛豫时间。非平衡演化过程中序参量的三阶矩和四阶矩会出现正、负值震荡，符号取决于观测时间，结果与平滑过渡区动力学模型一致。研究还发现，在平滑过渡区，非平衡演化持续时间非常短，非平衡对观察量的影响非常弱；但是在一级相变线上，非平衡弛豫的时间非常长，非平衡豫影响不可忽略。这些定性特征对实验确定QCD的临界点和相边界具有重要的指导意义。
摘要：
In this paper, a search for power-law fluctuations with fractality and intermittency analysis to explore the QCD phase diagram and the critical point is summarized. Experimental data on self-similar correlations and fluctuations with respect to the size of phase–space volume in various high energy heavy-ion collisions are presented, with special emphasis on background subtraction and efficiency correction of the measurement. Phenomenological modeling and theoretical work on the subject are discussed. Finally, we highlight possible directions for future research.
作者机构：
[Li, Zhiming] Key Lab Quark & Lepton Phys MOE, Wuhan 430079, Peoples R China.;Inst Particle Phys, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Wuhan 430079, Peoples R China.
摘要：
Within the framework of intermittency analysis, a search for critical fluctuations is ongoing to locate the possible critical point in the quantum chromodynamics phase diagram. In this study, self-similar critical fluctuations from a critical Monte Carlo (CMC) model have been incorporated into the cascade ultrarelativistic quantum molecular dynamics (UrQMD) model. This hybrid UrQMD+CMC model exhibits a clear power-law behavior of scaled factorial moment for charged particles in Au+Au collisions at root sNN = 7.7-200 GeV. By comparing the UrQMD+CMC model results with those from the STAR experiment, it is found that the value of a calculated scaling exponent falls in the range of the experimental measurement when 1-2 % signal of intermittency fluctuations is added into the UrQMD sample.
期刊：
International Journal of Modern Physics E,2021年30(07):2150056 ISSN：0218-3013
通讯作者：
Lizhu Chen
作者机构：
[Chen, Lizhu] Nanjing Univ Informat Sci & Technol, Sch Phys & Optoelect Engn, Nanjing 210044, Peoples R China.;[Zhao, YeYin; Wu, Yuanfang; Li, Xiaobing; Li, Zhiming] Cent China Normal Univ, Phys MOE, Key Lab Quark & Lepton, Wuhan 430079, Peoples R China.;[Zhao, YeYin; Wu, Yuanfang; Li, Xiaobing; Li, Zhiming] Cent China Normal Univ, Inst Particle Phys, Key Lab Quark & Lepton, Wuhan 430079, Peoples R China.
通讯机构：
[Lizhu Chen] S;School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China
关键词：
Percolation transition;various sizes of cluster;fixed point;QCD phase transition
摘要：
It is proposed that the O(n) spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of cluster in the Ising model are systematically studied. With a finite size system, we demonstrate how to use the finite size scaling and fixed point behavior to search for critical point. At critical point, the independency of system size is found from skewness and kurtosis of the maximum, second and third largest cluster and their correlations. It is similar to the Binder-ratio, which has provided a remarkable identification of the critical point. Through an explanation of the universal characteristic of skewness and kurtosis of the order parameter, a possible application to the relativistic heavy-ion collisions is also discussed.
作者机构：
[Li, Zhiming] Cent China Normal Univ, Key Lab Quark & Lepton Phys MOE, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Inst Particle Phys, Wuhan 430079, Peoples R China.
摘要：
Local density fluctuations near the QCD critical point has been suggested to exhibit a power-law behavior which can be probed by an intermittency analysis on scaled factorial moment (SFM) in relativistic heavyion collisions. The collision energy and centrality dependence of the second-order SFMs are systematically investigated in Au + Au collisions at root s(NN) = 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV within the UrQMD model. We estimate the noncritical background in the measurement of intermittency and propose a cumulative variable method to effectively remove the background contributions. We further study the effect of particle detection efficiency by implementing the RHIC (STAR) experimental tracking efficiencies in the UrQMD events. A cell-by-cell method is proposed for experimental application of efficiency corrections on SFM. This work can provide a guidance of background subtraction and efficiency correction for the experimental measurement of intermittency in the search of the QCD critical point in heavy-ion collisions.
