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Freeze-Out in a Hybrid Model

Freeze-Out in a Hybrid Model. Freeze-out Workshop, 6.5.09 Goethe-Universität Frankfurt Hannah Petersen. Outline. Short overview of the hybrid model Two freeze-out prescriptions Details about the implementation T and m B distributions Influence of transition criterion Multiplicities

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Freeze-Out in a Hybrid Model

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  1. Freeze-Out in a Hybrid Model Freeze-out Workshop, 6.5.09 Goethe-Universität Frankfurt Hannah Petersen

  2. Outline • Short overview of the hybrid model • Two freeze-out prescriptions • Details about the implementation • T and mB distributions • Influence of transition criterion • Multiplicities • Rapidity and transverse mass spectra • HBT and elliptic flow • Conclusion and outlook Freeze-out Workshop, 06.05.09

  3. Hybrid Approach • Essential to draw conclusions from final state particle distributions about initially created medium • The idea here: Fix the initial state and freeze-out learn something about the EoS and the effect of viscous dynamics 2) Hydrodynamic evolution or Transport calculation 3) Freeze-out via hadronic cascade (UrQMD) 1) Non-equilibrium initial conditions via UrQMD (H.P. et al., PRC 78:044901, 2008, arXiv: 0806.1695) Freeze-out Workshop, 06.05.09

  4. Equations of State Ideal relativistic one fluid dynamics: and • HG: Hadron gas including the same degrees of freedom as in UrQMD (all hadrons with masses up to 2.2 GeV) • CH: Chiral EoS from SU(3) hadronic Lagrangian with first order transition and critical endpoint • BM: Bag Model EoS with a strong first order phase transition between QGP and hadronic phase D. Rischke et al., NPA 595, 346, 1995, D. Zschiesche et al., PLB 547, 7, 2002 Papazoglou et al., PRC 59, 411, 1999 • Hadronization happens (if phase transition is included) during the hydrodynamic evolution • Transition to transport happens in the hadronic stage, same degrees of freedeom on both sides of the hypersurface Freeze-out Workshop, 06.05.09

  5. Freeze-out • Transition from hydro to transport when e < 730 MeV/fm³ (≈ 5 * e0) in all cells of one transverse slice (Gradual freeze-out, GF) iso-eigentime criterion • Transition when e < 5* e0 in all cells(Isochronuous freeze-out, IF) • Particle distributions are generated according to theCooper-Frye formula • with boosted Fermi or Bose distributions f(x,p) including mB and mS • Rescatterings and final decays calculated via hadronic cascade (UrQMD) Freeze-out Workshop, 06.05.09

  6. Our Approach • Need a Monte Carlo procedure that runs in reasonable computing time because we are interested in event-by-event physics • Isochronous or gradual freeze-out with hadronic cascade calculation for rescatterings and resonance decays • Loop over the grid and for each cell the following steps are done Freeze-out Workshop, 06.05.09

  7. Steps for the Particle Production • Numbers of each particle species in the cell • Sum to get the total particle number • Particle production according to Poisson distribution • Particle type chosen according to probabilities • Isospin randomly assigned, charge conservation • Generate four-momenta • Particle vector information is transferred back to UrQMD Freeze-out Workshop, 06.05.09

  8. Conservation Laws • Three loops to assure net-strangeness and baryon number at the same time • Energy conservation on the average (for gradual freeze-out in principle not on the hypersurface, but baryon number conservation helps) • First strange particles • Antistrange particles • Fill up baryon number • Charge conservation with tuned isospin Freeze-out Workshop, 06.05.09

  9. Isochronuous Freeze-out Distribution of the cells at freeze-out at Elab = 40 AGeV  Important inhomogeneities are naturally taken into account (A.Dumitru et al., Phys. Rev. C 73, 024902 (2006)) Freeze-out Workshop, 06.05.09

  10. Freeze-out Line • Parametrization of chemical freeze-out line taken from • Cleymans et al, • J.Phys. G 32, S165, 2006 • Green points are from • A.Dumitru et al., PRC 73, 024902, 2006 •  Mean values and widths are in line with other calculations 5*e0 Black: Gradual FO Red: Isochronuous FO Freeze-out Workshop, 06.05.09

