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A FAST HADRON FREEZE-OUT GENERATOR

A FAST HADRON FREEZE-OUT GENERATOR. FASTMC. a part of Universal Hydro Kinetic Model (UHKM). , R. Lednicky, T.A. Pocheptsov: Joint Institute for Nuclear Research, Dubna, Russia

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A FAST HADRON FREEZE-OUT GENERATOR

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  1. A FAST HADRON FREEZE-OUT GENERATOR FASTMC a part of Universal Hydro Kinetic Model (UHKM) , R. Lednicky, T.A. Pocheptsov: Joint Institute for Nuclear Research, Dubna, Russia I.P. Lokhtin, A.M. Snigirev , L.V. Malinina: Moscow State University, Institute of Nuclear Physics, Russia Iu.A. Karpenko, Yu.M. Sinyukov: Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine N.S. Amelin (PRC 74 064901(2006))

  2. Outline • 1. Introduction- motivation. • 2. Physical framework of the model . • 3. Hadron generation procedure . • 4. Model parameters. • Examples of calculations with generator and comparison with RHIC • experimental data • - particle ratios • - pseudorapidity • - pt-spectra • - correlation radii • 6. Conclusions, perspectives, status

  3. http://uhkm.jinr.ru The creation of the UHKM Universal Hydro Kinetic Model was initiated by Nikolai Amelin.

  4. FASTMC: Introduction-Motivation • LHC very high hadron multiplicitiesfairly fast MC- generators for event simulation. (I. P. Lokhtin and A. M.Snigirev, Phys. Lett. B378, 247 (1996), Z. Phys. C76, 99 (1997).) • FASTMC- fast Monte Carlo procedure of hadron generation • Matter is thermally equilibrated. Particle multiplicities are determined by the temperature and chemical potentials. Statistical model. Chemical freeze-out. • Particles can be generated on the chemical or thermal freeze-out hypersurface represented by a parameterization or a numerical solution of relativistic hydrodynamics. • - Standard parameterizations of the hadron freeze-out hypersurface and flow velocity profile under the assumption of a common chemical and thermal freeze-out. • so-calledBjorken-like (BlastWave) and Hubble-like parametrizations. • (F. Retiere and M. Lisa, Phys.Rev. C70 (2004) 044907; THERMINATOR: Thermal heavy-Ion generator A. Kisiel, T. Taluc, W. Broniowski, W. Florkowski, nucl-th/0504047)

  5. Introduction-Motivation • Decays of hadronic resonances is included (presently u,d and s quarks only). • Note that it is not pure “Blast-Wave” because the resonances are included - Besides standard space-like sectors associated with the volume decay, the hypersurface may also include non-space-like sectors related to the emission from the surface of expanding system (Kiev- Nantes model). -The C++ generator code is written under the ROOT framework.

  6. Physical framework of the model: Hadron multiplicities 1.We consider the hadronic matter created in heavy-ion collisions as a hydrodynamically expanding fireball with the equation of state of an ideal hadron gas. 2. “concept of effective volume” T=const and µ=const the total yield of particle species is: , total co-moving volume, ρ-particle number density 3. in central Au+Au or Pb+Pb collisions at GeV parametrizations of the T and µB: 4. All macroscopic characteristics of particle system (T,µi) are determined via a set of equilibrium distribution functions in the fluid element rest frame:

  7. Physical framework of the model: Hadron momentum distribution We suppose that a hydrodynamic expansion of the fireball ends by a sudden system breakup at given T and chemical potentials. Momentum distribution of produced hadrons keeps the thermal character of the equilibrium distribution. Cooper-Frye formula: The invariant weight It is convenient to transform the four-vectors into the fluid element rest frame, and calculate the weight in this frame In the case when the normal four-vector coincides with the fluid element flow velocity the weight is independent of x and isotropic in p. 100% efficiency the four-momenta of the generated particles transformed back to the fireball rest frame using the velocity field v.