作者机构：
[Li-Zhu Chen] School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China;[Ye-Yin Zhao; Jin Wu; Zhi-Ming Li; Yuan-Fang Wu] Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
关键词：
Binomial distribution;net-proton number;statistics;the sixth order cumulant
作者机构：
[Zhao, Yeyin; Yang, Peng; Wu, Yuanfang; Xu, Mingmei; Li, Zhiming] Cent China Normal Univ, Key Lab Quark & Lepton Phys MOE, Inst Particle Phys, Wuhan 430079, Peoples R China.;[Li, Lin] Wuhan Univ Technol, Sch Sci, Wuhan 430070, Peoples R China.;[Zhou, Yu] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA.
通讯机构：
[Wu, Yuanfang] C;Cent China Normal Univ, Key Lab Quark & Lepton Phys MOE, Inst Particle Phys, Wuhan 430079, Peoples R China.
摘要：
Radial flow can be directly extracted from the azimuthal distribution of mean transverse rapidity. We apply the event-plane method and the two-particle correlation method to estimate the anisotropic Fourier coefficient of the azimuthal distribution of mean transverse rapidity. Using the event sample generated by a multiphase transport model with string melting, we show that both methods are effective. For the two-particle correlation method to be reliable, the mean number of particles in an azimuthal bin must be above a certain threshold. Using these two methods, anisotropic radial flow can be estimated in a model-independent way in relativistic heavy-ion collisions.
作者机构：
[Li, Zhiming] Cent China Normal Univ, Key Lab Quark & Lepton Phys MOE, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Inst Particle Phys, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Zhiming] C;Cent China Normal Univ, Key Lab Quark & Lepton Phys MOE, Wuhan 430079, Peoples R China.
摘要：
It is shown that intermittency, a self-similar correlation with respect to the size of the phase space volume, is sensitive to critical density fluctuations of baryon numbers in a system belonging to the three-dimensional (3D) Ising universality class. The relation between intermittency index and relative baryon density fluctuation is obtained. We thus suggest that measuring the intermittency in relativistic heavy-ion collisions could be used as a good probe of density fluctuations associated with the QCD critical phenomena. From recent preliminary results on neutron density fluctuations in central Au + Au collisions at root s(NN) = 7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV at RHIC/STAR, the collision energy dependence of intermittency index is extracted and shows a non-monotonic behavior with a peak at around 20 - 27 GeV, indicating that the strength of intermittency becomes the largest in this energy region. The transport UrQMD model without implementing critical physics cannot describe the observed behavior. (C) 2019 The Authors. Published by Elsevier B.V.
作者机构：
[Zhang, Yanhua; Zhao, Yeyin; Wu, Yuanfang; Xu, Mingmei; Li, Zhiming] Cent China Normal Univ, Key Lab Quark & Lepton Phys MOE, Wuhan 430079, Hubei, Peoples R China.;[Zhang, Yanhua; Zhao, Yeyin; Wu, Yuanfang; Xu, Mingmei; Li, Zhiming] Cent China Normal Univ, Inst Particle Phys, Wuhan 430079, Hubei, Peoples R China.;[Chen, Lizhu] Nanjing Univ Informat Sci & Technol, Sch Phys & Optoelect Engn, Nanjing 210044, Jiangsu, Peoples R China.;[Pan, Xue] Chengdu Technol Univ, Sch Elect Engn, Chengdu 611730, Sichuan, Peoples R China.;[Zhou, Yu] Cent China Normal Univ, 1 Middle Sch, Wuhan 430223, Hubei, Peoples R China.
通讯机构：
[Wu, Yuanfang] C;Cent China Normal Univ, Key Lab Quark & Lepton Phys MOE, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Inst Particle Phys, Wuhan 430079, Hubei, Peoples R China.
摘要：
The critical point is a fixed point in finite-size scaling. To quantify the behavior of such a fixed point, we define, at a given temperature and scaling exponent ratio, the width of scaled observables for different sizes. The minimum of the width reveals the position of the fixed point, its corresponding phase transition temperature, and scaling exponent ratio. The value of this ratio tells the nature of the fixed point, which can be a critical point, a point of the first-order phase transition line, or a point of the crossover region. To demonstrate the effectiveness of this method, we apply it to three typical samples produced by the three-dimensional three-state Potts model. Results show the method to be more precise and effective than conventional methods. Finally, we discuss a possible application at the Beam Energy Scan program of the Relativistic Heavy Ion Collider.
