[Paper Review] The PHOBOS Glauber Monte Carlo

B. Alver, M. Baker+2 more|ArXiv.org|May 28, 2008

High-Energy Particle Collisions ResearchPhysics and Astronomy136 citations

TL;DR

This paper presents the PHOBOS Monte Carlo Glauber model for simulating initial-state geometry in heavy-ion collisions, using stochastic nucleon positioning and impact parameter sampling to calculate $N_{\text{part}}$, $N_{\text{coll}}$, and eccentricity. The key contribution is a publicly available, user-friendly implementation with detailed event-by-event observables, enabling precise studies of fluctuation-driven effects in relativistic heavy-ion physics at RHIC and the LHC.

ABSTRACT

``Glauber'' models are used to calculate geometric quantities in the initial state of heavy ion collisions, such as impact parameter, number of participating nucleons and initial eccentricity. The four RHIC experiments have different methods for Glauber Model calculations, leading to similar results for various geometric observables. In this document, we describe an implementation of the Monte Carlo based Glauber Model calculation used by the PHOBOS experiment. The assumptions that go in the calculation are described. A user's guide is provided for running various calculations.

Motivation & Objective

• To provide a detailed, reproducible implementation of the Monte Carlo Glauber model for initial-state geometry in heavy-ion collisions.
• To enable accurate calculation of event-by-event geometric observables such as $N_{\text{part}}$, $N_{\text{coll}}$, and eccentricity ($\epsilon_{\text{part}}$, $\epsilon_{\text{RP}}$) for PHOBOS analyses.
• To offer a user-friendly, extensible codebase with a tutorial and documentation for both experimental and theoretical applications.
• To support studies of fluctuations in the initial state by enabling event-by-event sampling of participant configurations.
• To standardize and document the PHOBOS-specific Glauber model implementation for consistency across analyses and collaboration with other experiments.

Proposed method

• Stochastic placement of nucleons within nuclei using radial probability distributions derived from electron scattering data, with a Fermi or Gaussian form for charge density.
• Incorporation of a minimum inter-nucleon separation ($d_{\text{min}}$) to prevent unphysical clustering, with default at 0.4 fm.
• Random sampling of impact parameter $b$ from a $b$-weighted distribution up to $b_{\text{max}} \approx 20$ fm, with nuclei positioned at $(-b/2, 0, 0)$ and $(b/2, 0, 0)$.
• Binary collisions determined by transverse distance: two nucleons collide if their separation is less than the 'ball diameter' $D = \sqrt{\sigma_{\text{NN}} / \pi}$.
• Use of the eikonal approximation: nucleons travel straight along the beam direction, with no longitudinal dynamics.
• Event-by-event calculation of geometric observables including $N_{\text{part}}$, $N_{\text{coll}}$, and moments of participant positions for eccentricity computation.

Experimental results

Research questions

• RQ1 How does the PHOBOS Monte Carlo Glauber model generate event-by-event initial-state geometry in heavy-ion collisions?
• RQ2 What is the impact of nucleon position stochasticity and minimum separation on the distribution of $N_{\text{part}}$ and $N_{\text{coll}}$?
• RQ3 How do participant eccentricity $\epsilon_{\text{part}}$ and reaction-plane eccentricity $\epsilon_{\text{RP}}$ vary with $N_{\text{part}}$ across different collision systems?
• RQ4 To what extent do event-by-event fluctuations in geometry affect the initial state of Au+Au, Cu+Cu, and Pb+Pb collisions at RHIC and LHC energies?
• RQ5 How can a standardized, publicly available Glauber model implementation support consistent analysis across heavy-ion experiments?

Key findings

• The model successfully reproduces expected distributions of $N_{\text{part}}$ and $N_{\text{coll}}$ for Cu+Cu, Au+Au, and Pb+Pb collisions at RHIC and LHC energies, as shown in Fig. 2 with 10,000 events.
• The participant eccentricity $\epsilon_{\text{part}}$ is found to be significantly larger than $\epsilon_{\text{RP}}$ at low $N_{\text{part}}$, indicating strong non-Gaussian fluctuations in the initial state.
• For all systems, $\epsilon_{\text{part}}$ decreases with increasing $N_{\text{part}}$, reflecting the smoothing of geometry in central collisions.
• The code implementation supports accurate calculation of $\epsilon_{\text{part}}$ using the formula $\epsilon_{\text{part}} = \sqrt{(\text{VarY}-\text{VarX})^2 + 4\text{VarXY}^2}/(\text{VarY}+\text{VarX})$, with event-by-event moments stored in the output ntuple.
• The total nucleus-nucleus cross section is calculated internally during the Run() function and accessible via GetTotXSect(), with values consistent across event samples.
• The model is validated through comparison of $N_{\text{part}}$ and $N_{\text{coll}}$ distributions with expectations, and the code is publicly available for use in standalone or embedded analysis workflows.