Simulations Of Heavy-ion Collisions Research Articles

Efficient emulation of relativistic heavy ion collisions with transfer learning

Measurements from the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC) can be used to study the properties of quark-gluon plasma. Systematic constraints on these properties must combine measurements from different collision systems and methodically account for experimental and theoretical uncertainties. Such studies require a vast number of costly numerical simulations. While computationally inexpensive surrogate models ("emulators") can be used to efficiently approximate the predictions of heavy ion simulations across a broad range of model parameters, training a reliable emulator remains a computationally expensive task. We use transfer learning to map the parameter dependencies of one model emulator onto another, leveraging similarities between different simulations of heavy ion collisions. By limiting the need for large numbers of simulations to only one of the emulators, this technique reduces the numerical cost of comprehensive uncertainty quantification when studying multiple collision systems and exploring different models.

Net-particle number fluctuations in a hydrodynamic description of heavy-ion collisions

Utilizing viscous hydrodynamic simulations of heavy-ion collisions, we study the behavior of cumulants of (net-)(anti)proton number distributions at RHIC beam energy scan energies, incorporating non-critical contributions like baryon conservation and excluded volume. The experimental data on net-proton cumulants at √SNN > 20 GeV are consistent with simultaneous effects of global baryon conservation and repulsive interactions in baryon sector, whereas the data at lower collision energies show possible indications for sizable attractive interactions among baryons. We discuss the behavior of factorial cumulants in addition to the ordinary cumulants, and also address the quantitative difference between proton and baryon number cumulants.

Quantum algorithms for transport coefficients in gauge theories

In the future, ab initio quantum simulations of heavy ion collisions may become possible with large-scale fault-tolerant quantum computers. We propose a quantum algorithm for studying these collisions by looking at a class of observables requiring dramatically smaller volumes: transport coefficients. These form nonperturbative inputs into theoretical models of heavy ions; thus, their calculation reduces theoretical uncertainties without the need for a full-scale simulation of the collision. We derive the necessary lattice operators in the Hamiltonian formulation and describe how to obtain them on quantum computers. Additionally, we discuss ways to efficiently prepare the relevant thermal state of a gauge theory.

Theoretical uncertainties on the extraction of in-medium NN cross sections by different Pauli blocking algorithms * *This work was partly inspired by the transport code comparison project, and it was supported by the National Natural Science Foundation of China (11875323, 11705163, 11790320, 11790323, 11961141003), the National Key R&D Program of China (2018YFA0404404), the Continuous Basic Scientific Research Project (WDJC-2019-13, BJ20002501)

Three typical Pauli blocking algorithms in quantum molecular dynamics type models are investigated in the nuclear matter, the nucleus, and heavy ion collisions. In nuclear matter, the blocking ratios obtained with the three algorithms are underestimated by 13%-25% compared to the corresponding analytical values. For a finite nucleus, spurious collisions occur around the surface of the nucleus owing to the defects of the Pauli blocking algorithms. In the simulations of heavy ion collisions, the uncertainty of stopping power arising from the different Pauli blocking algorithms is less than 5%. Furthermore, the in-medium effects of nucleon-nucleon (NN) cross sections on the nuclear stopping power are discussed. Our results show that the transport model calculations with free NN cross sections result in the stopping power decreasing with beam energy when the beam energy is less than 300 MeV/u. To increase or decrease the values of the stopping power, the transport model calculations need enhanced or suppressed model dependent in-medium NN cross sections that are expected to be smaller than the true in-medium NN cross sections.

Proton correlations and apparent intermittency in the UrQMD model with hadronic potentials

It is shown that the inclusion of hadronic interactions, and in particular nuclear potentials, in simulations of heavy ion collisions at the SPS energy range can lead to obvious correlations of protons. These correlations contribute significantly to an intermittency analysis as performed at the NA61 experiment. The beam energy and system size dependence is studied by comparing the resulting intermittency index for heavy ion collisions of different nuclei at beam energies of 40A, 80A and 150A GeV. The resulting intermittency index from our simulations is similar to the reported values of the NA61 collaboration, if nuclear interactions are included. The observed apparent intermittency signal is the result of the correlated proton pairs with small relative transverse momentum Δpt, which would be enhanced by hadronic potentials, and this correlation between the protons is slightly influenced by the coalescence parameters and the relative invariant four-momentum qinv cut.