  11. Temperatures Rapidity distribution of the transition temperatures Chemical FO by Cleymans et al. Isochronuous Freeze-out Gradual Freeze-out Freeze-out Workshop, 06.05.09

  12. Chemical Potentials Rapidity distribution of the chemical potentials at the transition Isochronuous Freeze-out Gradual Freeze-out Freeze-out Workshop, 06.05.09

  13. Transition Times • Transition times along beam direction for the gradual freeze-out • At lower energies outer layers freeze-out first • At higher energies transition begins in the center Mimics iso-eigentime criterion Freeze-out Workshop, 06.05.09

  14. Isochronuous Freeze-out Full symbols: 40 AGeV Open symbols: 11 AGeV Freeze-out Workshop, 06.05.09

  15. Final State Interactions Freeze-out Workshop, 06.05.09

  16. Multiplicities vs. Energy full lines: hybrid model (IF) squares: hybrid model (GF) dotted lines: UrQMD-2.3 symbols: experimental data • Both models are purely hadronic without phase transition, but different underlying dynamics • Gradual transition improves multistrange hyperon yields  Results for particle multiplicities from AGS to SPS are similar Strangeness is enhanced in the hybrid approach due to local equilibration L X W (H.P. et al., PRC 78:044901, 2008) p K P Central (b<3.4 fm) Pb+Pb/Au+Au collisions Data from E895, NA49 Freeze-out Workshop, 06.05.09

  17. Rapidity Spectra full lines: hybrid model (IF) squares: hybrid model (GF) dotted lines: UrQMD-2.3 symbols: experimental data  Rapidity spectra for pions and kaons have a very similar shape in both calculations Freeze-out Workshop, 06.05.09

  18. mT Spectra Blue: pions Green: protons Red: kaons 11 AGeV 160 AGeV Full line: hybrid model (IF) Dashed line: hybrid model (GF) Dotted line: UrQMD-2.3 40 AGeV (H.P. et al., PRC 78:044901, 2008) • mT spectra are very similar at lower energies (11,40 AGeV) • <mT> is higher in hydro calculation at Elab=160 AGeV Central (b<3.4 fm) Pb+Pb/Au+Au collisions Freeze-out Workshop, 06.05.09

  19. <mT> Excitation Function (H.P. et al., arXiv: 0902.4866, JPG in print) Hadronic hydro calculation with different freeze-out scenarios  Freeze-out treatment is important Dynamics (viscosity) and equation of state are crucial input Data from E866, NA49 Freeze-out Workshop, 06.05.09

  20. RO/RS Ratio • Hydro phase leads to smaller ratios • Hydro to transport transition does not matter, if final rescattering is taken into account • EoS dependence is visible, but not as strong as previuosly predicted (factor of 5) Data from NA49 (Q. Li, H.P. et al., PLB 674, 111, 2009) Freeze-out Workshop, 06.05.09

  21. Elliptic Flow • Smaller mean free path in the hot and dense phase leads to higher elliptic flow • At lower energies: hybrid approach reproduces the pure UrQMD result • Gradual freeze-out leads to a better description of the data (H.P. et.al., arXiv:0901.3821, PRC in print) Data from E895, E877, NA49, Ceres, Phenix, Phobos, Star Freeze-out Workshop, 06.05.09

  22. Conclusions and Outlook • Hadronization is done during the hydrodynamic evolution according to equation of state • Two prescriptions of the transition from hydro to transport have been developed • Gradual freeze-out leads overall to a better description of experimental data • Improve hypersurface (Schlei-Code) and test sensitivity on criteria • Couple freeze-out routine to parton cascade • Dynamical coupling of transport and hydro approach Freeze-out Workshop, 06.05.09

  23. Backup

  24. Initial State • Contracted nuclei have passed through each other • Energy is deposited • Baryon currents have separated • Energy-, momentum- and baryon number densities are mapped onto the hydro grid • Event-by-event fluctuations are taken into account • Spectators are propagated separately in the cascade (nucl-th/0607018, nucl-th/0511021) Elab=40 AGeV b=0 fm (J.Steinheimer, H.P. et al., PRC 77,034901,2008) Freeze-out Workshop, 06.05.09

  25. Freeze-out Workshop, 06.05.09

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