Source-linked AI summary
GLISSANDO: GLauber Initial-State Simulation AND mOre
Wojciech Broniowski, Maciej Rybczynski, Piotr Bozek
TL;DR
GLISSANDO addresses the need for a flexible, publicly available Glauber Monte-Carlo tool for modeling relativistic heavy-ion collision initial states. It implements multiple source and collision models, nuclear configurations, fluctuating weights, and geometry analyses, producing profiles and event characteristics for further studies. The program provides applications including cross-section and centrality determination, eccentricity analysis, fluctuation studies, and correlations of event quantities.
Problem
Publicly available Glauber Monte-Carlo software specifically dedicated to initial-state generation was lacking, while implementation details vary across broader codes.
Method
GLISSANDO generates nuclear configurations, collision sources, deposited-strength fluctuations, geometry profiles, and event observables using multiple Glauber models and configurable nuclear-position algorithms.
Results
The program provides applications for determining A+B cross sections and centrality classes, analyzing fixed- and variable-axes eccentricities, studying event-by-event fluctuations, and correlating event quantities.
Takeaways & Limitations
GLISSANDO supplies stored profiles and event information for further analyses involving jet quenching, hydrodynamics, elliptic flow, fluctuations, and proton- or deuteron-nucleus collisions.
Takeaways & Limitations
Full event output generates about 10 MB per 10,000 events and should be used only when another program will analyze the full results.
Abstract
from arXiv · showhide
GLISSANDO is a Glauber Monte-Carlo generator for early-stages of relativistic heavy-ion collisions, written in c++ and interfaced to Root. Several models are implemented: the wounded-nucleon model, the binary collisions model, the mixed model, and the model with hot-spots. Subtleties of the distribution of nucleon in the nucleus are discussed. The original geometric distribution of sources in the transverse plane can be superimposed with a statistical distribution simulating the dispersion in the generated transverse energy in each individual collision. The program generates inter alia the fixed axes (standard) and variable-axes (participant) two-dimensional profiles of the density of sources in the transverse plane and their Fourier components. These profiles can be used in further analyses of physical phenomena, such as the the jet quenching, event-by-event hydrodynamics, or analysis of the elliptic flow and its fluctuations. Characteristics of the event (multiplicities, eccentricities, Fourier coefficients, etc.) are evaluated and stored in a file for further off-line studies. A number of scripts is provided for that purpose. Supplied variants of the code can also be used for the proton-nucleus and deuteron-nucleus collisions.
Program summary
GLISSANDO is a publicly available Glauber Monte-Carlo generator for relativistic heavy-ion initial states, designed to expose model details and support varied event-by-event analyses. It implements flexible source, nuclear-profile, geometry, and collision-model choices, with outputs usable in further studies.
- Program summary: The generator supports wounded-nucleon, binary-collision, mixed, and hot-spot source models with configurable transverse-energy weights.Weights can represent varying deposition from individual elementary collisions.
- Program summary: GLISSANDO provides a publicly available package dedicated specifically to Glauber Monte-Carlo initial-state calculations.The authors motivate it by the lack of a published public package focused on this task and by differences among broader codes.
- Program summary: Users can vary nuclear density profiles, wounding profiles, source displacements, and short-range nucleon-nucleon repulsion algorithms.The program includes hard-sphere or Gaussian wounding and two algorithms for generating nuclei with repulsion constraints.
- Program summary: Variable-geometry analysis and fixed- and variable-axes density profiles are built in, including corresponding Fourier radial profiles.The outputs account for fluctuations of the fireball center of mass and moment-of-inertia axes.
- Program summary: The stored profiles and event characteristics support jet-quenching, hydrodynamic, elliptic-flow, fluctuation, and event-by-event analyses.The code also supports proton-nucleus and deuteron-nucleus collisions and uses C++ with ROOT libraries.
2 Basic method
The simulation generates nuclear configurations, collision sources, deposited strengths, and event-level observables while accounting for finite nucleon size, center-of-mass effects, and short-range repulsion. It offers multiple collision prescriptions and parameterizations intended to reproduce measured nuclear profiles.
- 2 Basic method: The event simulation generates nucleon positions, source positions and relative deposited strengths, then computes event observables and fireball profiles for output.The third stage is performed on the fly with source generation.
- 2.1 Generation of positions of nucleons: Finite nucleon size requires folding the nucleon-center distribution with the single-nucleon charge profile to reproduce the electron-scattering density.The authors use a Gaussian nucleon charge profile and adjust Woods-Saxon parameters accordingly.