  8. Physical framework of the model: Freeze-out surfaceparameterizations At relativistic energies, due to dominant longitudinal motion, it is convenient to substitute the Cartesian coordinates t, z by the Bjorken ones , , Similarly, it is convenient to parameterize the fluidflow four-velocity at a point x in terms of thelongitudinal z and transverse r fluid flow rapidities: , Representing the freeze-out hypersurface by the equation the hypersurface element: for the azimuthaly symmetric hypersurface we further assume the longitudinal boost invariance The local quantities (such as particle density) are then functions of τ and r only For the simplest freeze-out hypersurface

  9. Physical framework of the model: Freeze-out surfaceparameterizations The Bjorken model with hypersurface Assuming and the linear transverse flow rapidity profile: here R is the fireball transverse radius; The total effective volume for particle production at We refer this choice of the freeze-out hyper-surface and the flow 4-velocity profile as the Bjorken-like parametrization We also consider so called Cracow model scenario corresponding to the Hubble-like freeze-out hypersurface and spherically-symmetric Hubble flow with four-velocity

  10. Hadron generation procedure Initialization of the chosen model parameters The particle three-momenta in the fluid element rest frames according to the probability by sampling uniformly distributed cos(θ*p) and φ*p Calculation of Veff and particle number densities von Neumann rejection/acceptance procedure to account for diff. between the true prob. and prob. corresponding to 3-5. Residual weight simulated x, p are accepted W> ξ- a test variable randomly simulated in [0,W_max], otherwise-> 3 The mean multiplicities Multiplicities by Poisson distr. Simulation of particle freeze-out 4-coordinates in the fireball rest frame : on each hypersurface segment accord. to the element by sampling uniformly distributed r,η, φ the hadron four-momentum is boosted to the fireball rest frame Calculation of the corresponding collective flow four-velocities The two-body, three-body and many-body decays are simulated with the branching ratios calculated via ROOT utilities;-- Boltzmann equation solver

  11. Hadron generation procedure It should be stressed that a high generation speed is achieved due to 100 % generation efficiency of the freeze-out four-coordinates and four-momenta in steps 3-5 as well as due to a weak non-uniformity of the residual weight W in the cases of practical interest. For example, in the Bjorken-like model, the increase of the maximal transverse flow rapidity from zero to 0.65 leads only to a few percent decrease of the generation speed. Compared, e.g., to THERMINATOR our generator appears more than two order of magnitude faster.

  12. Validation of the fast MC procedure In the Boltzmann approximation for the equilibrium distribution function, the transverse momentum spectrum in the Bjorken-like model takes the form:

  13. Validation of the MC procedure: Exact formulae (solid line), the corresponding MC results (black triangles), MC results obtained with a constant residual weight (black points). transverse flow rapidity

  14. Model parameters: • 1.Number of events to generate. • 2.Thermodynamic parameters at chemical freeze-out: • T temperature • {µB, µS, µQ}chemical potentials per a unit charge • 3.As an option, γS < 1taking into account the strangeness suppression • 4. Volume parameters: • τ-the freeze-out proper time • R- firebal transverse radius • 5. -maximal transverse flow rapidity for Bjorken-like parametrization • ηmax -maximal space-time longitudinal rapidity whichdetermines the rapidity interval [- ηmax, ηmax] in the collision center-of-mass system. • 7.To account for the violation of the boost invariance, an option corresponding to the substitutionof the uniform distribution of the space-time longitudinalrapidity by a Gaussian distribution. • 8. Option to calculate T, µB using phenomenological dependence of

  15. The parameters used to model central Au+Au collisions at = 200 GeV parameter Bjorken-like Hubble-like T, GeV 0.165 0.165 µB, GeV 0.028 0.028 µS, GeV 0.007 0.007 µQ, GeV -0.001 -0.001 γS 1 (0.8) 1 (0.8) τ, fm/c 6.1 9.65 R, fm 10.0 8.2 ηmax2 (3,5) 2 (3,5) ρu max0.65 - Particle number ratios near mid-rapidity in centralAu + Au collisions = 200 GeV FASTMC PHENIX π -/π + 0.98 0.984 ± 0.004 K-/K+ 0.94 0.933 ±0.008 K-/ π +0.21 0.162 ± 0.001 p-/p0.71 0.731 ± 0.011

  16. Examples of calculations and comparison with RHIC experimental data: Particle ratios near mid-rapidity in central Au + Au collisions at = 130 GeV. T = 0.168 GeV, µB = 0.041 GeV, µS= 0.010 GeV and µQ= -0.001 GeV.

