[Paper Review] (3+1)-D viscous hydrodynamics CLVisc at finite net baryon density: identified particle spectra, anisotropic flows and flow fluctuations across BES energies

Xiang-Yu Wu, Guang-You Qin+2 more|arXiv (Cornell University)|Jul 11, 2021

High-Energy Particle Collisions Research4 citations

TL;DR

This study extends the (3+1)-D viscous hydrodynamics model CLVisc to include net baryon number conservation and baryon diffusion via Israel-Stewart-like equations, using the NEOS-BQS EoS and event-by-event initial conditions from the Monte-Carlo Glauber model. It successfully reproduces identified particle spectra, anisotropic flows, and flow fluctuations across RHIC-BES energies (7.7–62.4 GeV), showing mild increases in mean transverse momentum and flow with energy due to enhanced radial flow, and finds that relative elliptic flow fluctuations are insensitive to collision energy, consistent with STAR data.

ABSTRACT

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.

Motivation & Objective

• To develop a realistic event-by-event hydrodynamic framework that incorporates finite net baryon density for studying QGP at RHIC-BES energies.
• To address the limitations of standard hydrodynamics in low-energy heavy-ion collisions where baryon number conservation and diffusion effects are non-negligible.
• To provide a benchmark model for understanding bulk properties of QGP and probing the QCD phase diagram, including the critical point.
• To simulate the full evolution of QCD matter from pre-equilibrium to chemical freeze-out using consistent initial conditions, EoS, and afterburner.

Proposed method

• Extends the (3+1)-dimensional viscous hydrodynamics code CLVisc to include net baryon number conservation and second-order Israel-Stewart-like equations for baryon diffusion current.
• Uses the NEOS-BQS equation of state that accounts for finite baryon chemical potential to close the hydrodynamic equations of motion.
• Generates fluctuating initial energy and net baryon density profiles using the Monte-Carlo Glauber model for event-by-event simulations.
• Applies the SMASH afterburner to simulate the dynamical evolution of the dilute hadron gas after the hydrodynamic stage.
• Performs event-by-event simulations across a wide range of beam energies (7.7–62.4 GeV) and centralities to compute observables like spectra, flow, and cumulant ratios.
• Computes multi-particle cumulant ratios such as $v_2\{2\}/v_2\{4\}$ to quantify flow fluctuations and their energy dependence.

Experimental results

Research questions

• RQ1 How do identified particle spectra and mean transverse momenta evolve with collision energy and centrality in the BES energy range?
• RQ2 To what extent do anisotropic flows ($v_2$, $v_3$) increase with beam energy, and what drives this increase?
• RQ3 How do relative flow fluctuations, quantified by $v_2\{2\}/v_2\{4\}$, depend on collision energy and centrality?
• RQ4 Is the model's prediction for flow fluctuations consistent with preliminary STAR data across BES energies?
• RQ5 Can the inclusion of baryon diffusion and finite baryon density in viscous hydrodynamics improve the description of particle spectra and flows at low energies?

Key findings

• The model successfully reproduces the mass, centrality, and collision energy dependencies of identified particle spectra and mean transverse momenta across 7.7–62.4 GeV.
• Mean transverse momenta increase mildly with beam energy and centrality, primarily due to enhanced radial flow in denser and more central systems.
• The proton mean transverse momentum is more sensitive to collision energy than pions or kaons, consistent with radial flow dominance.
• Elliptic ($v_2$) and triangular ($v_3$) flows increase mildly with beam energy, driven by growing radial flow rather than initial geometry changes.
• The multi-particle cumulant ratio $v_2\{2\}/v_2\{4\}$ shows a non-monotonic centrality dependence, with minimal relative fluctuations in mid-central collisions due to dominant geometric effects.
• Relative elliptic flow fluctuations ($v_2\{2\}/v_2\{4\}$) are insensitive to collision energy, in agreement with preliminary STAR data.