- 2.1 Generation of positions of nucleons: Center-of-mass shifting shrinks the generated distribution, while nucleon repulsion increases the nuclear radius by about 1%, requiring compensation of the bare distribution parameters.The correction is needed to obtain the desired effective nuclear distribution.
- 2.1 Generation of positions of nucleons: GLISSANDO provides two nucleon-repulsion procedures, “fix-last” and “return-to-beginning,” enforcing a minimum separation d between nucleon centers.The first regenerates only the current nucleon; the second returns to the beginning after a forbidden placement.
- 2.1 Generation of positions of nucleons: The parameterizations for d = 0, 0.4, and 0.8 fm reproduce Woods-Saxon center distributions that, after folding, closely reproduce the electron-scattering profile.These formulas are implemented for the fixed-last method and require specified input settings.
- 2.2 Collision: After positioning the nuclei at impact parameter b, wounded nucleons and binary collisions are counted using hard-sphere or Gaussian prescriptions.The Gaussian option determines collision or wounding probabilities through a smooth transverse-distance profile.
3 Models
GLISSANDO implements wounded-nucleon, binary-collision, mixed, and hot-spot source models, with optional statistical fluctuations in source weights. These models assign relative deposited strengths to sources and preserve the corresponding event-average normalization.
- GLISSANDO implements wounded-nucleon, binary-collision, mixed, and hot-spot models for generating source distributions.
- Relative deposited strength: The wounded-nucleon model assigns RDS 1/2 to each wounded nucleon, while binary collisions receive RDS 1 at their collision points.
- Relative deposited strength: The mixed model assigns (1 − α)/2 to wounded nucleons and α to binary collisions, giving average RDS (1 − α)Nw/2 + αNbin.The parameter α ranges from 0 for the pure wounded-nucleon model to 1 for binary collisions only; fits cited in the paper give α = 0.145 at √sNN = 19.6 GeV.
- Hot-spot model: Hot spots model rare accepted binary collisions as sources with large RDS, causing event-to-event fluctuations while retaining the mixed-model average weight.The model uses σbin ≃ 2 mb and accepts candidate collisions with probability σbin/σw.
- Weight fluctuations: Statistical Poisson or gamma weights can be superimposed independently on wounded-nucleon and binary-collision sources.GLISSANDO supports no superposition, Poisson superposition, and gamma superposition through MODEL; the distribution parameters are Uw and Ubin.
- Weight fluctuations: Because the superposition distributions have ⟨w⟩ = 1, the average event RDS remains (1 − α)Nw/2 + αNbin.The general assignment is (1 − α)w/2 for wounded nucleons and αwσw/σbin for accepted hot-spot collisions.
4 Fixed- and variable-axes quantities
GLISSANDO characterizes fireball geometry using fixed-axes and variable-axes profiles, moments, and harmonic decompositions. Variable-axes analysis recenters and rotates each event to its principal geometry, while higher harmonics are suppressed and only a few moments are needed to parameterize the profile.
- Reference frames: Fixed-axes analysis uses the reaction-plane frame, whereas variable-axes analysis recenters each event and aligns it with the major principal axis of its second harmonic moment.The two analyses are also called standard and participant, respectively.
- Density profiles: The fireball density is expanded into radial Fourier harmonics, with symmetry eliminating selected sine or cosine components for equal or unequal nuclei.For equal nuclei, reflection symmetry removes the sine functions; unequal nuclei retain a more general decomposition.
- Radial moments: The weighting power k in radial moments is arbitrary, with k = 2 typical and larger k values emphasizing the system’s outer region.
- Variable-axes quantities: Variable-axes profiles rotate each event by its fluctuating principal-axis angle before averaging, producing participant-frame density and moments.The rotation is performed after shifting sources to the fireball center of mass and computing the ellipse of inertia.
- Variable-axes quantities: Higher harmonics are suppressed in variable-axes profiles and moments, so only a few moments effectively parameterize the profile.
- Physical interpretation: Center-of-mass shifting produces a slightly more compact distribution, while variable geometry increases initial eccentricity and affects elliptic flow analyses.
- Output and applications: GLISSANDO stores fixed- and variable-axes moments, two-dimensional profiles, and harmonic decompositions for later studies of medium shape and hydrodynamic or jet-quenching initial conditions.
5 Typical sequence of running
The running sequence covers installation, executable selection, nuclear-profile checks, event simulations, centrality determination, and eccentricity or density-profile analysis.
- Installation: GLISSANDO requires ROOT and creates executables for nucleus–nucleus, proton–nucleus, deuteron–nucleus, profile, and Gaussian-wounding simulations.The programs implement hard-sphere or Gaussian wounding profiles depending on the executable and build configuration.
