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Collective flow has been found to be similar between small colliding systems ($p$ $+$ $p$ and $p$ $+$ A collisions) and large colliding systems (peripheral A $+$ A collisions) at the CERN Large Hadron Collider. In order to study the differences of collective flow between small and large colliding systems, we employ a point cloud network to identify $p$ $+$ Pb collisions and peripheral Pb $+$ Pb collisions at $\sqrt{s_{NN}} =$ 5.02 TeV generated from a multiphase transport model (AMPT). After removing the discrepancies in the pseudorapidity distribution and the $p_{\rm T}$ spectra, we capture the discrepancy in collective flow. Although the verification accuracy of our PCN is limited due to similar event-by-event distributions of elliptic and triangular flow, we demonstrate that collective flow between $p$ $+$ Pb collisions and peripheral Pb $+$ Pb collisions becomes more distinct with increasing final hadron multiplicity and parton scattering cross section. This study not only highlights the potential of PCN techniques in advancing the understanding of collective flow in varying colliding systems, but more importantly lays the groundwork for the future PCN-related research., Comment: 10 pages, 11 figures, final published version

Though being seemingly disparate and with relatively new intersection, high energy nuclear physics and machine learning have already begun to merge and yield interesting results during the last few years. It's worthy to raise the profile of utilizing this novel mindset from machine learning in high energy nuclear physics, to help more interested readers see the breadth of activities around this intersection. The aim of this mini-review is to introduce to the community the current status and report an overview of applying machine learning for high energy nuclear physics, to present from different aspects and examples how scientific questions involved in high energy nuclear physics can be tackled using machine learning., Comment: 30 pages, 20 figures, mini-review

Relativistic collision of isobaric systems is found to be valuable in differentiating the nucleon distributions for nuclei with the same mass number. In recent contrast experiment of $^{96}_{44}\text{Ru}+^{96}_{44}\text{Ru}$ versus $^{96}_{40}\text{Zr}+^{96}_{40}\text{Zr}$ collisions at $\sqrt{s_\text{NN}} = 200~\text{GeV}$, the ratios of multiplicity distribution, elliptic flow, triangular flow, and radial flow are precisely measured and found to be significantly different from unity, indicating the difference in the shapes of the isobar pair. In this work, we investigate the feasibility of nuclear structure reconstruction from heavy-ion collision observables. We perform Bayesian Inference with employing the Monte-Carlo Glauber model as an estimator of the mapping from nuclear structure to the final state observables and to provide the mock data for reconstruction. By varying combination of observables included in the mock data, we find it plausible to infer Woods--Saxon parameters from the observables. We also observe that single-system multiplicity distribution for the isobar system, rather than their ratio, is crucial to simultaneously determine the nuclear structure for the isobar system., Comment: Previously entitled "How does Bayesian analysis infer the nucleon distributions in isobar collisions?"

Bayesian methods are used to constrain the density dependence of the QCD Equation of State (EoS) for dense nuclear matter using the data of mean transverse kinetic energy and elliptic flow of protons from heavy ion collisions (HIC), in the beam energy range $\sqrt{s_{\mathrm{NN}}}=2-10 GeV$. The analysis yields tight constraints on the density dependent EoS up to 4 times the nuclear saturation density. The extracted EoS yields good agreement with other observables measured in HIC experiments and constraints from astrophysical observations both of which were not used in the inference. The sensitivity of inference to the choice of observables is also discussed., Comment: Replaced with the published version

We present lattice QCD calculations of valence parton distribution function (PDF) of pion employing next-to-next-leading-order (NNLO) perturbative QCD matching. Our calculations are based on three gauge ensembles of 2+1 flavor highly improved staggered quarks and Wilson--Clover valance quarks, corresponding to pion mass $m_\pi=140$~MeV at a lattice spacing $a=0.076$~fm and $m_\pi=300$~MeV at $a=0.04, 0.06$~fm. This enables us to present, for the first time, continuum-extrapolated lattice QCD results for NNLO valence PDF of the pion at the physical point. Applying leading-twist expansion for renormalization group invariant (RGI) ratios of bi-local pion matrix elements with NNLO Wilson coefficients we extract $2^{\mathrm{nd}}$, $4^{\mathrm{th}}$ and $6^{\mathrm{th}}$ Mellin moments of the PDF. We reconstruct the Bjorken-$x$ dependence of the NNLO PDF from real-space RGI ratios using a deep neural network (DNN) as well as from momentum-space matrix elements renormalized using a hybrid-scheme. All our results are in broad agreement with the results of global fits to the experimental data carried out by the xFitter and JAM collaborations., Comment: 25 pages, 29 figures, version published in PRD

