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Evolution of Hot, Dissipative Quark Matter in Relativistic Nuclear Collisions

Azwinndini Muronga, Dirk H. Rischke

TL;DR

This paper tackles the evolution of hot, dissipative quark matter created in relativistic nuclear collisions by solving causal Müller–Israel–Stewart hydrodynamics in a 3D Bjorken cylinder setup. It demonstrates that shear viscosity reduces longitudinal pressure, enhances transverse flow, and leads to harder $p_T$ spectra and smaller $R_{out}/R_{side}$ compared with ideal fluid dynamics. The authors connect these dynamics to observable signatures by computing single-particle spectra and HBT radii via Cooper–Frye freeze-out on isotherms and two-particle correlations, including dissipative corrections to the distribution function. The study finds that viscous effects produce entropy and increase final multiplicity, and they predict changes in HBT radii consistent with a more compact, rapidly expanding emission region. They also outline a roadmap for future work, including hadronization, finite baryon density, a phase-transition EOS, and elliptic flow in non-symmetric geometries for a more realistic comparison with experimental data.

Abstract

Non-ideal fluid dynamics with cylindrical symmetry in transverse direction and longitudinal scaling flow is employed to simulate the space-time evolution of the quark-gluon plasma produced in heavy-ion collisions at RHIC energies. The dynamical expansion is studied as a function of initial energy density and initial time. A causal theory of dissipative fluid dynamics is used instead of the standard theories which are acausal. We compute the parton momentum spectra and HBT radii from two-particle correlation functions. We find that, in non-ideal fluid dynamics, the reduction of the longitudinal pressure due to viscous effects leads to an increase of transverse flow and a decrease of the ratio $R_{out}/R_{side}$ as compared to the ideal fluid approximation.

Evolution of Hot, Dissipative Quark Matter in Relativistic Nuclear Collisions

TL;DR

This paper tackles the evolution of hot, dissipative quark matter created in relativistic nuclear collisions by solving causal Müller–Israel–Stewart hydrodynamics in a 3D Bjorken cylinder setup. It demonstrates that shear viscosity reduces longitudinal pressure, enhances transverse flow, and leads to harder spectra and smaller compared with ideal fluid dynamics. The authors connect these dynamics to observable signatures by computing single-particle spectra and HBT radii via Cooper–Frye freeze-out on isotherms and two-particle correlations, including dissipative corrections to the distribution function. The study finds that viscous effects produce entropy and increase final multiplicity, and they predict changes in HBT radii consistent with a more compact, rapidly expanding emission region. They also outline a roadmap for future work, including hadronization, finite baryon density, a phase-transition EOS, and elliptic flow in non-symmetric geometries for a more realistic comparison with experimental data.

Abstract

Non-ideal fluid dynamics with cylindrical symmetry in transverse direction and longitudinal scaling flow is employed to simulate the space-time evolution of the quark-gluon plasma produced in heavy-ion collisions at RHIC energies. The dynamical expansion is studied as a function of initial energy density and initial time. A causal theory of dissipative fluid dynamics is used instead of the standard theories which are acausal. We compute the parton momentum spectra and HBT radii from two-particle correlation functions. We find that, in non-ideal fluid dynamics, the reduction of the longitudinal pressure due to viscous effects leads to an increase of transverse flow and a decrease of the ratio as compared to the ideal fluid approximation.

Paper Structure

This paper contains 12 sections, 61 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Basics of non-ideal fluid dynamics
  3. Transport Equations
  4. Longitudinal boost invariance with transverse expansion
  5. Initial Conditions, Equation of state and transport coefficients
  6. Transverse spectra and HBT radii
  7. Freeze-out prescription
  8. Two Particle Correlations and HBT Radii
  9. Dissipative corrections to the distribution function
  10. Non-ideal versus ideal fluid dynamics
  11. Conclusions and Outlook
  12. Particle spectra and HBT radii from a cylindrically symmetric freeze-out surface

Figures (5)

  • Figure 1: The components of the shear stress tensor in units of $p_0=\varepsilon_0/3$ as a function of $r/R_0$, where $R_0$ is the initial radius of the system, at different times $t=\tau_i+n\Delta t$, $\Delta t = 0.025$ fm/c.
  • Figure 2: The freeze-out time $\tau_f(r)$ as a function of transverse coordinate $r$. (a) VNI scenario, (b) RHIC scenario.
  • Figure 3: Parton $p_\perp$ distribution for the RHIC scenario.
  • Figure 4: The mean transverse momentum (a), multiplicity (b) and transverse energy (c). The solid curves are for the ideal fluid evolution and the dashed curves are for the non-ideal fluid evolution.
  • Figure 5: HBT radii and the ratio $R_{out}/R_{side}$. The solid curves are for the ideal fluid and the dashed curves are for the non-ideal fluid.