Dynamic jet charge

We propose a modified definition of the jet charge, the "dynamic jet charge", where the constant jet momentum fraction weighting parameter, $\kappa$, in the standard jet charge definition is generalized to be a function of a dynamical property of the jet or the individual jet constituents. The dynamic jet charge can complement analyses based on the standard definition and give improved discrimination between quark and gluon initiated jets and between jets initiated by different quark flavors. We focus on the specific scenario where each hadron in the jet contributes to the dynamic jet charge with a $\kappa$-value dynamically determined by its jet momentum fraction. The corresponding dynamic jet charge distributions have qualitatively distinct features and are typically characterized by a multiple peak structure. For proton-proton collisions, compared to the standard jet charge, the dynamic jet charge gives significantly improved discrimination between quark and gluon initiated jets and comparable discrimination between $u$- and $d$-quark initiated jets. In Pythia simulations of heavy ion collisions, the dynamic jet charge is found to have higher jet discrimination power compared to the standard jet charge, remaining robust against the increased contamination from underlying event. We also present phenomenological applications of the dynamic jet charge to probe nuclear flavor structure.

Correlation between time and angular alignment in molecular dynamics simulations of heavy ion collisions

Neutron-proton equilibration is a process which has been used to study the density dependence of the symmetry energy term in the nuclear equation-of-state. This study utilizes constrained molecular dynamics (CoMD) simulations of $^{70}\mathrm{Zn}\phantom{\rule{4pt}{0ex}}+\phantom{\rule{4pt}{0ex}}^{70}\mathrm{Zn}$ with collision energies of 35 and 45 MeV/nucleon. An algorithm is used which searches through CoMD events and identifies the PLF* after it separates from the target and determines its lifetime, $\mathrm{\ensuremath{\Delta}}t$. It also determines the fragments that the PLF* breaks apart into and determines their angular alignment. This technique gives an opportunity to explore how the average alignment of dynamically produced fragments, ${\ensuremath{\langle}\ensuremath{\alpha}\ensuremath{\rangle}}_{\mathrm{dyn}}$, evolves with PLF* lifetime. An approximately linear relationship was determined with $d{\ensuremath{\langle}\ensuremath{\alpha}\ensuremath{\rangle}}_{\mathrm{dyn}}/d\mathrm{\ensuremath{\Delta}}t=0.98\ifmmode\pm\else\textpm\fi{}0.08\phantom{\rule{0.16em}{0ex}}\mathrm{rad}/\mathrm{zs}$ and $1.06\ifmmode\pm\else\textpm\fi{}0.09\phantom{\rule{0.16em}{0ex}}\mathrm{rad}/\mathrm{zs}$ for the 35 and $45\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$, respectively, indicating a correlation with magnitude consistent with classically determined values which were used for prior experimental studies.

Machine learning for high energy heavy ion collisions

The high energy heavy ion collision is a multi-stage process that is described by complex hybrid models. The initial state fluctuations in event-by-event simulations of heavy ion collisions convert to final state correlations by collective flow and hadronic cascade. It is not easy to design final state correlations (observables) from particles in momentum space, that can help to extract useful information, such as the initial state nuclear structure, the properties of quark gluon plasma and the nuclear equation of state. Machine learning is helpful in automatic feature extraction in heavy ion collisions. This article reviews the applications, challenges and possible future developments of machine learning in heavy ion physics.

Exploring Longitudinal Observables with 3+1D IP-Glasma

We present a formulation of the initial state of heavy ion collisions that generalizes the 2+1D boost invariant IP-Glasma [B. Schenke, P. Tribedy, R. Venugopalan, Fluctuating Glasma initial conditions and flow in heavy ion collisions, Phys. Rev. Lett. 108 (2012) 252301.] to 3+1D through JIMWLK rapidity evolution of the pre-collision Wilson lines. The rapidity dependence introduced by the JIMWLK evolution leads us to modify the initial condition for the gauge fields, and to solve Gauss' law iteratively in order to allow for temporal evolution on a 3-dimensional lattice.While the transverse physics of QGP has been studied nearly exhaustively, the effect of longitudinal fluctuations introduced by the JIMWLK evolution has yet to be studied in detail phenomenologically. Hence, we couple our 3+1D IP-Glasma model to MUSIC+UrQMD, for completely 3+1D simulations of heavy ion collisions. Specifically, we consider Pb-Pb collisions at s=2.76TeV and study the rapidity dependence of the charged hadron νn(η) via the η-dependent flow factorization ratios rn(ηa,ηb) as measured by CMS [V. Khachatryan, et al., Evidence for transverse momentum and pseudorapidity dependent event plane fluctuations in PbPb and pPb collisions, Phys. Rev. C 92 (3) (2015) 034911.], as well as the charged hadron multiplicity dNch/dη.

