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Heavy ion event generator HYDJET++ (HYDrodynamics plus JETs)

I. P. Lokhtin, L. V. Malinina, S. V. Petrushanko, A. M. Snigirev, I. Arsene, K. Tywoniuk

arXiv:0809.2708v2hep-ph

TL;DR

The paper addresses the need for fast Monte Carlo tools that jointly model collective soft production and hard in-medium processes in relativistic heavy-ion collisions. HYDJET++ combines independent hydrodynamic and fragmentation components, providing a generator for RHIC, LHC, and lower-energy studies subject to its collision-scope restrictions.

  • Problem

    Existing heavy-ion event generators generally do not simultaneously treat collective flow in soft production and hard in-medium multi-parton production.

  • Method

    HYDJET++ independently combines a hydrodynamic thermal state with a hard multi-parton-fragmentation state, including flow, resonance decays, rescattering, energy loss, and nuclear shadowing.

  • Results

    HYDJET++ provides a generator for heavy-ion multiparticle production from RHIC and LHC energies down to √s ∼10 GeV per nucleon pair.

  • Takeaways & Limitations

    The generator supports simultaneous studies of low- and high-pT production, collective flow, jet quenching, and detector-related heavy-ion analyses across multiple facilities.

  • Takeaways & Limitations

    HYDJET++ applies only to symmetric AA collisions of heavy ions with A >∼40 at √s >∼10 GeV per nucleon pair, with possible inadequacy in very peripheral collisions and very forward rapidities.

Abstract

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HYDJET++ is a Monte-Carlo event generator for simulation of relativistic heavy ion AA collisions considered as a superposition of the soft, hydro-type state and the hard state resulting from multi-parton fragmentation. This model is the development and continuation of HYDJET event generator (Lokhtin & Snigirev, 2006, EPJC, 45, 211). The main program is written in the object-oriented C++ language under the ROOT environment. The hard part of HYDJET++ is identical to the hard part of Fortran-written HYDJET and it is included in the generator structure as a separate directory. The soft part of HYDJET++ event is the "thermal" hadronic state generated on the chemical and thermal freeze-out hypersurfaces obtained from the parameterization of relativistic hydrodynamics with preset freeze-out conditions. It includes the longitudinal, radial and elliptic flow effects and the decays of hadronic resonances. The corresponding fast Monte-Carlo simulation procedure, C++ code FAST MC (Amelin et al., 2006, PRC, 74, 064901; 2008, PRC, 77, 014903) is adapted to HYDJET++. It is designed for studying the multi-particle production in a wide energy range of heavy ion experimental facilities: from FAIR and NICA to RHIC and LHC.

PROGRAM SUMMARY

HYDJET++ simulates heavy-ion events by independently superposing soft hydrodynamic hadroproduction and hard multi-parton fragmentation. It combines flow, resonance decays, partonic energy loss, and nuclear effects in a fast C++/ROOT framework usable across a broad energy range, within stated collision restrictions.

  • Physics coverage: The generator includes longitudinal, radial, and elliptic flow, resonance decays, and medium effects needed to model soft and hard observables in high-multiplicity collisions.The motivation is to provide fast but realistic Monte Carlo tools spanning bulk low-pT production and hard jets.
  • Model structure: HYDJET++ superposes independent soft hydro-type and hard multi-parton-fragmentation states in each heavy-ion event.The model continues HYDJET and uses C++ under ROOT, while retaining a separate Fortran-written hard component.
  • Hard production: The hard component uses PYTHIA and PYQUEN to generate jets, simulate rescattering with radiative and collisional energy loss, and hadronize the resulting partons.Multiple PYQUEN jets are included in the event according to a binomial distribution.
  • Soft production: The soft component generates thermal hadrons on chemical and thermal freeze-out hypersurfaces parameterized from relativistic hydrodynamics.FAST MC provides the adapted fast simulation procedure, with multiplicities modeled around a mean proportional to participating nucleons.
  • Scope and restrictions: HYDJET++ is intended for symmetric AA collisions of heavy ions with A >∼40 and c.m.s. energy √s >∼10 GeV per nucleon pair.Very peripheral collisions near b ∼2RA and very forward rapidities may produce inadequate results.

1 Introduction

Heavy-ion studies require fast Monte Carlo models that jointly describe collective soft flow and hard in-medium parton production. HYDJET++ addresses this gap by combining hydrodynamic thermal production with jet production, quenching, and other medium effects across RHIC, LHC, and lower-energy applications.

