Marcus Bleicher, WWND 2008 A fully integrated (3+1) dimensional Hydro + Boltzmann Hybrid Approach Marcus Bleicher Institut für Theoretische Physik Goethe Universität Frankfurt Germany

Marcus Bleicher, WWND 2008 in collaboration with Hannah Petersen Jan Steinheimer Gerhard Burau Qingfeng Li Dirk Rischke Horst Stoecker

Marcus Bleicher, WWND 2008 Outline  Motivation  Model Description  Time Evolution  Multiplicities and Rapidity Spectra  and v 2 Excitation Function  HBT correlations  Conclusion and Outlook

Marcus Bleicher, WWND 2008 Historical Note Direct emission of multiple strange baryons in ultrarelativistic heavy ion collisions from the phase boundary. A. Dumitru, S.A. Bass, M. Bleicher, H. Stoecker, W. Greiner, Phys.Lett.B460: ,1999 Hadronic freezeout following a first order hadronization phase transition in ultrarelativistic heavy ion collisions. S.A. Bass, A. Dumitru, M. Bleicher, L. Bravina, E. Zabrodin, H. Stoecker, W. Greiner, Phys.Rev.C60:021902,1999 Dynamics of hot bulk QCD matter: From the quark gluon plasma to hadronic freezeout. S.A. Bass, A. Dumitru, Phys.Rev.C61:064909,2000 Flow at the SPS and RHIC as a quark gluon plasma signature. D. Teaney, J. Lauret, Edward V. Shuryak, Phys.Rev.Lett.86: ,2001 A Hydrodynamic description of heavy ion collisions at the SPS and RHIC. D. Teaney, J. Lauret, E.V. Shuryak, e-Print: nucl-th/ Only simplified hydrodynamics used ‘Arbitrary’ initial conditions

Marcus Bleicher, WWND 2008 Present Approaches Hadronic dissipative effects on elliptic flow in ultrarelativistic heavy-ion collisions. T. Hirano, U. Heinz, D. Kharzeev, R. Lacey, Y. Nara, Phys.Lett.B636: , D hydro + cascade model at RHIC. C. Nonaka, S.A. Bass, Nucl.Phys.A774: ,2006 (3+1)dim. hydrodynamics ‘Arbitrary’ initial conditions Results On Transverse Mass Spectra Obtained With Nexspherio F. Grassi, T. Kodama, Y. Hama, J.Phys.G31:S1041-S1044,2005 See also recent work of K. Werner

Marcus Bleicher, WWND 2008 Motivation Fix the initial state and freeze-out  learn something about the EoS and the effect of viscous dynamics 1) Non-equilibrium initial conditions via UrQMD 2) Hydrodynamic evolution or Transport calculation 3) Freeze-out via hadronic cascade (UrQMD)

Marcus Bleicher, WWND 2008 Are difference between hydro and transport as big as expected? Investigation of differences between UrQMD: –non-equilibrium (Boltzmann) transport approach –hadron-string and resonance dynamics UrQMD+Hydro: –non-equilibrium initial conditions –ideal hydrodynamic evolution for the hot and dense phase –Freeze-out via hadronic cascade J.Steinheimer et al., Phys.Rev.C77:034901,2008 arXiv:

Marcus Bleicher, WWND 2008 Initial State I coupling between UrQMD initial state and hydrodynamic evolution at: contracted nuclei have passed through each other –initial NN scatterings have proceeded –energy is deposited hadrons are represented by a Gaussian with finite width with the proper normalisation

Marcus Bleicher, WWND 2008 Single Event – Initial State Energy density distribution at E lab =40 AGeV, t start = 2.6 fm  Event-by-event fluctuations are naturally taken into account  

Marcus Bleicher, WWND 2008 (3+1)d Hydrodynamic Evolution Ideal relativistic one fluid hydrodynamics and Hadron gas equation of state (EoS) –No phase transition included –Baseline check –All hadrons with masses up to 2.2 GeV are included (consistent with UrQMD) D. Rischke et al., Nucl. Phys. A 595, 346 (1995), M. Gyulassy, D. Rischke, B. Zhang, Nucl.Phys.A613: ,1997

Marcus Bleicher, WWND 2008 Freeze-out I hydrodynamic evolution until –  < 730 MeV/fm³ (≈ 5 *  0 ) in all cells isochronous freeze-out is performed via the Cooper-Frye formula with boosted Fermi or Bose distributions f(x,p) including  B and  S rescatterings and final decays calculated via hadronic cascade (UrQMD)

Marcus Bleicher, WWND 2008 Time scales E lab (AGeV)t start (fm)t hydro (fm)

Marcus Bleicher, WWND 2008 Freeze out conditions

Marcus Bleicher, WWND 2008 Freeze-out II Distribution of the cells at freeze-out Important inhomogeneities are naturally taken into account (cf. A.Dumitru et al., Phys. Rev. C 73, (2006))

Marcus Bleicher, WWND 2008 Dependence on Freeze-out Variation of the freeze-out criterium does not affect the meson multiplicities Higher values are for E lab =40 AGeV while lower values are for E lab =11 AGeV

Marcus Bleicher, WWND 2008 Dependence on t start Variation of starting time by a factor 4 changes results only by 10 %

Marcus Bleicher, WWND 2008 Baryon density distribution Time evolution of the baryon density is smooth 1) in the reaction plane2) in a central cell B/0B/0

Marcus Bleicher, WWND 2008 Time Evolution

Marcus Bleicher, WWND 2008 Multiplicities  Both models are purely hadronic without phase transition, but different underlying dynamics  results for particle multiplicities from AGS to SPS are surprisingly similar  strangeness is enhanced in the hybrid approach due to local equilibration full lines: hybrid model dotted lines: UrQMD-2.3 symbols: experimental data   KP

Marcus Bleicher, WWND 2008 Rapidity Distribution

Marcus Bleicher, WWND 2008

Excitation Function  Resonance excitations and non-equilibrium effects in intermediate energy regime lead to a softening of the EoS in pure UrQMD calculation  hybrid calculation with hadronic EoS just raises as a function of beam energy

Marcus Bleicher, WWND 2008 Elliptic Flow  Smaller mean free path in the hot and dense phase leads to a better description of the data  at lower energies: hybrid approach jumps to the pure UrQMD value  analysis with different EoS including a phase transition is needed (H. Petersen et.al., Phys. Rev. C 74, (2006))

Marcus Bleicher, WWND 2008 HBT I

Marcus Bleicher, WWND 2008 HBT II Ro/Rs improves with hydro phase

Marcus Bleicher, WWND 2008 Conclusion and Outlook First results from the comparison of a transport and a hybrid calculation with the same initial conditions and freeze-out –Multiplicities are surprisingly similar –Strangeness is enhanced due to local equilibration – and v 2 excitation functions are different –HBT is changed Further studies of different EoS with explicit phase transition are needed