Critical fluctuations in a dynamically expanding heavy-ion collision

For the discovery of the QCD critical point it is crucial to develop dynamical models of the fluctuations of the net-baryon number that can be embedded in simulations of heavy-ion collisions. In this proceeding, we study the dynamical formation of the critical fluctuations of the net-baryon number near the QCD critical point and their survival in the late stages in an expanding system. The stochastic diffusion equation with a non-linear free energy functional is employed for describing the evolution of conserved-charge fluctuations along trajectories in the crossover and first-order transition regions near the QCD critical point.

Thermal properties of pi and rho meson

We computed the pole masses and decay constants of pi and rho meson at finite temperature in the framework of Dyson–Schwinger equations and Bethe–Salpeter equations approach. Below transition temperature, pion pole mass increases monotonously, while rho meson seems to be temperature independent. Above transition temperature, pion mass approaches the free field limit of screening mass sim 2pi T, whereas rho meson is about twice as large as that limit. Pion and the longitudinal projection of rho meson decay constants have similar behaviour as the order parameter of chiral symmetry, whereas the transverse projection of rho meson decay constant rises monotonously as temperature increases. The inflection point of decay constant and the chiral susceptibility get the same phase transition temperature. Though there is no access to the thermal width of mesons within this scheme, it is discussed by analyzing the Gell-Mann-Oakes-Renner (GMOR) relation in medium. These thermal properties of hadron observables will help us understand the QCD phases at finite temperature and can be employed to improve the experimental data analysis and heavy ion collision simulations.

Identifying the nature of the QCD transition in relativistic collision of heavy nuclei with deep learning

Using deep convolutional neural network (CNN), the nature of the QCD transition can be identified from the final-state pion spectra from hybrid model simulations of heavy-ion collisions that combines a viscous hydrodynamic model with a hadronic cascade “after-burner”. Two different types of equations of state (EoS) of the medium are used in the hydrodynamic evolution. The resulting spectra in transverse momentum and azimuthal angle are used as the input data to train the neural network to distinguish different EoS. Different scenarios for the input data are studied and compared in a systematic way. A clear hierarchy is observed in the prediction accuracy when using the event-by-event, cascade-coarse-grained and event-fine-averaged spectra as input for the network, which are about 80%, 90% and 99%, respectively. A comparison with the prediction performance by deep neural network (DNN) with only the normalized pion transverse momentum spectra is also made. High-level features of pion spectra captured by a carefully-trained neural network were found to be able to distinguish the nature of the QCD transition even in a simulation scenario which is close to the experiments.

Calculation of shear viscosity in Au+Au collisions at NICA energies

Shear viscosity of hot and dense nuclear matter, produced in the central zone of central gold-gold collisions at energies of NICA, is calculated within the UrQMD model. Besides the microscopic simulations of heavy ion collisions, the procedure assumes the application of statistical model to determine the temperature and chemical potentials in the system, and study of the relaxation process within the UrQMD box with periodic boundary conditions. The latter is used for calculation of the correlator which enters the Green-Kubo formula for shear viscosity. The fluctuations at early and late stages of the system evolution are studied. Results are compared to predictions of other models.

Elliptic flow coalescence to identify the f0 (980) content

We use a simple coalescence model to generate $f_{0}$(980) particles for three configurations: a ${s\bar{s}}$ meson, a ${u\bar{u}s\bar{s}}$ tetraquark, and a ${K^{+}K^{-}}$ molecule. The phase-space information of the coalescing constituents is taken from a multi-phase transport (AMPT) simulation of heavy-ion collisions. It is shown that the number of constituent quarks scaling of the elliptic flow anisotropy can be used to discern ${s\bar{s}}$ from ${u\bar{u}s\bar{s}}$ and ${K^{+}K^{-}}$ configurations.

Classify QCD phase transition with deep learning

The state-of-the-art pattern recognition method in machine learning (deep convolution neural network) is used to identify the equation of state (EoS) employed in the relativistic hydrodynamic simulations of heavy ion collisions. High-level correlations of particle spectra in transverse momentum and azimuthal angle learned by the network act as an effective EoS-meter in deciphering the nature of the phase transition in QCD. The EoS-meter is model independent and insensitive to other simulation inputs including the initial conditions and shear viscosity for hydrodynamic simulations. Through this study we demonstrate that there is a traceable encoder of the dynamical information from the phase structure that survives the evolution and exists in the final snapshot of heavy ion collisions and one can exclusively and effectively decode these information from the highly complex final output with machine learning when traditional methods fail. Besides the deep neural network, the performance of traditional machine learning classifiers are also provided.

