Steffen A. BassModeling of RHIC Collisions #1 Steffen A. Bass Duke University Relativistic Fluid Dynamics Hybrid Macro+Micro Transport flavor dependent.

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Presentation transcript:

Steffen A. BassModeling of RHIC Collisions #1 Steffen A. Bass Duke University Relativistic Fluid Dynamics Hybrid Macro+Micro Transport flavor dependent freeze-out Hard-Probes I: Jet-Quenching Hard-Probes II: Heavy Quarks Hard Probe - Medium Interactions in 3D-Hydrodynamics in collaboration with: M. Asakawa B. Mueller C. Nonaka T. Renk J. Ruppert

Steffen A. BassModeling of RHIC Collisions #2 The Great Wall Heavy-ion collisions at RHIC have produced a state of matter which behaves similar to an ideal fluid  (3+1)D Relativistic Fluid Dynamics and hybrid macro+micro models are highly successful in describing the dynamics of bulk QCD matter Jet energy-loss calculations have reached a high level of technical sophistication (BDMPS, GLV, higher twist…), yet they employ only very simple/primitive models for the evolution of the underlying deconfined medium…  need to overcome The Great Wall and treat medium and hard probes consistently and at same level of sophistication!

Steffen A. BassModeling of RHIC Collisions #3 Relativistic Fluid Dynamics C. Nonaka & S.A. Bass: PRC in print, nucl-th/

Steffen A. BassModeling of RHIC Collisions #4 Relativistic Fluid Dynamics transport of macroscopic degrees of freedom based on conservation laws:  μ T μν =0  μ j μ =0 for ideal fluid: T μν = (ε+p) u μ u ν - p g μν and j i μ = ρ i u μ Equation of State needed to close system of PDE’s: p=p(T,ρ i )  connection to Lattice QCD calculation of EoS initial conditions (i.e. thermalized QGP) required for calculation Hydro assumes local thermal equilibrium, vanishing mean free path This particular implementation:  fully 3+1 dimensional, using (τ,x,y,η) coordinates  Lagrangian Hydrodynamics  coordinates move with entropy-density & baryon-number currents  trace adiabatic path of each volume element

Steffen A. BassModeling of RHIC Collisions #5 3D-Hydro: Parameters EOS (entropy density)  =0  0 =0.5   =1.5  max =55 GeV/fm 3, n Bmax =0.15 fm -3  0 =0.6 fm/c longitudinal profile: transverse profile: Initial Conditions: Energy Density: Baryon Number Density: Parameters: Initial Flow: v L =  Bjorken’s solution); v T =0 Equation of State: Bag Model + excluded volume 1 st order phase transition (to be replaced by Lattice EoS)

Steffen A. BassModeling of RHIC Collisions #6 3D-Hydro: Results separate chemical f.o. simulated by rescaling p,K 1 st attempt to address all data w/ 1 calculation  decent agreement  centrality dependence of v 2 problematic b=6.3 fm Nonaka & Bass, PRC in print (nucl-th/ ) See also Hirano; Kodama et al.

Steffen A. BassModeling of RHIC Collisions #7 Hybrid Hydro+Micro Approaches C. Nonaka & S.A. Bass: PRC in print, nucl-th/

Steffen A. BassModeling of RHIC Collisions #8 Full 3-d Hydrodynamics QGP evolution Cooper-Frye formula UrQMD t fm/c hadronic rescattering Monte Carlo Hadronization TCTC T SW Bass & Dumitru, PRC61,064909(2000) Teaney et al, nucl-th/ Nonaka & Bass, PRC & nucl-th/ Hirano et al. PLB & nucl-th/ D-Hydro + UrQMD Model ideally suited for dense systems –model early QGP reaction stage well defined Equation of State parameters: –initial conditions –Equation of State Hydrodynamics + micro. transport (UrQMD) no equilibrium assumptions  model break-up stage  calculate freeze-out  includes viscosity in hadronic phase parameters: –(total/partial) cross sections matching condition: use same set of hadronic states for EoS as in UrQMD generate hadrons in each cell using local T and μ B

Steffen A. BassModeling of RHIC Collisions #9 3D-Hydro+UrQMD: Results  good description of cross section dependent features & non-equilibrium features of hadronic phase

Steffen A. BassModeling of RHIC Collisions #10 3D-Hydro+UrQMD: Reaction Dynamics Hadronic Phase: significant rescattering ±3 units in y moderate increase in v 2 rescattering of multi-strange baryons strongly suppressed rescattering narrows v 2 vs. η distribution

Steffen A. BassModeling of RHIC Collisions #11 3D-Hydro+UrQMD: Freeze-Out full 3+1 dimensional description of hadronic freeze-out; relevant for HBT

Steffen A. BassModeling of RHIC Collisions #12 Hard Probes I: Jet-Quenching T. Renk, J. Ruppert, C. Nonaka & S.A. Bass: nucl-th/ A. Majumder & S.A. Bass: in preparation

Steffen A. BassModeling of RHIC Collisions #13 Jet-Quenching in a Realistic Medium use BDMPS jet energy loss formalism (Salgado & Wiedemann: PRD68: ) define local transport coefficient along trajectory ξ: connect to characteristic gluon frenqency: medium modeled via: 1.2+1D Hydro (Eskola et al.) 2.parameterized evolution (Renk) 3.3+1D Hydro (Nonaka & Bass) ± 50% spread in values for K  systematic error in tomography analysis due to different medium treatment  need more detailed analysis to gain predictive power see talk by T. Renk for details

Steffen A. BassModeling of RHIC Collisions #14 Azimuthal Dependence of Energy-Loss pathlength of jet through medium varies as function of azimuthal angle  distinct centrality and reaction plane dependence  stronger constraints on tomographic analysis collective flow effect on q:  only small modification of shape (ρ: flow rapidity; α: angle of trajectory wrt flow)

Steffen A. BassModeling of RHIC Collisions #15 Hard Probes II: Heavy-Quarks S.A. Bass, M. Asakawa & B. Mueller: in preparation

Steffen A. BassModeling of RHIC Collisions #16 Diffusion of Heavy Quarks in a Hydrodynamic Medium propagation of heavy quarks in a QGP medium resembles a diffusion process use evolution of 3D-Hydro as medium  T, μ and v flow are known as function of r& τ  describe propagation with a Langevin Eqn: drag coefficient κ/2T can be locally calculated from 3D hydro evolution Teaney & Moore: PRC 71, (2005) Van Hees, Greco & Rapp: PRC73, (’06) Bass, Asakawa & Mueller in preparation

Steffen A. BassModeling of RHIC Collisions #17 Summary and Outlook Heavy-Ion collisions at RHIC have produced a state of matter which behaves similar to an ideal fluid  Hydro+Micro transport approaches are the best tool to describe the soft, non-perturbative physics at RHIC after QGP formation  fully (3+1)D implementations are available and work very well the same hydrodynamic evolution should be utilized as medium for sophisticated jet energy-loss (currently: BDMPS and HT) and heavy quark diffusion calculations  azimuthal dependence of jet energy-loss improves constraints on jet- tomography parameters  consistent treatment of hard and soft physics in one framework next step:  incorporate effects of hard probes on medium

Steffen A. BassModeling of RHIC Collisions #18 The End