Beam Energy Scan Research Articles

Heavy-Ion Collisions toward High-Density Nuclear Matter.

In the present paper, the current efforts in heavy-ion collisions toward high-density nuclear matter will be discussed. First, the essential points learned from RHIC and LHC will be reviewed. Then, the present data from the STAR Beam Energy Scan are discussed. Finally, the current efforts, NICA, FAIR, HIAF, and J-PARC-HI (heavy ion) are described. In particular, the efforts of the J-PARC-HI project are described in detail.

(3+1) -D viscous hydrodynamics at finite net baryon density: Identified particle spectra, anisotropic flows, and flow fluctuations across energies relevant to the beam-energy scan at RHIC

To study the bulk properties of the quark-gluon-plasma (QGP) produced at the beam energy scan (BES) energies at the Relativistic Heavy Ion Collider (RHIC), we extend the (3+1)-dimensional viscous hydrodynamics CLVisc to include net baryon number conservation and Israel-Stewart-like equation for baryon diffusion with the NEOS-BQS equation of state, fluctuating initial conditions from Monte-Carlo Glauber model, and the afterburner SMASH. This integrated framework is shown to provide a good description of identified particle spectra, mean transverse momenta and anisotropic flows for different centralities and over a wide range of collision energies (7.7-62.4 GeV). It is found that the mean momenta of identified particles and anisotropic flows increases mildly with the collision energy due to larger radial flow. We further compute the multiple-particle cumulant ratio $v_2\{4\}/v_2\{2\}$ of elliptic flow across BES energies, and find that the relative fluctuations of elliptic flow are insensitive to the collision energy, consistent with the preliminary STAR data. Our model provides a benchmark for understanding the RHIC-BES data and studying the critical properties and phase structure of hot and dense QCD matter.

Lattice simulations of the QCD chiral transition at real baryon density

State-of-the-art lattice QCD studies of hot and dense strongly interacting matter currently rely on extrapolation from zero or imaginary chemical potentials. The ill-posedness of numerical analytic continuation puts severe limitations on the reliability of such methods. Here we use the more direct sign reweighting method to perform lattice QCD simulation of the QCD chiral transition at finite real baryon density on phenomenologically relevant lattices. This method does not require analytic continuation and avoids the overlap problem associated with generic reweighting schemes, so has only statistical but no uncontrolled systematic uncertainties for a fixed lattice setup. This opens up a new window to study hot and dense strongly interacting matter from first principles. We perform simulations up to a baryochemical potential-temperature ratio of $\mu_B/T=2.5$ covering most of the RHIC Beam Energy Scan range in the chemical potential. We also clarify the connection of the approach to the more traditional phase reweighting method.

Constructing probability density function of net-proton multiplicity distributions using Pearson curve method

The probability density functions of proton, anti-proton, and net-proton multiplicity distributions are constructed from the Beam Energy Scan results of the STAR experiment using the Pearson curve method. The constructed distributions of proton and anti-proton are compared with Poisson and Binomial distributions. The net-proton probability distributions are compared with Skellam distributions to study the O(4) criticality near the chiral crossover transition. The $$C_{6}/C_{2}$$ results estimated from the obtained PDFs are compared with Skellam and Binomial baselines for the Beam Energy Scan data. The current study shows some signatures of O(4) criticality, which can be further investigated by precision measurements of the cumulants and understanding the contribution of non-critical fluctuations to them. This study also provides a baseline for the higher order cumulant measurement in the upcoming RHIC BES II program and future LHC run.

Off-equilibrium non-Gaussian fluctuations near the QCD critical point: an effective field theory perspective

The non-Gaussian fluctuations of baryon density are sensitive to the presence of the conjectured QCD critical point. Their observational consequences are crucial for the ongoing experimental search for this critical point through the beam energy scan program at Relativistic Heavy Ion Collider (RHIC). In the expanding fireball created in a heavy-ion collision, critical fluctuations would inescapably fall out of equilibrium and require a systematic description within a dynamical framework. In this paper, we employ newly developed effective field theory (EFT) for fluctuating hydrodynamics to study the real-time critical non-Gaussian fluctuations of a conserved charge density. In particular, we derive the evolution equations for multi-point correlators of density fluctuations and obtain the closed-form solutions with arbitrary initial conditions that can readily be implemented in realistic simulations for heavy-ion collisions. We find that non-linear interactions among noise fields, which are missing in traditional stochastic hydrodynamics, could potentially contribute to the quartic (fourth-order) fluctuations in the scaling regime even at tree level in off-equilibrium situations.