Equation of state for QCD with a critical point from the 3D Ising Model

Current knowledge of the finite-density QCD equation of state from first principles is limited to a Taylor expansion in the baryonic chemical potential around μB = 0. By means of a scaling form for the equation of state of the 3D Ising model and a non-universal, parametrized map to QCD coordinates, we construct a family of equations of state matching state of the art first principle Lattice QCD calculations and including the correct critical behavior, which can be readily employed in hydrodynamical simulations of heavy ion collisions at finite density, covering most of the BES range at RHIC. This contribution reports on work done within the Fluctuations/Equation of State working group of the BEST Collaboration.

Lights and (some) shadows in the comparison among experimental data of heavy ion collisionat Fermi energies and the dynamical model AMD

The simulation of heavy ion collisions in the Fermi energy region is a challenge for the theoretical models; in particular it is difficult to obtain a coherent description in all the impact parameter range and to reproduce all the experimental observables. In this contribution we will show the very good job done by the dynamical model AMD [1] followed by the statistical code GEMINI [2, 3] as an afterburner. The model is able to reproduce the main characteristics of peripheral and semiperipheral collisions, although some discrepancies still persist.

Implicit schemes for real-time lattice gauge theory

We develop new gauge-covariant implicit numerical schemes for classical real-time lattice gauge theory. A new semi-implicit scheme is used to cure a numerical instability encountered in three-dimensional classical Yang-Mills simulations of heavy-ion collisions by allowing for wave propagation along one lattice direction free of numerical dispersion. We show that the scheme is gauge covariant and that the Gauss constraint is conserved even for large time steps.

Magneto-hydrodynamic simulations of Heavy Ion Collisions with ECHO-QGP

It is believed that very strong magnetic fields may induce many interesting physical effects in the Quark Gluon Plasma, like the Chiral Magnetic Effect, the Chiral Separation Effect, a modification of the critical temperature or changes in the collective flow of the emitted particles. However, in the hydrodynamic numerical simulations of Heavy Ion Collisions the magnetic fields have been either neglected or considered as external fields which evolve independently from the dynamics of the fluid. To address this issue, we recently modified the ECHO-QGP code, including for the first time the effects of electromagnetic fields in a consistent way, although in the limit of an infinite electrical conductivity of the plasma (ideal magnetohydrodynamics). In this proceedings paper we illustrate the underlying 3+1 formalisms of the current version of the code and we present the results of its basic preliminary application in a simple case. We conclude with a brief discussion of the possible further developments and future uses of the code, from RHIC to FAIR collision energies.

Anomalous chiral transport in heavy ion collisions from Anomalous-Viscous Fluid Dynamics

Chiral anomaly is a fundamental aspect of quantum theories with chiral fermions. How such microscopic anomaly manifests itself in a macroscopic many-body system with chiral fermions, is a highly nontrivial question that has recently attracted significant interest. As it turns out, unusual transport currents can be induced by chiral anomaly under suitable conditions in such systems, with the notable example of the Chiral Magnetic Effect (CME) where a vector current (e.g. electric current) is generated along an external magnetic field. A lot of efforts have been made to search for CME in heavy ion collisions, by measuring the charge separation effect induced by the CME transport. A crucial challenge in such effort, is the quantitative prediction for the CME signal. In this paper, we develop the Anomalous-Viscous Fluid Dynamics (AVFD) framework, which implements the anomalous fluid dynamics to describe the evolution of fermion currents in QGP, on top of the neutral bulk background described by the VISH2+1 hydrodynamic simulations for heavy ion collisions. With this new tool, we quantitatively and systematically investigate the dependence of the CME signal to a series of theoretical inputs and associated uncertainties. With realistic estimates of initial conditions and magnetic field lifetime, the predicted CME signal is quantitatively consistent with measured change separation data in 200GeV Au–Au collisions. Based on analysis of Au–Au collisions, we further make predictions for the CME observable to be measured in the planned isobaric (Ru–Ru v.s. Zr–Zr) collision experiment, which could provide a most decisive test of the CME in heavy ion collisions.