  17. Pseudo-rapidity spectrum of charged hadrons PHOBOS data on pseudo-rapidity spectrum of charged hadrons in central Au+Au collisions at =200 GeV (black points) our MC results obtained within the Bjorken-like and Hubble-like models for different values of (lines). Single freeze-out scenario allows to fix the effective volume

  18. p_t spectra The mid-rapidity PHENIX data on π, K and proton p_t spectra in Au+Au collisions at 200 GeV with our MC results obtained within the Bjorken-like and Hubble-like models. . For kaons, the discrepancy can be diminished with the help of the strangeness suppression parameter γs of 0.8 The overestimated slope of the kaon and proton p_t spectra can also be related with the oversimplified assumption of a common thermal and chemical freeze-out or insufficient number of the accounted heavy resonance states.

  19. Momentum correlations Due to the effects of QS and FSI, the momentum correlations of two or more particles at small relative momenta in their center-of-mass system are sensitive to the space-time characteristics of the production process so serving as a correlation femtoscopy tool. q = p1- p2 , x = x1- x2 w=1+cos qx . The corresponding correlation widths are usually parameterized in terms of the Gaussian correlation radii R_i: side out transverse pair velocity vt long beam We choose as the reference frame the longitudinal co-moving system (LCMS)

  20. Momentum correlations STAR collaboration data (open points) FASTMC Tth=Tch=165 MeV, R=10 fm, τ=6.1 fm/c (solid line) FASTMC Tth=Tch=165 MeV, R=8 fm, τ=9 fm/c (dashed line) FASTMC Tth=Tch=165 MeV, R=8 fm, τ=9 fm/c (dashed line) with negative r-t correlation coefficient (red dotted line) T=165 MeV T=100 MeV T=130 MeV

  21. Momentum correlations: other approaches The concept of a later thermal freeze-out occurring at Tth<Tchand with no multiplicity constraint on the thermal effective volume can help to resolve this problem: More realistic models as compared with the simple Bjorken-like and Hubble-like ones (particularly, consider a more complex form of the freeze-out hypersurface taking into account particle emission from the surface of expanding system M.S.Borysova, Yu.M.Sinyukov, S.V.Akkelin, B.Erazmus and Iu.A.Karpenko, Phys. Rev. C 73, 024903 (2006) and study the problem of particle rescattering and resonance excitation after the chemical and/or thermal freeze-out (only minor effect of elastic rescatterings on particle spectra and correlations is expected N.S.Amelin, R.Lednicky, L.V.Malinina, T.A.Pocheptsov and Y.M.Sinyukov, Phys. Rev. C 73, 044909 (2006) For the latter, our earlier developed C++ kinetic code can be coupled to FASTMC. F. Retiere and M. Lisa, Phys.Rev. C70 (2004) 044907

  22. Conclusions • We have developed a MC simulation procedure and the corresponding C++ code allowing for a fast but realistic description of multiple hadron production in central relativistic heavy ion collisions. • A high generation speed and an easy control through input parameters make our MC generator code particularly useful for detector studies. • -As options, we have implemented two freeze-out scenarios with coinciding and with different chemical and thermal freeze-outs. • Also implemented are various options of the freeze-out hypersurface parameterizations • -The generator code is quite flexible and allows the user to add other scenarios and freeze-out surface parameterizations as well as additional hadron species in a simple manner. • -We have compared the RHIC experimental data with our MC generation results obtained within the single freeze-out scenario and Bjorken-like and Hubble-like freeze-out surface parameterizations.

  23. Status and Perspectives http://uhkm.jinr.ru The fast MC procedure is extended to describe non-central collisions. Scenarios with single f.o. and thermal f.o. are implemented in the model Generation from the external file containing SPHES output is tested and very soon will be accessible in our site. FASTMChydro + high-pt part related to the partonic states: We are studying influence of the mini-jet production on CFs at RHIC energies. Jet-quenching model PYTHIA/PYthiaQUENched is implemented. FASTMS is implemented in AliRoot We started to study the possibility to add the QGSM inelastic cascade part to UKM elastic cascade. SPHES is tested and very soon will be accessible for users in our site.

  24. Additional slides

  25. Preliminary:

  26. Jet-quenching model PYQUEN/PYTHIA is implemented. High-p_t part related to the partonic states created in ultra-relativistic heavy PYTHYA+PYQUEN (I.P.Lokhtin and A.M.Snigirev, Eur. Phys. J. C 45, 211 (2006).)

  27. Momentum correlations The fitted correlation radii and strength parameter are compared with those measured by STAR collaboration The Bjorken-like model describes the decrease of the correlation radii with increasing k_t but overestimates their values.The situation is even worth with the Hubble-like model which is more constraint than the Bjorken-like one and yields the longitudinal radius by a factor two larger.

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