  • Motivation: Heavy-ion experiments use Monte Carlo generators to study QCD matter through multiparticle production across a wide range of collision energies.Fast realistic tools are especially needed at the LHC because of very high parton and hadron multiplicities.
  • 1 Introduction: Existing generators commonly omit either collective flow with hard production or in-medium high-pT parton production.HIJING includes jet production and quenching without significant flow, while THERMINATOR describes thermal production without hard partons.
  • HYDJET++ approach: HYDJET++ combines detailed soft hadroproduction with hard multi-parton production, medium-induced rescattering, and energy loss.Its event is the superposition of independent soft hydro-type and hard fragmentation states.
  • Energy range: At lower energies, the hard contribution becomes smaller while the soft component becomes a multi-parameter fit to data.The model is optimized for RHIC and LHC but can be used down to √s ∼10 GeV per nucleon pair at facilities such as FAIR and NICA.
  • Limitations: The model is restricted to symmetric AA collisions of heavy ions at √s >∼10 GeV and may be inadequate for very peripheral collisions or very forward rapidities.The hydro-type approximation is considered valid for central and semi-central collisions, while other production mechanisms may matter at very forward rapidities.

2 Physics model

HYDJET++ combines independently treated soft hydrodynamic and hard multi-parton components. Its hard-sector modeling includes collisional and radiative parton energy loss in an expanding QCD medium, while the soft-sector description uses a boost-invariant plasma evolution and parameterized flow.

  • HYDJET++ superposes independently treated soft hydro-type and hard multi-parton-fragmentation states.
  • The hard component models parton rescattering through both collisional and radiative energy loss.The collisional contribution is treated in the high-momentum-transfer limit, while radiative loss uses the BDMS formalism.
  • The hard-sector radiation treatment incorporates coherent medium-induced gluon emission and integrates radiated energies from the LPM minimum up to the initial parton energy.The model uses a small-angle parameterization for the gluon emission spectrum, with alternative wide-angle and collinear forms envisaged.
  • The rescattering medium is modeled as a boost-invariant longitudinally expanding QGP using a Bjorken scaling solution, with transverse expansion and viscosity omitted for numerical simplicity.Initial formation time, temperature, and active-flavour number are input parameters; non-central initial conditions are calculated from nuclear geometry.
  • The model includes nuclear shadowing and constructs hard nucleon-nucleon sub-collisions with PYTHIA-based jet production modified by PYQUEN.The hard multi-parton framework is inherited from HYDJET, while PYQUEN accounts for rescattering and energy loss in single hard sub-collisions.

3 Simulation procedure

HYDJET++ initializes collision geometry and cross sections, then independently simulates hard multi-parton and soft thermal states before combining their event records. Hard-state generation includes jet selection, optional shadowing and quenching, while soft-state generation initializes chemical and thermal freeze-out parameters.

  • Event initialization: PYTHIA initialization calculates inelastic and hard NN cross sections, tabulates nuclear geometry, and samples or fixes the impact parameter for each event.The procedure then calculates binary NN sub-collisions and participant nucleons.
  • Event assembly: After independent generation, soft and hard outputs are joined into a common event record containing particle coordinates, momenta, and decay products.Hard-state hadron formation uses PYTHIA, with resonance decays optionally following the SHARE decay table.
  • Hard-state generation: The hard state samples jet-producing NN sub-collisions with probability pjet=Sigjet/Sigin and selects their pp, np, or nn collision type.Accepted hard sub-collisions generate multi-parton production through PYTHIA.
  • Hard-state generation: Jet quenching modifies PYTHIA partons through radiative and collisional energy loss, transverse recoil, and rescattering until they leave the QGP or become thermalized.The default includes both radiative and collisional loss; alternative single-loss modes are available.
  • Hard-state generation: Shadowing optionally accepts hard sub-collisions using a factor dependent on parton type, momentum fractions, momentum-transfer scale, and production position.This test is applied for Pb, Au, Pd, or Ca beam ions when shadowing is enabled.
  • Soft-state generation: The soft state initializes chemical and thermal freeze-out parameters and includes stable hadrons and u,d,s resonances from the SHARE particle table.The resulting state is generated when soft hadroproduction is enabled.

4 Overview of HYDJET++ software structure

HYDJET++ combines C++/ROOT and Fortran components with particle and decay data files, configurable input files, and ROOT event output. Its parameters control freeze-out, flow, decays, jet production, shadowing, and PYQUEN energy loss, with RHIC-fitted and LHC-extrapolated defaults.

  • Core structure: HYDJET++ uses an object-oriented C++ main program under ROOT, while the Fortran hard component is retained as a separate directory.The package structure includes particle data, input and output files, and C++ and Fortran routines.
  • Particle and decay data: The soft component stores properties for 360 stable hadrons and resonances in particles.data and decay channels with branching ratios in tabledecay.txt.These files follow the structure of SHARE and THERMINATOR particle data tables.
  • Input parameters: RunInputHydjet controls collision, freeze-out, flow, decay, jet, shadowing, and PYQUEN parameters, including temperatures, chemical potentials, geometry, and anisotropies.Input flags can switch hydro production, jet production, jet quenching, hadron decays, weak decays, and shadowing on or off.
  • Default configurations: RHIC default parameters were fitted to data, whereas LHC defaults are a rough extrapolation from RHIC and may be varied by the user.The available templates target Au+Au at √s = 200A GeV and Pb+Pb at √s = 5500A GeV.
  • Input parameters: Users must specify the event count, beam energy, nuclear mass, and centrality-generation settings, while the random seed and other defaults may be changed.The impact parameter can be fixed or sampled between specified limits.
  • Output: The ROOT output contains the full event tree, including primary particles, decay products, coordinates, momenta, and parent indices for reconstructing event history.The output is written to a user-specified file or RunOutput.root by default.

