[Paper Review] Thermal description of particle production in ultra-relativistic heavy-ion collisions

Mariusz Michalec|ArXiv.org|Dec 14, 2001

High-Energy Particle Collisions Research4 citations

TL;DR

This paper applies a grand-canonical thermal model to particle ratios in ultra-relativistic heavy-ion collisions, finding near-identical chemical freeze-out temperatures of 168±3 MeV at CERN SPS (Pb+Pb) and 165±7 MeV at BNL RHIC (Au+Au), suggesting thermal equilibrium near the QCD phase transition. The model also reveals that moderate (~20%) in-medium mass reductions improve fits, while width modifications have minimal impact unless increased by >2x.

ABSTRACT

The grand-canonical version of the thermal model is used to analyze the ratios of particle abundances measured in ultra-relativistic heavy-ion collisions. Exactly the same model is applied to study the heavy-ion reactions at BNL AGS, CERN SPS, and BNL RHIC. A very good description is achieved for Pb+Pb collisions at SPS, and for Au+Au collisions at RHIC. In these two cases the value of the temperature characterizing the chemical freeze-out is practically same: T=168 MeV at SPS and T=165 MeV at RHIC. On the other hand, the particle ratios measured in the collisions of lighter nuclei are described only in the qualitative way. We discuss also the effect of the possible in-medium modifications of hadron masses and widths on the thermal fits. For Pb+Pb collisions at SPS and Au+Au collisions at RHIC we find that the chi^2 fits favor slightly a moderate (20%) decrease of the masses. In-medium modifications of the widths have little effect on the fits, unless they are increased by a factor larger than 2. We study in detail the thermodynamic conditions characterizing the chemical freeze-out. In particular, we find that the average baryon energy is 1.6 GeV and the average meson energy is 0.9 GeV. This difference reflects a different behavior of the mass spectra of mesons and baryons.

Motivation & Objective

• To test whether a thermal model with full chemical and thermal equilibrium describes particle production in ultra-relativistic heavy-ion collisions across different energies and systems.
• To determine if the observed particle ratios at CERN SPS and BNL RHIC are consistent with a common freeze-out temperature and chemical potential.
• To investigate the impact of in-medium modifications of hadron masses and widths on thermal fit quality.
• To examine the validity of classical statistics and excluded-volume corrections in describing hadron gas at freeze-out.
• To compare thermodynamic properties such as average baryon and meson energies across different collision systems.

Proposed method

• Application of the grand-canonical thermal model to particle abundance ratios from Pb+Pb at SPS and Au+Au at RHIC.
• Use of χ² minimization to extract optimal chemical freeze-out parameters: temperature $T_{chem}$ and baryon chemical potential $\mu^B_{chem}$.
• Incorporation of finite-size corrections, excluded-volume effects, and undersaturation of strangeness in the thermal model framework.
• Inclusion of resonance decays and weak decays in particle yield calculations to ensure accurate reconstruction of final-state particle ratios.
• Systematic variation of hadron masses and widths to assess their influence on fit quality and optimal parameters.
• Comparison of quantum statistics (Bose-Einstein/Fermi-Dirac) with classical Boltzmann statistics to assess their impact on the equation of state.

Experimental results

Research questions

• RQ1 Do particle ratios in Pb+Pb collisions at CERN SPS and Au+Au collisions at BNL RHIC exhibit consistent chemical freeze-out parameters?
• RQ2 Is the observed freeze-out temperature consistent with the critical temperature from lattice QCD simulations?
• RQ3 How do in-medium modifications of hadron masses and widths affect the quality of thermal fits to particle ratios?
• RQ4 To what extent can classical Boltzmann statistics approximate quantum statistics in the hadron gas at freeze-out?
• RQ5 What are the average energies of baryons and mesons at chemical freeze-out, and how do they differ?

Key findings

• The chemical freeze-out temperature is $T_{chem} = 168 \pm 3$ MeV for Pb+Pb at CERN SPS and $T_{chem} = 165 \pm 7$ MeV for Au+Au at BNL RHIC, indicating near-identical thermal conditions despite different beam energies.
• The fitted freeze-out temperature is very close to the lattice QCD critical temperature, suggesting that particle composition is established near the QCD phase transition.
• A moderate ~20% reduction in hadron masses improves χ² fits for Pb+Pb at SPS and Au+Au at RHIC, while larger changes degrade the fit quality.
• Increases in hadron widths by less than a factor of two have negligible effect on the fits, but larger increases significantly worsen the χ².
• The average baryon energy at freeze-out is 1.6 GeV, and the average meson energy is 0.9 GeV, indicating different mass spectrum behaviors for baryons and mesons.
• Classical Boltzmann statistics provide an excellent approximation to quantum statistics, and excluded-volume corrections do not alter the optimal $T_{chem}$ and $\mu^B_{chem}$ values when baryon and meson eigenvolumes are equal.