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Manuscript Title: Heavy ion event generator HYDJET++ (HYDrodynamics plus JETs)
Authors: I.P. Lokhtin, L.V. Malinina, S.V. Petrushanko, A.M. Snigirev, I. Arsene, K. Tywoniuk
Program title: HYDJET++, version 2
Catalogue identifier: AECR_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 180(2009)779
Programming language: C++ (however there is a Fortran-written part which is included in the generator structure as a separate directory).
Computer: PC - hardware independent (both C++ and Fortran compilers and ROOT environment [1] (http://root.cern.ch/) should be installed).
Operating system: Linux (Scientific Linux, Red Hat Enterprise, FEDORA, etc.).
RAM: 50 MBytes (determined by ROOT requirements)
Keywords: Monte-Carlo event generators, relativistic heavy ion collisions, hydrodynamics, QCD jets, partonic energy loss, flow, quark-gluon plasma.
PACS: 24.10.Lx, 24.85.+p, 25.75.-q, 25.75.Bh, 25.75.Dw, 25.75.Ld, 25.75.Nq.
Classification: 11.2.

External routines: ROOT [1] (http://root.cern.ch/), PYTHIA event generator (version 6.401 or later) (http://home.thep.lu.se/~torbjorn/Pythia.html), PYQUEN event generator (version 1.5 or later) (http://lokhtin.web.cern.ch/lokhtin/pyquen/)

Nature of problem:
The experimental and phenomenological study of multi-particle production in relativistic heavy ion collisions is expected to provide valuable information on the dynamical behaviour of strongly-interacting matter in the form of quark-gluon plasma (QGP) [2-4], as predicted by lattice Quantum Chromodynamics (QCD) calculations. Ongoing and future experimental studies in a wide range of heavy ion beam energies require the development of new Monte-Carlo (MC) event generators and improvement of existing ones. Especially for experiments at the CERN Large Hadron Collider (LHC), implying very high parton and hadron multiplicities, one needs fast (but realistic) MC tools for heavy ion event simulations [5-7]. The main advantage of MC technique for the simulation of high-multiplicity hadroproduction is that it allows a visual comparison of theory and data, including if necessary the detailed detector acceptances, responses and resolutions. The realistic MC event generator has to include maximum possible number of observable physical effects, which are important to determine the event topology: from the bulk properties of soft hadroproduction (domain of low transverse momenta pT ~< 1GeV/c) such as collective flows, to hard multi-parton production in hot and dense QCD-matter, which reveals itself in the spectra of high-pT particles and hadronic jets. Moreover, the role of hard and semi-hard particle production at LHC can be significant even for the bulk properties of created matter, and hard probes of QGP became clearly observable in various new channels [8-11]. In the majority of the available MC heavy ion event generators, the simultaneous treatment of collective flow effects for soft hadroproduction and hard multi-parton in-medium production (medium-induced partonic rescattering and energy loss, so called "jet quenching") is lacking. Thus, in order to analyze existing data on low and high-pT hadron production, test the sensitivity of physical observables at the upcoming LHC experiments (and other future heavy ion facilities) to the QGP formation, and study the experimental capabilities of constructed detectors, the development of adequate and fast MC models for simultaneous collective flow and jet quenching simulations is necessary. HYDJET++ event generator includes detailed treatment of soft hadroproduction as well as hard multi-parton production, and takes into account known medium effects.

Solution method:
A heavy ion event in HYDJET++ is a superposition of the soft, hydro-type state and the hard state resulting from multi-parton fragmentation. Both states are treated independently. HYDJET++ is the development and continuation of HYDJET MC model [12]. The main program is written in the object-oriented C++ language under the ROOT environment [1]. The hard part of HYDJET++ is identical to the hard part of Fortran-written HYDJET [13] (version 1.5) and is included in the generator structure as a separate directory. The routine for generation of single hard NN collision, generator PYQUEN [12,14], modifies the "standard" jet event obtained with the generator PYTHIA 6.4 [15]. The event-by-event simulation procedure in PYQUEN includes
  1. generation of initial parton spectra with PYTHIA and production vertexes at given impact parameter;
  2. rescattering-by-rescattering simulation of the parton path in a dense zone and its radiative and collisional energy loss;
  3. final hadronization according to the Lund string model for hard partons and in-medium emitted gluons.
Then the PYQUEN multi-jets generated according to the binomial distribution are included in the hard part of the event. The mean number of jets produced in an AA event is the product of the number of binary NN sub-collisions at a given impact parameter and the integral cross section of the hard process in NN collisions with the minimum transverse momentum transfer pTmin . In order to take into account the effect of nuclear shadowing on parton distribution functions, the impact parameter dependent parameterization obtained in the framework of Glauber-Gribov theory [16] is used. 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 (the adapted C++ code FAST MC [17,18]). Hadron multiplicities are calculated using the effective thermal volume approximation and Poisson multiplicity distribution around its mean value, which is supposed to be proportional to the number of participating nucleons at a given impact parameter of AA collision. The fast soft hadron simulation procedure includes
  1. generation of the 4-momentum of a hadron in the rest frame of a liquid element in accordance with the equilibrium distribution function;
  2. generation of the spatial position of a liquid element and its local 4-velocity in accordance with phase space and the character of motion of the fluid;
  3. the standard von Neumann rejection/acceptance procedure to account for the difference between the true and generated probabilities;
  4. boost of the hadron 4-momentum in the center mass frame of the event;
  5. the two- and three-body decays of resonances with branching ratios taken from the SHARE particle decay table [19].
The high generation speed in HYDJET++ is achieved due to almost 100% generation effciency of the "soft" part because of the nearly uniform residual invariant weights which appear in the freeze-out momentum and coordinate simulation. Although HYDJET++ is optimized for very high energies of RHIC and LHC colliders (c.m.s. energies of heavy ion beams √s = 200 and 5500 GeV per nucleon pair respectively), in practice it can also be used for studying the particle production in a wider energy range down to √s ~ 10 GeV per nucleon pair at other heavy ion experimental facilities. As one moves from very high to moderately high energies, the contribution of the hard part of the event becomes smaller, while the soft part turns into just a multi-parameter fit to the data.