关键词：
High cumulants;statistical uncertainty;statistics;QCD phase transition
摘要：
We study the influence of measured high cumulants of conserved charges on their associated statistical uncertainties in relativistic heavy-ion collisions. With a given number of events, the measured cumulants randomly fluctuate with an approximately normal distribution, while the estimated statistical uncertainties are found to be correlated with corresponding values of the obtained cumulants. Generally, with a given number of events, the larger the cumulants we measure, the larger the statistical uncertainties that are estimated. The error-weighted averaged cumulants are dependent on statistics. Despite this effect, however, it is found that the three sigma rule of thumb is still applicable when the statistics are above one million.
作者机构：
[Chen, Lizhu; Cui, Fenping] Nanjing Univ Informat Sci & Technol, Sch Phys & Optoelect Engn, Nanjing 210044, Jiangsu, Peoples R China.;[Chen, Lizhu; Wu, Yuanfang; Li, Zhiming] Cent China Normal Univ, Key Lab Quark & Lepton Phys MOE, Wuhan 430079, Peoples R China.;[Chen, Lizhu; Wu, Yuanfang; Li, Zhiming] Cent China Normal Univ, Inst Particle Phys, Wuhan 430079, Peoples R China.
通讯机构：
[Chen, Lizhu] N;[Chen, Lizhu] C;Nanjing Univ Informat Sci & Technol, Sch Phys & Optoelect Engn, Nanjing 210044, Jiangsu, Peoples R China.;Cent China Normal Univ, Key Lab Quark & Lepton Phys MOE, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Inst Particle Phys, Wuhan 430079, Peoples R China.
关键词：
The sixth order cumulant;Statistics;Non-critical contributions;Heavy-ion collisions
摘要：
We investigate the measurement of the sixth order cumulant and its ratio to the second order cumulant (C-6/C-2) in relativistic heavy-ion collisions. The influence of statistics and different methods of centrality bin width correction on C-6/C-2 of net-proton multiplicity distributions is demonstrated. There is no satisfactory method to extract C-6/C-2 with the current statistics recorded at lower energies by STAR at RHIC. With statistics comparable to the expected statistics at the planned future RHIC Beam Energy Scan II (BES II), no energy dependence of C-6/C-2 is observed in central collisions using the UrQMD model. We find that if the transition signal is as strong as predicted by the PQM model, then it is hopefully observed at the upcoming RHIC BES II. (C) 2016 Elsevier B.V. All rights reserved.
作者机构：
[Lin, Yufu; Li, Zhiming] Cent China Normal Univ, Key Lab Quark & Lepton Phys MOE, Wuhan 430079, Hubei, Peoples R China.;[Lin, Yufu; Li, Zhiming] Cent China Normal Univ, Inst Particle Phys, Wuhan 430079, Hubei, Peoples R China.;[Chen, Lizhu] Nanjing Univ Informat Sci & Technol, Sch Phys & Optoelect Engn, Nanjing 210044, Jiangsu, Peoples R China.
通讯机构：
[Li, Zhiming] C;Cent China Normal Univ, Key Lab Quark & Lepton Phys MOE, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Inst Particle Phys, Wuhan 430079, Hubei, Peoples R China.
摘要：
Fluctuations of conserved quantities are believed to be sensitive observables to probe the signature of the QCD phase transition and critical point. It was argued recently that measuring the genuine correlation functions (CFs) could provide cleaner information on possible nontrivial dynamics in heavy-ion collisions. With the AMPT (a multiphase transport) model, the centrality and energy dependence of various orders of CFs of net protons in Au + Au collisions at sNN=7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV are investigated. The model results show that the number of antiprotons is important and should be taken into account in the calculation of CFs at high energy and/or in peripheral collisions. It is also found that the contribution of antiprotons is more important for higher order correlations than for lower ones. The CFs of antiprotons and mixed correlations play roles comparable to those of protons at high energies. Finally, we make comparisons between the model calculation and experimental data measured in the STAR experiment at the BNL Relativistic Heavy Ion Collider.
期刊：
International Journal of Modern Physics: Conference Series,2014年29(1460224):1460224 ISSN：2010-1945
作者机构：
[Zhiming Li] Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
摘要：
Higher cumulant of baryon number is suggested to be a good probe of critical point of QCD phase transition in relativistic heavy ion collisions. The energy and centrality dependence of dynamical kurtosis for Au + Au collisions at RHIC beam energies are measured. The dynamical kurtosis of both net and total protons are studied and their sign behaviors are discussed. The results are compared with those from transport model of AMPT. The contribution of non-critical effect on centrality definition is investigated.