- Nuclear profile: The nuclear-density workflow fits generated radial densities to a Woods–Saxon shape and adjusts bare parameters when an expulsion distance is used.The examples compare d = 0 fm with d = 0.4 fm for gold and display the resulting fit parameters in Fig. 2.
- Running simulations: Single-event hot-spot simulations produce transverse-energy distributions, while minimum-bias mixed-model runs support centrality classification by b, Nw, and RDS.RDS corresponds in essence to multiplicity-based centrality because produced-particle numbers are proportional to RDS.
- Eccentricity analysis: The scripts evaluate fixed- and variable-axes eccentricities and scaled fluctuations as functions of wounded-nucleon count, with rebinning available for smoothing.The supplied example uses rebinning parameter 1 and compares the two eccentricity conventions.
- Profile analysis: GLISSANDO stores two-dimensional fireball densities and Fourier components for later analyses such as jet quenching, event-by-event hydrodynamics, and elliptic-flow studies.The interpolation template generates values from stored two-dimensional or one-dimensional histograms.
6 Muliplicity fluctuations
The output includes quantities relevant to multiplicity fluctuations when the wounded-nucleon count in one nucleus is fixed.
- Multiplicity fluctuations: GLISSANDO provides average and scaled-variance histograms for target wounded nucleons, binary collisions, and RDS at fixed projectile wounded-nucleon number.These calculations are identified as relevant for multiplicity fluctuations at CERN SPS.
7 Other results
GLISSANDO output can be explored interactively to obtain correlations between event-level collision quantities.
- Interactive results: The ROOT browser can generate an event-by-event correlation plot between wounded nucleons and binary collisions for minimum-bias gold–gold collisions.The workflow selects the events tree and draws nwAB against nbin.
8 Using the full event tree
The full event tree stores source-level information for offline processing, but enabling it substantially increases output size.
- Full event tree: Setting FULL to 1 generates a full event tree containing each source’s X and Y coordinates, RDS weight, and event number.Additional event information, including the impact parameter, is stored in the events tree.
- Offline processing: The full event information can be processed offline with other programs through the retrieve.exe template.The sample command takes a GLISSANDO output file as input.
- Storage caveat: FULL=1 produces about 10MB per 10000 events, so it should be enabled only when another analysis program will use the full results.This is an explicit storage and usage caveat for full-event output.
9 Summary
GLISSANDO is presented as a flexible, publicly available tool for heavy-ion physics studies. Its openness supports checking, extending, and applying the code to several event-level analyses.
- GLISSANDO is intended as a useful tool for the heavy-ion community because of its flexibility and simplicity.
- The publicly available code allows users to perform check-ups, additions, and improvements.
- Provided applications include determining A+B cross-sections and centrality classes, analyzing fixed- and variable-axes eccentricities, studying event-by-event fluctuations, and correlating quantities.
A Content of the package
The package contains executables, source and build files, input configurations, and ROOT or Mathematica scripts supporting several collision systems and analyses.
- The package includes source files, headers, interpolation and retrieval code, installation scripts, and multiple makefiles.
- Input files cover minimum-bias and centrality-selected gold-gold collisions at RHIC, S-Pb collisions at SPS, proton-nucleus and deuteron-nucleus collisions, hot spots, and LHC Pb-Pb predictions.
- The package provides inputs for the hot-spot model and LHC predictions for Pb-Pb collisions.
- Included scripts analyze centrality, eccentricity, center-of-mass coordinates, two-dimensional density, Fourier profiles, labels, and stored output files.
- Additional files support profile folding, typical runs, single-event generation, and generic GLISSANDO input.
B Description of input and output
GLISSANDO accepts configurable model parameters and records simulation outputs in ROOT files. The package documentation identifies the parameter and stored-data tables used to describe these interfaces.
- Basic model parameters can be supplied in the input file, while commented lines use default values.
- The output GLISSANDO file stores variables documented in the package's data tables.
- Table B.1 describes the parameters of the input file.
C Description of the ROOT scripts
The ROOT scripts operate on GLISSANDO output files to inspect stored data and generate centrality, eccentricity, coordinate, density, and Fourier-profile analyses.
- Each ROOT script is called with the name of the ROOT file generated by GLISSANDO, with an empty argument selecting glissando.root by default.
- The scripts provide information about stored ROOT files and generate centrality windows for minimum-bias calculations.
- The eccentricity scripts plot mean and scaled standard deviation against Nw or, alternatively, impact parameter b.
- The dxdy script produces event-by-event standard deviations of fireball center-of-mass coordinates as a function of Nw.
- The density and profile2 scripts plot fixed-axes and variable-axes spatial distributions and Fourier profiles of RDS.