Search

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 $\sqrt{s_\mathrm{NN}}$ = 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., Comment: 8 pages, 6 figures, published version

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 effectivelly 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., Comment: 8 pages, 7 figures, published version

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., Comment: 12 pages, 5 figures. Accepted by IJMPE

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 heavy-ion collisions. The collision energy and centrality dependence of the second-order SFMs are systematically investigated in Au $+$ Au collisions at $\sqrt{s_{NN}}$ = 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., Comment: Replaced with the published version

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., Comment: 8 pages, 4 figures

The high-order cumulants and factorial cumulants of conserved charges are suggested to study the critical dynamics in heavy ion collisions. In this paper, using parametric representation of the 3-dimensional Ising model, the sign distribution on the phase diagram and temperature dependence of the cumulants and factorial cumulants is studied and compared. In the vicinity of the critical point, the cumulants and factorial cumulants can not be distinguished. Far away from the critical point, sign changes occur in the factorial cumulants comparing with the same order cumulants. The cause of these sign changes is analysed. They may be used to measure the distance to the critical point., Comment: 11 pages, 3 figures

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 $\sqrt{s_{NN}}$ = 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., Comment: Replaced with the published version

Taking doubly charged particles, positive-negative charge pair production and the effects of volume fluctuations into account, the Poisson baseline of the fluctuations of net-charge is studied. Within the Poisson baseline, the cumulants of net-charge are derived. Comparing to the Skellam baseline of net-charge, we infer that doubly charged particles broaden the distributions of net-charge, while positive-negative charge pairs narrow the distributions. Using the ratios of doubly charged particles and positive-negative charge pairs from neutral resonance decays to the total positive charges from THERMINATOR 2, the first four orders of moments and the corresponding moment products are calculated in the Poisson baseline for Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV at RHIC/STAR. We find that the standard deviation is mainly influenced by the resonance decay, while the third and fourth order moments and corresponding moment products are mainly modified and fit the data of RHIC/STAR much better after including the effects of volume fluctuations., Comment: 6 pages, 2 figures, to be published by Chinese Physics C

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 if the transition signal is as strong as predicted by the PQM model, then it is hopefully observed at the upcoming RHIC BES II.

Using a multi-phase transport model (AMPT) that includes both initial partonic and hadronic interactions, we study neighboring bin multiplicity correlations as a function of pseudorapidity in Au+Au collisions at $\sqrt{s_{NN}} = 7.7-62.4$ GeV. It is observed that for $\sqrt{s_{NN}} < $19.6GeV Au+Au collisions, the short-range correlations of final particles have a trough at central pseudorapidity, while for $\sqrt{s_{NN}} > $19.6GeV AuAu collisions, the short-range correlations of final particles have a peak at central pseudorapidity. Our findings indicate that the pseudorapidity dependence of short-range correlations should contain some new physical information, and are not a simple result of the pseudorapidity distribution of final particles. The AMPT results with and without hadronic scattering are compared. It is found that hadron scattering can only increase the short-range correlations to some level, but is not responsible for the different correlation shapes for different energies. Further study shows that the different pseudorapidity dependence of short-range correlations are mainly due to partonic evolution and the following hadronization scheme., Comment: 5 pages, 3 figures, submitted to CPC

We study statistics dependence of the probability distributions and the means of measured moments of conserved quantities, respectively. The required statistics of all interested moments and their products are estimated based on a simple simulation. We also explain why the measured moments are underestimated when the statistics are insufficient.With the statistics at RHIC/BES, the second and third order moments can be reliably obtained based on the method of Centrality bin width correction (CBWC), which can not be applied for the fourth order moments at low energy. With planning statistics at RHIC/BES II, and improved CBWC method, $\kappa\sigma^2$ in a finer centrality bin scale should be measurable. This will help us to understand the current observation of energy and centrality dependence of high-order moments., Comment: 11 pages, 6 figures

By the sample generated by the AMPT with string melting model, we compare the azimuthal distributions of multiplicity, total transverse rapidity, and mean transverse rapidity. It is demonstrated that the azimuthal distribution of mean transverse rapidity is a good probe of the radial kinetic expansion. The anisotropic part of the distribution characterizes the anisotropic nature of the radial expansion, and isotropic part is combinations of thermal motion and isotropic radial expansion., Comment: 4pages,7figures

By the generator of the UrQMD model, event statistics for the products of kurtosis ($\kappa$) and variance ($\sigma^2$) of net-proton and net-charge multiplicity distributions are carefully studied. It is shown that the statistics at RHIC/BES below $\sqrt {s_{NN}} < 19.6$ GeV are not sufficient for using the method of Centrality Bin Width Correction (CBWC). Corresponding results are systematically underestimated. A way to improve the CBWC method is proposed. It can remove the statistics dependence of the data and reduce the initial size fluctuation as well., Comment: 6 pages, 5 figures

The Poisson-liked statistical fluctuations, which are caused by the finite number of produced particles, are firstly estimated for the cumulants of conserved charges, i.e., the cumulants of net-baryon, net-electric charge, and net-strangeness. They turn out to be the same as those baselines derived from Hadron Resonance Gas (HRG) model. The energy and centrality dependence of net-proton cumulants at the Relativistic Heavy-Ion Collider (RHIC) are demonstrated to be mainly caused by statistical fluctuations. Subtracting the statistical fluctuations, the dynamical kurtosis of net- and total-proton from two versions of the AMPT model and the UrQMD model at current RHIC beam energies are presented. It is found that the observed sign change in the kurtosis of net-proton can not be reproduced by these three transport models. There is no significant difference between net- and total-proton kurtosis in model calculations, in contrary to the data at RHIC., Comment: 7 pages, 2 figures