Strange Hadron Production in Au+Au Collisions at √SNN = 54.4 GeV

The RHIC Beam Energy Scan (BES) program was proposed to study the QCD phase transition. As a sensitive probe to the transition from the hadron gas to the Quark-Gluon Plasma, the particle ratios of strange hadrons are measured to study the properties of nuclear matter. Recently, the production of strange hadrons (KS0, Λ, Ξ, Ω, and ϕ) at mid-rapidity (|y|<0.5) in Au+Au collisions at √SNN = 54.4 GeV were measured by the STAR experiment at RHIC. In this paper nuclear modification factor, baryon-to-meson ratio, as well as the overall integrated yields of these strange hadrons at √SNN = 54.4 GeV are presented. In particular, the multi-strange baryon-to-meson ratio N(Ω− + Ω¯+)/[2N(ϕ)] is studied and compared to previous measurements from other BES energies. The strange-hadron-to-pion ratios versus charged hadron multiplicity are also studied and compared to the measurements in heavy-ion collisions at higher energies.

Dynamic modeling for heavy-ion collisions

Recent theory progress in (3+1)D dynamical descriptions of relativistic nuclear collisions at finite baryon density are reviewed. Heavy-ion collisions at different collision energies produce strongly coupled nuclear matter to probe the phase structure of Quantum Chromodynamics (QCD). Dynamical frameworks serve as a quantitative tool to study properties of hot QCD matter and map collisions to the QCD phase diagram. Outstanding challenges are highlighted when confronting theoretical models with the current and forthcoming experimental measurements from the RHIC beam energy scan program.

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.

Off-of-equilibrium effects on Kurtosis Along Strangeness-Neutral Trajectories

The Beam Energy Scan program at the Relativistic Heavy Ion Collider (RHIC) is searching for the QCD critical point. The main signal for the critical point is the kurtosis of the distribution of proton yields obtained on an event by event basis where one expects a peak at the critical point. However, its exact behavior is still an open question due to out-of-equilibrium effects and uncertainty in the equation of state. Here we use a simplistic hydrodynamic model that enforces strangeness-neutrality, selecting trajectories that pass close to the critical point. We vary the initial conditions to estimate the effect of out-of-equilibrium hydrodynamics on the kurtosis signal.

QCD Critical Point and Net-Proton Number Fluctuations at RHIC-STAR

In the search of QCD phase boundary and critical point, higher-order cumulants of conserved quantities are proposed as promising observables and have been studied extensively both experimentally and theoretically. In this paper we present cumulant ratios up to 6th-order of net-proton number distributions in Au+Au collisions at √SNN = 7.7 - 200 GeV from STAR Beam Energy Scan program phase I and √S = 200 GeV p + p collisions. The results are compared with various models and Lattice QCD calculations.

Study of strange matter in STAR with express analysis

The STAR experiment provides a perfect machinery for studying strange matter for more than two decades. Recently, we developed the express procedure, which allows online monitoring of the collected physics data. The high quality of express calibration and reconstruction provides a unique possibility to run the express production and observe almost in real time strange particles including mesons, hyperons, resonances and even hypernuclei.The STAR Beam Energy Scan II program, including fixed target Au+Au collisions taken in 2018–2021, is particularly suited to study hypernuclei. Light hypernuclei are expected to be abundantly produced in low energy heavy-ion collisions. Measurements of hypernuclei production and their properties will provide information on the hyperon-nucleon interactions, which are essential ingredients for understanding nuclear matter equation of state at high net-baryon densities, such as inside neutron stars.With the heavy fragment trigger introduced for the 2021 data taking, we were able to run the express production at the STAR High Level Trigger farm. The collected data were suffcient to observe the decay process ofΛ5He →4Hepπ−with more than 11σ significance, measure binding energy as a function of hypernuclei mass, and study hypernuclei decay properties with the Dalitz plot technique.

