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Hydrodynamization and thermalization in heavy-ion collisions: a kinetic theory perspective

Caio V. P. de Brito, Gabriel S. Denicol

TL;DR

This work addresses how hydrodynamics emerges in the early, rapidly expanding quark–gluon plasma by comparing exact kinetic‑theory solutions to hydrodynamic closures in Bjorken flow. Using the Boltzmann equation in relaxation‑time approximation, solved via the method of moments for irreducible moments $\varrho_{n,\ell}$, it shows that the energy‑momentum tensor can be well described by hydrodynamics even when the single‑particle distribution $f_{\mathbf{k}}$ remains far from local equilibrium, as $\pi/\varepsilon$ stays near hydrodynamic values while $\delta f_{\mathbf{k}}$ deviates substantially from the 14‑moment closure. The 14‑moment truncation underestimates the true nonequilibrium distribution, and photon observables, including the photon emission rate $k_0 \frac{d N}{d^3 \mathbf{k}}$ and the momentum anisotropy $\epsilon_{2,\mathbf{k}}$, reveal stronger non‑equilibrium signals at low $k_0/T$ and an increasing discrepancy at higher $k_0/T$, suggesting early photons as potential probes of hydro versus kinetic behavior. The study underscores the need for moment resummation in kinetic descriptions and provides a kinetic‑theory benchmark for interpreting early‑time photon signals and the validity range of hydrodynamic modeling in heavy‑ion collisions.

Abstract

Understanding the applicability of fluid-dynamical models to describe the hot and dense matter produced in the early stages of hadronic collisions is a fundamental problem in the field. In particular, it is not clear to what degree this hydrodynamization process requires proximity to a local equilibrium state. In this contribution, we study this problem in kinetic theory considering an ultrarelativistic gas undergoing strong longitudinal expansion, assuming Bjorken flow. We solve the Boltzmann equation and verify that the system displays considerable deviations from local equilibrium, even though the energy-momentum tensor is well described by fluid dynamics. We further quantify this effect computing the emission of photons in the quark-gluon plasma and verify whether this deviation from equilibrium can be observed.

Hydrodynamization and thermalization in heavy-ion collisions: a kinetic theory perspective

TL;DR

This work addresses how hydrodynamics emerges in the early, rapidly expanding quark–gluon plasma by comparing exact kinetic‑theory solutions to hydrodynamic closures in Bjorken flow. Using the Boltzmann equation in relaxation‑time approximation, solved via the method of moments for irreducible moments , it shows that the energy‑momentum tensor can be well described by hydrodynamics even when the single‑particle distribution remains far from local equilibrium, as stays near hydrodynamic values while deviates substantially from the 14‑moment closure. The 14‑moment truncation underestimates the true nonequilibrium distribution, and photon observables, including the photon emission rate and the momentum anisotropy , reveal stronger non‑equilibrium signals at low and an increasing discrepancy at higher , suggesting early photons as potential probes of hydro versus kinetic behavior. The study underscores the need for moment resummation in kinetic descriptions and provides a kinetic‑theory benchmark for interpreting early‑time photon signals and the validity range of hydrodynamic modeling in heavy‑ion collisions.

Abstract

Understanding the applicability of fluid-dynamical models to describe the hot and dense matter produced in the early stages of hadronic collisions is a fundamental problem in the field. In particular, it is not clear to what degree this hydrodynamization process requires proximity to a local equilibrium state. In this contribution, we study this problem in kinetic theory considering an ultrarelativistic gas undergoing strong longitudinal expansion, assuming Bjorken flow. We solve the Boltzmann equation and verify that the system displays considerable deviations from local equilibrium, even though the energy-momentum tensor is well described by fluid dynamics. We further quantify this effect computing the emission of photons in the quark-gluon plasma and verify whether this deviation from equilibrium can be observed.
Paper Structure (3 sections, 8 equations, 2 figures)

This paper contains 3 sections, 8 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Kinetic Theory in Bjorken flow
  3. Results and discussion

Figures (2)

  • Figure 1: Left panel: Shear-stress rescaled by the energy density as a function of time. Right panel: nonequilibrium single-particle momentum distribution as function of $k_0/T$.
  • Figure 2: Photon momentum anisotropy as function of $k_0/T$ at time $\tau = 0.8$ fm.