In this proceeding, the deep Convolutional Neural Networks (CNNs) are deployed to recognize the order of QCD phase transition and predict the dynamical parameters in Langevin processes. To overcome the intrinsic randomness existed in a stochastic process, we treat the final spectra as image-type inputs which preserve sufficient spatiotemporal correlations. As a practical example, we demonstrate this paradigm for the scalar condensation in QCD matter near the critical point, in which the order parameter of chiral phase transition can be characterized in a $1+1$-dimensional Langevin equation for $\sigma$ field. The well-trained CNNs accurately classify the first-order phase transition and crossover from $\sigma$ field configurations with fluctuations, in which the noise does not impair the performance of the recognition. In reconstructing the dynamics, we demonstrate it is robust to extract the damping coefficients $\eta$ from the intricate field configurations., Comment: Contribution to: SQM2021

A deep convolutional neural network (CNN) is developed to study symmetry energy $E_{\rm sym}(\rho)$ effects by learning the mapping between the symmetry energy and the two-dimensional (transverse momentum and rapidity) distributions of protons and neutrons in heavy-ion collisions. Supervised training is performed with labelled data-set from the ultrarelativistic quantum molecular dynamics (UrQMD) model simulation. It is found that, by using proton spectra on event-by-event basis as input, the accuracy for classifying the soft and stiff $E_{\rm sym}(\rho)$ is about 60% due to large event-by-event fluctuations, while by setting event-summed proton spectra as input, the classification accuracy increases to 98%. The accuracy for 5-label (5 different $E_{\rm sym}(\rho)$) classification task are about 58% and 72% by using proton and neutron spectra, respectively. For the regression task, the mean absolute error (MAE) which measures the average magnitude of the absolute differences between the predicted and actual $L$ (the slope parameter of $E_{\rm sym}(\rho)$) are about 20.4 and 14.8 MeV by using proton and neutron spectra, respectively. Fingerprints of the density-dependent nuclear symmetry energy on the transverse momentum and rapidity distributions of protons and neutrons can be identified by convolutional neural network algorithm., Comment: 6 pages, 7 figures

A novel method for identifying the nature of QCD transitions in heavy-ion collision experiments is introduced. PointNet based Deep Learning (DL) models are developed to classify the equation of state (EoS) that drives the hydrodynamic evolution of the system created in Au-Au collisions at 10 AGeV. The DL models were trained and evaluated in different hypothetical experimental situations. A decreased performance is observed when more realistic experimental effects (acceptance cuts and decreased resolutions) are taken into account. It is shown that the performance can be improved by combining multiple events to make predictions. The PointNet based models trained on the reconstructed tracks of charged particles from the CBM detector simulation discriminate a crossover transition from a first order phase transition with an accuracy of up to 99.8%. The models were subjected to several tests to evaluate the dependence of its performance on the centrality of the collisions and physical parameters of fluid dynamic simulations. The models are shown to work in a broad range of centralities (b=0-7 fm). However, the performance is found to improve for central collisions (b=0-3 fm). There is a drop in the performance when the model parameters lead to reduced duration of the fluid dynamic evolution or when less fraction of the medium undergoes the transition. These effects are due to the limitations of the underlying physics and the DL models are shown to be superior in its discrimination performance in comparison to conventional mean observables., Comment: 12 pages, 7 figures. Matches published version

Bottomonium states are key probes for experimental studies of the quark-gluon plasma (QGP) created in high-energy nuclear collisions. Theoretical models of bottomonium productions in high-energy nuclear collisions rely on the in-medium interactions between the bottom and antibottom quarks. The latter can be characterized by the temperature ($T$) dependent potential, with real ($V_R(T,r)$) and imaginary ($V_I(T,r)$) parts, as a function of the spatial separation ($r$). Recently, the masses and thermal widths of up to $3S$ and $2P$ bottomonium states in QGP were calculated using lattice quantum chromodynamics (LQCD). Starting from these LQCD results and through a novel application of deep neural network, here, we obtain $V_R(T,r)$ and $V_I(T,r)$ in a model-independent fashion. The temperature dependence of $V_R(T,r)$ was found to be very mild between $T\approx0-334$~MeV. For $T=151-334$~MeV, $V_I(T,r)$ shows a rapid increase with $T$ and $r$, which is much larger than the perturbation-theory-based expectations., Comment: 16 pages, 10 figures; Published version; Data for plots enclosed