5 Installation instructions

Installing HYDJET++ on Linux requires C++ and Fortran compilers plus ROOT libraries and include files. The package is compiled from the main HYDJET directory into tree- or histogram-output executables.

  • Package contents: The downloadable package contains the Makefile, input files, HYDJET source and data directories, PYQUEN Fortran files, and documentation.The archive includes RHIC and LHC input templates.
  • Requirements: Linux installation requires C++ and Fortran compilers together with ROOT libraries and include files.The main programs support ROOT tree or histogram output.
  • Compilation: Running make builds HYDJET for ROOT tree output, while make -f Makefile_HISTO builds HYDJET_HISTO for histogram output.The resulting executable is created in the main HYDJET directory.

6 Validation of HYDJET++ with experimental RHIC data

HYDJET++ is validated against RHIC Au+Au data across particle yields, spectra, pseudorapidity distributions, and elliptic flow. The model combines hydro and jet contributions to describe observables over a broad kinematic range.

  • Hadron abundances: Hadron abundance ratios were used to fix chemical freeze-out parameters for central Au+Au collisions at √s = 200A GeV.The fitted parameters include T_ch = 0.165 GeV and γs = 1.
  • Low-pT spectra: Low-pT pion, kaon, and proton spectra fixed the thermal freeze-out temperature at T_th = 0.1 GeV and central maximal transverse flow rapidity at ρmax = 1.1.The fits used transverse-mass spectra near mid-rapidity across collision centralities.
  • Pseudorapidity spectra: The pseudorapidity distributions of charged hadrons constrain the maximum longitudinal flow rapidity to ηmax = 3.3 and separate hydro and jet multiplicity contributions.The relative soft and hard contributions are fixed through the centrality dependence of dN/dη.
  • High-pT spectra: High-pT charged-pion spectra constrain PYQUEN energy-loss parameters using τ0 = 0.4 fm/c, Nf = 2, and T0 = 0.3 GeV.The model obtains a reasonable fit to STAR data at √s = 200A GeV across centralities.
  • Elliptic flow: HYDJET++ reproduces charged-hadron elliptic-flow measurements for two centrality sets using hydro and jet components.The flow parameters δ and ϵ affect differential azimuthal dependences but not azimuthally integrated observables.

7 Test run description

The test run provides ROOT macros for generating and reading the three main validation observables: charged-hadron pseudorapidity, positive-pion transverse momentum, and charged-hadron elliptic flow.

  • Available macros: The RootMacros directory contains scripts for comparing HYDJET++ observables with Au+Au data at √s = 200A GeV.The macros support different collision centralities.
  • Pseudorapidity: fig_eta_Phobos.C and fig_eta_Phobos_read.C generate charged-hadron pseudorapidity spectra and use PHOBOS data.The read macro requires the user to specify the number of events.
  • Transverse momentum: fig_PTH_STAR.C and fig_PTH_STAR_read.C generate positive-pion transverse-momentum spectra and use STAR data.The read macro requires the user to specify the number of events.
  • Elliptic flow: fig_v2_STAR.C and fig_v2_STAR_read.C generate charged-hadron elliptic-flow coefficients v2(pT) using STAR data.The read macro specifies the number of events through fig_v2_test_read.C.

8 Conclusion

HYDJET++ models relativistic heavy-ion collisions as a superposition of soft hydrodynamic and hard multi-parton fragmentation states. It reproduces diverse RHIC observables and can be applied across a wider energy range, down to √s ∼10 GeV per nucleon pair.

  • Model scope: HYDJET++ combines thermal soft hadroproduction with hard multi-parton fragmentation, including collective flow, resonance decays, jet quenching, and nuclear shadowing.The soft state is generated on chemical and thermal freeze-out hypersurfaces, while the hard component is inherited from HYDJET.
  • Validation: The generator simultaneously reproduces hadron yields, pseudorapidity and transverse-momentum spectra, and elliptic flow for RHIC Au+Au collisions across centralities.These observables are described over a wide kinematic range.
  • Energy range: HYDJET++ can study multi-particle production down to √s ∼10 GeV per nucleon pair at other heavy-ion facilities.Although optimized for RHIC and LHC energies, the conclusion identifies a wider usable energy range.
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