Recent studies on hypernuclei lifetimes from STAR

The hyperon-nucleon (Y-N) interaction is an essential ingredient in the description of the equation-of-state of high-baryon-density matter. Light hypernuclei (A = 3, 4), being simple Y-N bound states, serve as cornerstones of our understanding of the Y-N interaction. Thus, precise measurements of their lifetimes are important, as they provide stringent tests to hyperon-nucleon interaction models. The yields of light hypernuclei are expected to increase from high to low energy heavy-ion collisions due to the increase in baryon density. As a result, the STAR Beam Energy Scan II program, which spans an energy range of √sNN = 3.0 − 27.0 GeV, is particularly suited for hypernuclei studies. In these proceedings, recent results on the lifetimes of light hypernuclei (3ΛH, 4ΛH, 4ΛHe) measured in √sNN = 3.0 and 7.2 GeV Au+Au collisions are presented. The relative branching ratio R3 of the 3ΛH is intimately related to its lifetime. A new R3 measurement using data from √sNN = 3.0 GeV Au+Au collisions is reported. These results will be compared to previous measurements and theoretical calculations, and the physics implications will be discussed.

Directed flow of Λ from heavy-ion collisions and hyperon puzzle of neutron stars

We examine the Λ potential from the chiral effective field theory (χEFT) via the Λ directed flow from heavy-ion collisions. We implement the Λ potential obtained from the χEFT in a vector potential version of relativistic quantum molecular dynamics. We find that the Λ potentials obtained from the χEFT assuming weak momentum dependence reproduce the Λ directed flow measured by the STAR collaboration in the Beam Energy Scan program. While the Λ directed flow is not very sensitive to the density dependence of the potential, the directed flow at large rapidities is susceptible to the momentum dependence. Thus understanding the directed flow of hyperons in a wide range of beam energy and rapidity is helpful in understanding hyperon potentials in dense matter.

Cumulants of the chiral order parameter in a nonequilibrium Bjorken expansion with a QCD critical point

To understand experimentally obtained net-proton number cumulants in the search for the QCD critical point, we study a dynamical model based on an effective quark-meson Lagrangian with chiral symmetry. We investigate the evolution of the expanding medium created in a heavy-ion collision using a spatially homogeneous fluid and a time-dependent order parameter, the sigma field evolved by a Langevin equation. We extract cumulants of the sigma field along a parametrized freeze-out curve and match the obtained freeze-out points to corresponding beam energies. These cumulants can be related to cumulants of the net-proton number through the sigma-proton coupling to provide a qualitative comparison to experimental data from STAR’s beam energy scan program. We demonstrate that the presence of the spinodal or mixed phase region around the first-order chiral phase transition allows for a wide interval of cumulants at the lowest beam energies.

Probing early-time longitudinal dynamics with the Λ hyperon's spin polarization in relativistic heavy-ion collisions

We systematically study the hyperon global polarization's sensitivity to the collision systems' initial longitudinal flow velocity in hydrodynamic simulations. By explicitly imposing local energy-momentum conservation when mapping the initial collision geometry to macroscopic hydrodynamic fields, we study the evolution of systems' orbital angular momentum (OAM) and fluid vorticity. We find that a simultaneous description of the $\Lambda$ hyperons' global polarization and the slope of pion's directed flow can strongly constrain the size of longitudinal flow at the beginning of hydrodynamic evolution. We extract the size of the initial longitudinal flow and the fraction of orbital angular momentum in the produced QGP fluid as a function of collision energy with the STAR measurements in the RHIC Beam Energy Scan program. We find that there is about 100-200 $\hbar$ OAM that remains in the mid-rapidity fluid at the beginning of hydrodynamic evolution. We further exam the effects of different hydrodynamic gradients on the spin polarization of $\Lambda$ and $\bar{\Lambda}$. The gradients of $\mu_B/T$ can change the ordering between $\Lambda$'s and $\bar{\Lambda}$'s polarization.

The BEST framework for the search for the QCD critical point and the chiral magnetic effect

The Beam Energy Scan Theory (BEST) Collaboration was formed with the goal of providing a theoretical framework for analyzing data from the Beam Energy Scan (BES) program at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory. The physics goal of the BES program is the search for a conjectured QCD critical point as well as for manifestations of the chiral magnetic effect. We describe progress that has been made over the previous five years. This includes studies of the equation of state and equilibrium susceptibilities, the development of suitable initial state models, progress in constructing a hydrodynamic framework that includes fluctuations and anomalous transport effects, as well as the development of freezeout prescriptions and hadronic transport models. Finally, we address the challenge of integrating these components into a complete analysis framework. This document describes the collective effort of the BEST Collaboration and its collaborators around the world.

