[Paper Review] Hydrodynamic analysis of non-central Pb+Pb collisions at 158A GeV

Tetsufumi Hirano, Keiichi Tsuda+1 more|ArXiv.org|Nov 27, 2000

High-Energy Particle Collisions Research3 citations

TL;DR

This study presents the first full (3+1) dimensional relativistic hydrodynamic simulation of non-central Pb+Pb collisions at 158 A GeV, using tuned initial conditions from central collision data to reproduce transverse mass spectra and rapidity distributions. It introduces a Monte Carlo method to accurately compute particle yields from resonance decays and validates the wounded nucleon scaling ansatz for initial conditions in non-central collisions, showing good agreement with experimental pion rapidity data from NA49 and WA98.

ABSTRACT

We analyze non-central heavy-ion collisions at the relativistic energy within a full (3+1) dimensional hydrodynamic model. First, the initial parameters in the hydrodynamic model are chosen so that we reproduce the experimental data of both the rapidity distribution and the slope of transverse mass distribution in central Pb + Pb collisions at 158 $A$ GeV at the CERN SPS. We next study the validity of the ansatz of wounded nucleon scaling for the initial condition of the hydrodynamic model through analysis of the rapidity distribution of negative pions in non-central collisions. Moreover, a simple Monte Carlo method is introduced to exactly calculate the particle distribution from resonance decays.

Motivation & Objective

• To develop a comprehensive (3+1) dimensional hydrodynamic model for non-central Pb+Pb collisions at SPS energy to study collective flow and phase transition phenomena.
• To calibrate initial conditions in the hydrodynamic model using central collision data (rapidity and transverse mass spectra) for consistency and predictive power.
• To test the validity of the wounded nucleon scaling ansatz for initial energy density in non-central collisions using experimental pion rapidity distributions.
• To implement and apply a novel Monte Carlo method for exact calculation of particle spectra from resonance decays, including phase-space and momentum distributions.
• To provide a foundation for future hydrodynamic studies of elliptic flow, QGP phase transitions, and anisotropic flows in heavy-ion collisions.

Proposed method

• A full (3+1) dimensional relativistic hydrodynamic model is employed, solving the relativistic hydrodynamic equations with a realistic equation of state (EOS) for nuclear matter.
• Initial conditions are set using central collision data (rapidity and transverse mass spectra) to fix freeze-out temperature and radial flow velocity.
• The wounded nucleon scaling ansatz is tested by comparing simulated pion rapidity distributions in non-central collisions with experimental data from NA49 and WA98.
• A stochastic Monte Carlo algorithm is developed to compute particle yields from resonance decays: random momenta are sampled from the Bose-Einstein distribution in the resonance rest frame, then boosted to the lab frame.
• The method includes momentum generation, angular sampling, Lorentz boosting, and net emission/absorption counting via the four-current $P^\mu d\sigma_\mu$ on the freeze-out hyper-surface.
• Final particle spectra are obtained by summing contributions from all fluid elements on the freeze-out hyper-surface, with normalization using total emitted/absorbed resonance numbers.

Experimental results

Research questions

• RQ1 Is the wounded nucleon scaling ansatz valid for setting initial energy density in non-central Pb+Pb collisions at 158 A GeV?
• RQ2 Can a full (3+1) dimensional hydrodynamic model reproduce the rapidity distribution of negative pions in non-central collisions?
• RQ3 How accurately can resonance decays be simulated in hydrodynamic models using a Monte Carlo approach?
• RQ4 What is the impact of initial condition tuning on the predictive power of hydrodynamic models in non-central heavy-ion collisions?
• RQ5 Does the hydrodynamic model with tuned parameters provide a consistent description of both central and non-central Pb+Pb collisions at SPS energy?

Key findings

• The wounded nucleon scaling ansatz provides a good description of initial energy density in non-central Pb+Pb collisions, as confirmed by agreement with experimental pion rapidity distributions.
• The full (3+1)D hydrodynamic model successfully reproduces the rapidity distribution of negative pions in non-central collisions, validating the model's predictive capability.
• The Monte Carlo method for resonance decay contributions is effective and numerically stable, enabling accurate particle spectrum calculations from complex decay chains.
• The model's initial conditions, calibrated on central collision data, yield consistent radial flow and freeze-out temperature parameters across central and non-central events.
• The simulation demonstrates that hydrodynamics remains a viable framework for describing non-central heavy-ion collisions at SPS energy, especially for collective flow and phase transition studies.
• The study establishes a benchmark for future (3+1)D hydrodynamic simulations by providing a validated method for resonance decay contributions and initial condition tuning.