The appearance of the inflection point in the equation of state (EoS) is associated with the second order phase transition. The high cumulants of conserved quantities near the critical point are corresponding to the high derivatives of the EoS near the inflection point. The critical behavior of high cumulants of conserved charge near the QCD critical point, in particular, the sign change, is closely related to the appearance of inflection point. We show in general how the times of sign change of high cumulants relate to the order of derivative. We also demonstrate that the character of inflection point of EoS is as visible as the sign change of high cumulants in 3 systems, i.e., van der Waals equation of fluid, magnetization of spin models and the baryon number density of QCD matter. Therefore, we propose that the EoS, or the mean of baryon number density, should be measured and studied together with its higher cumulants in exploring QCD critical point in heavy ion collisions., Comment: 10 pages, 3 figures

With the help of AMPT default model, we study the influence of initial size (centrality of collisions) on higher cumulant ratios of net-proton distributions. If the centrality is presented by impact parameter, there is a strong centrality dependent, in particular, in those peripheral collisions. This dependence is slightly reduced if the centrality is presented by number of participant, or charged multiplicity. However, the dynamical ratios are almost centrality independent. So the centrality dependence of dynamical ratios at RHIC beam energy scan are presented., Comment: 3 pages, 2 figures

Considering different universality classes of the QCD phase transitions, we perform the Monte Carlo simulations of the 3-dimensional $O(1, 2, 4)$ models at vanishing and non-vanishing external field, respectively. Interesting high cumulants of the order parameter and energy from O(1) (Ising) spin model, and the cumulants of the energy from O(2) and O(4) spin models are presented. The critical features of the cumulants are discussed. They are instructive to the high cumulants of the net baryon number in the QCD phase transitions., Comment: 6 pages, 5 figures

We suggest the azimuthal distribution of mean transverse (radial) rapidity of the final state particles as a more direct measure of the transverse motion of the source than the standard azimuthal multiplicity distribution. Using a sample generated by the AMPT model with string melting, we demonstrate that the azimuthal amplitude of the suggested distribution characterizes the anisotropic radial flow, and coincides with the parameter of anisotropic radial rapidity extracted from a generalized blast-wave parametrization., Comment: 5 pages, 4 figures

Azimuthal distributions of radial (transverse) momentum, mean radial momentum, and mean radial velocity of final state particles are suggested for relativistic heavy ion collisions. Using transport model AMPT with string melting, these distributions for Au + Au collisions at 200 GeV are presented and studied. It is demonstrated that the distribution of total radial momentum is more sensitive to the anisotropic expansion, as the anisotropies of final state particles and their associated transverse momentums are both counted in the measure. The mean radial velocity distribution is compared with the radial {\deg}ow velocity. The thermal motion contributes an isotropic constant to mean radial velocity.

We propose a forward-backward multiplicity correlation function $C^N_{FB}$, which is experimentally accessible, to measure the noncollectivity contribution. We find that $C^N_{FB}$ is sensitive to the jet contribution for the particle-rich case. Surprisingly, it will automatically decrease for the particle-rare case. Our study indicates that similar decreasing trend observed previously is mainly driven by particle scarcity instead of jets. The function is studied in Au+Au collision at $\sqrt{s_{NN}}=200$ GeV with a multiphase transport model (AMPT). We find that the jet fraction is about 10% at transverse momentum ($p_T$) around 2.5 GeV/$c$ and reaches up to 30% at 3.5 GeV/$c$. The implication of this study in the investigation of the noncollectivity contribution in elliptic anisotropy parameter $v_2$ is also discussed., Comment: 5 pages, 4 figures

Higher moments of net-proton Binder ratio, which is suggested to be a good experimental measurement to locate the QCD critical point, is measured in relativistic heavy ion collisions. We firstly estimate the effect of statistical fluctuations of the third and forth order Binder ratios. Then the dynamical Binder ratio is proposed and investigated in both transport and statistical models. The energy dependence of dynamical Binder ratios with different system sizes at RHIC beam scan energies are presented and discussed., Comment: 5 pages, 3 figures

Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. Using 3D-Ising model, the critical behavior of Binder ratios and ratios of high order cumulants of order parameter are fully presented. Binder ratio is shown to be a step function of temperature. The critical point is the intersection of the ratios of different system sizes between two platforms. From low to high temperature through the critical point, the ratios of third order cumulants change their values from negative to positive in a valley shape, and ratios of fourth order cumulants oscillate around zero. The normalized ratios, like the Skewness and Kurtosis, do not diverge with correlation length, in contrary with corresponding cumulants. Applications of these characters in search critical point in relativistic heavy ion collisions are discussed., Comment: 4 pages, 4 figures, updated contents

In order to trace the initial interaction in ultra-relativistic heavy ion collision in all azimuthal directions, two azimuthal multiplicity-correlation patterns -- neighboring and fixed-to-arbitrary angular-bin correlation patterns -- are suggested. From the simulation of Au + Au collisions at 200 GeV by using the Monte Carlo models RQMD with hadron re-scattering and AMPT with and without string melting, we observe that the correlation patterns change gradually from out-of-plane preferential one to in-plane preferential one when the centrality of collision shifts from central to peripheral, meanwhile the anisotropic collective flow v_2 keeps positive in all cases. This regularity is found to be model and collision energy independent. The physics behind the two opposite trends of correlation patterns, in particular, the presence of out-of-plane correlation patterns at RHIC energy, are discussed., Comment: 5pages, 4figures