Elliptic flow splittings in the Polyakov–Nambu–Jona-Lasinio transport model

To incorporate the effect of gluons on the evolution dynamics of the quark matter produced in relativistic heavy-ion collisions, we extend the three-flavor Nambu--Jona-Lasinio (NJL) transport model to include the contribution from the Polyakov loops. Imbedding the resulting pNJL partonic transport model in an extended multiphase transport (extended AMPT) model, we then study the elliptic flow splittings between particles and their antiparticles in relativistic heavy-ion collisions at beam energy scan energies. We find that a weak quark vector interaction in the partonic phase is able to describe the elliptic flow splitting between protons and antiprotons in heavy-ion collisions at $\sqrt{{s}_{NN}}=7.7$ to 39 GeV. Knowledge of the quark vector interaction is useful for understanding the equation of state of quark matter at large baryon chemical potentials and thus the location of the critical point in the QCD phase diagram.

Freezeout properties of different light nuclei at the RHIC beam energy scan

We study the transverse momentum spectra of light nuclei (deuteron, anti-deuteron and triton) produced in Gold-Gold (Au-Au) collisions in different centrality bins by the blast wave model with Tsallis statistics. The model results are in agreement with the experimental data measured by STAR Collaboration in special transverse momentum ranges. We extracted the kinetic freezeout temperature, transverse flow velocity and kinetic freezeout volume. It is observed that kinetic freezeout temperature and transverse flow velocity increases initially, and then saturates from 14.5–39 GeV, while the kinetic freezeout volume increase initially up to 19.6 GeV but saturates from 19.6–39 GeV. This may indicate that the phase transition starts in part volume that ends in the whole volume at 39 GeV and the critical point may exists somewhere in the energy range of 14.5–39 GeV. The present work observed that the kinetic freezeout temperature, transverse flow velocity and kinetic freezeout volume has a decreasing trend from central to peripheral collisions. We found the freezeout volume of triton is smaller than those of deuteron and anti-deuteron, which shows that triton freezeout earlier than that of deuteron and anti-deuteron.

Nonequilibrium kinetic freeze-out properties in relativistic heavy ion collisions from energies employed at the RHIC beam energy scan to those available at the LHC

In this paper, we investigate the kinetic freeze-out properties in relativistic heavy ion collisions at different collision energies. We present a study of standard Boltzmann-Gibbs blast-wave (BGBW) fits and Tsallis blast-wave (TBW) fits performed on the transverse momentum spectra of identified hadrons produced in $\mathrm{Au}+\mathrm{Au}$ collisions at collision energies of $\sqrt{{s}_{\mathrm{NN}}}=7.7$--200 GeV at the Relativistic Heavy Ion Collider (RHIC), and in $\mathrm{Pb}+\mathrm{Pb}$ collisions at collision energies of $\sqrt{{s}_{\mathrm{NN}}}=2.76$ and 5.02 TeV at the Large Hadron Collider (LHC). The behavior of strange and multistrange particles is also investigated. We found that the TBW model describes data better than the BGBW one overall, and the contrast is more prominent as the collision energy increases as the degree of nonequilibrium of the produced system is found to increase. From TBW fits, the kinetic freeze-out temperature at the same centrality shows a weak dependence of collision energy between 7.7 and 39 GeV, while it decreases as collision energy continues to increase up to 5.02 TeV. The radial flow is found to be consistent with zero in peripheral collisions at RHIC energies but sizable at LHC energies and central collisions at all RHIC energies. We also observed that the strange hadrons, with higher temperature and similar radial flow, approach equilibrium more quickly from peripheral to central collisions than light hadrons. The dependence of temperature and flow velocity on nonequilibrium parameter ($q\ensuremath{-}1$) is characterized by two second-order polynomials. Both $a$ and $d\ensuremath{\xi}$ from the polynomials fit, related to the influence of the system bulk viscosity, increase toward lower RHIC energies.

Many-body forces and nucleon clustering near the QCD critical point

It has been proposed that one can look for the QCD critical point (CP) by the Beam Energy Scan (BES) accurately monitoring event-by-event fluctuations. This experimental program is under way at the BNL RHIC collider. Separately, it has been studied how clustering of nucleons at freezeout affects proton multiplicity distribution and light nuclei production. It was found that even a minor increase of the range of nuclear forces dramatically increases clustering, while large correlation length $\xi$ near CP makes attraction due to binary forces unrealistically large. In this paper we show that repulsive many-body forces near CP should overcome the binary ones and effectively suppress clustering. We also discuss current experimental data and point out locations at which a certain drop in clustering may already be observed.