It is non-trivial to recognize phase transitions and track dynamics inside a stochastic process because of its intrinsic stochasticity. In this paper, we employ the deep learning method to classify the phase orders and predict the damping coefficient of fluctuating systems under Langevin's description. As a concrete set-up, we demonstrate this paradigm for the scalar condensation in QCD matter near the critical point, in which the order parameter of chiral phase transition can be characterized in a $1+1$-dimensional Langevin equation for $\sigma$ field. In a supervised learning manner, the Convolutional Neural Networks(CNNs) accurately classify the first-order phase transition and crossover based on $\sigma$ field configurations with fluctuations. Noise in the stochastic process does not significantly hinder the performance of the well-trained neural network for phase order recognition. For mixed dynamics with diverse dynamical parameters, we further devise and train the machine to predict the damping coefficients $\eta$ in a broad range. The results show that it is robust to extract the dynamics from the bumpy field configurations., Comment: 7 pages, 6 figures

A new method of event characterization based on Deep Learning is presented. The PointNet models can be used for fast, online event-by-event impact parameter determination at the CBM experiment. For this study, UrQMD and the CBM detector simulation are used to generate Au+Au collision events at 10 AGeV which are then used to train and evaluate PointNet based architectures. The models can be trained on features like the hit position of particles in the CBM detector planes, tracks reconstructed from the hits or combinations thereof. The Deep Learning models reconstruct impact parameters from 2-14 fm with a mean error varying from -0.33 to 0.22 fm. For impact parameters in the range of 5-14 fm, a model which uses the combination of hit and track information of particles has a relative precision of 4-9 % and a mean error of -0.33 to 0.13 fm. In the same range of impact parameters, a model with only track information has a relative precision of 4-10 % and a mean error of -0.18 to 0.22 fm. This new method of event-classification is shown to be more accurate and less model dependent than conventional methods and can utilize the performance boost of modern GPU processor units., Comment: Replaced with version accepted for publication. 10 pages, 8 figures

We study the effect of thermal charm production on charmonium regeneration in high energy nuclear collisions. By solving the kinetic equations for charm quark and charmonium distributions in Pb+Pb collisions, we calculate the global and differential nuclear modification factors $R_{AA}(N_{part})$ and $R{AA}(p_t)$ for $J/\Psi$s. Due to the thermal charm production in hot medium, the charmonium production source changes from the initially created charm quarks at SPS, RHIC and LHC to the thermally produced charm quarks at Future Circular Collider (FCC), and the $J/\Psi$ suppression ($R_{AA}<1$) observed so far will be replaced by a strong enhancement ($R_{AA}>1$) at FCC at low transverse momentum., Comment: 6 pages, 3 figures

The early stage of high multiplicity pp, pA and AA collider is represented by a nearly quarkless, hot, deconfined pure gluon plasma. According to pure Yang-Mills Lattice Gauge Theory, this hot pure glue matter undergoes, at a high temperature, $T_c = 270$ MeV, a first order phase transition into a confined Hagedorn-GlueBall fluid. These new scenario should be characterized by a suppression of high $p_T$ photons and dileptons, baryon suppression and enhanced strange meson production. We propose to observe this newly predicted class of events at LHC and RHIC., Comment: 7 pages, 6 figures

We investigate with a transport approach the cold and hot nuclear matter effects on the charmonium transverse momentum distributions in relativistic heavy ion collisions. The newly defined nuclear modification factor $r_{AA}=\langle p_{T}^2\rangle_{AA}/\langle p_{T}^2\rangle_{pp}$ and elliptic flow $v_2$ for $J/\psi$ are sensitive to the nature of the hot medium and the thermalization of heavy quarks. From SPS through RHIC to LHC colliding energies, we observe dramatic changes in the centrality dependence of $r_{AA}$. We find that at LHC energy, the finally observed charmonia are dominated by the regeneration from thermalized heavy quarks., Comment: 11 pages,10 figures