Restrictions:
HYDJET++ is only applicable for symmetric AA collisions of heavy (A ~> 40) ions at high energies (c.m.s. energy √s ~> 10 GeV per nucleon pair). The results obtained for very peripheral collisions (with the impact parameter of the order of two nucleus radii, b ~ 2RA,) and very forward rapidities may be not adequate.

Additional comments:
Accessibility http://cern.ch/lokhtin/hydjet++

Running time:
The generation of 100 central (0-5%) Au+Au events at √s = 200A GeV (Pb+Pb events at √s = 5500A GeV) with default input parameters takes about 7 (85) minutes on a PC 64 bit Intel Core Duo CPU @ 3 GHz with 8 GB of RAM memory under Red Hat Enterprise.

References:
[1] I.P. Lokhtin, A.M. Snigirev, Eur. Phys. J. C 46 (2006) 211.
[2] N.S. Amelin, R. Lednicky, T.A. Pocheptsov, I.P. Lokhtin, L.V. Malinina, A.M. Snigirev, Iu.A. Karpenko and Yu.M. Sinyukov, Phys. Rev. C 74 (2006) 064901.
[3] N.S. Amelin, I. Arsene, L. Bravina, Iu.A. Karpenko, R. Lednicky, I.P. Lokhtin, L.V. Malinina, A.M. Snigirev and Yu.M. Sinyukov, Phys. Rev. C 77 (2008) 014903.
[4] Proceedings of 20th International Conference on Ultra-Relativistic Nucleus- Nucleus Collisions Quark Matter 2008 (Jaipur, India, February 4-10, 2008), J. Phys. G, in press.
[5] F. Carminati et al. [ALICE Collaboration], J. Phys. G 30 (2004) 1517.
[6] B. Alessandro et al. [ALICE Collaboration], J. Phys. G 32 (2006) 1295.
[7] D. d Enterria et al. [CMS Collaboration], J. Phys. G 34 (2007) 2307.
[8] N. Armesto (ed.) et al., J. Phys. G 35 (2008) 054001.
[9] A. Accardi et al., CERN-2004-009-B, e-print: hep-ph/0310274.
[10] M. Bedjidian et al., CERN-2004-009-C, e-print: hep-ph/0311048.
[11] F. Arleo et al., CERN-2004-009-C, e-print: hep-ph/0311131.
[12] I.P. Lokhtin and A.M. Snigirev, Eur. Phys. J. C 45 (2006) 211.
[13] http://cern.ch/lokhtin/hydro/hydjet.html .
[14] http://cern.ch/lokhtin/pyquen .
[15] T. Sjostrand, S. Mrenna and P. Skands, JHEP 0605 (2006) 026 (http://home.thep.lu.se/~torbjorn/Pythia.html).
[16] K. Tywoniuk, I.C. Arsene, L. Bravina, A.B. Kaidalov and E. Zabrodin, Phys. Lett. B 657 (2007) 170.
[17] N.S. Amelin et al., Phys. Rev. C 74 (2006) 064901.
[18] N.S. Amelin et al., Phys. Rev. C 77 (2008) 014903. 41
[17] N.S. Amelin et al., Phys. Rev. C 74 (2006) 064901.
[18] N.S. Amelin et al., Phys. Rev. C 77 (2008) 014903.
[19] G. Torrieri at al., Comput. Phys. Coommun. 167 (2005) 229.