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Hard Probe - Medium Interactions in 3D-Hydrodynamics

Hard Probe - Medium Interactions in 3D-Hydrodynamics. 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. in collaboration with: M. Asakawa B. Mueller

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Hard Probe - Medium Interactions in 3D-Hydrodynamics

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  1. Hard Probe - Medium Interactions in 3D-Hydrodynamics 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 in collaboration with: • M. Asakawa • B. Mueller • C. Nonaka • T. Renk • J. Ruppert Steffen A. Bass

  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. Bass

  3. Relativistic Fluid Dynamics C. Nonaka & S.A. Bass: PRC in print, nucl-th/0607018 Steffen A. Bass

  4. Relativistic Fluid Dynamics • transport of macroscopic degrees of freedom • based on conservation laws:μTμν=0 μjμ=0 • for ideal fluid:Tμν= (ε+p) uμ uν - p gμν and jiμ = ρi uμ • Equation of State needed to close system of PDE’s:p=p(T,ρi) • 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. Bass

  5. 0=0.6 fm/c max=55 GeV/fm3, nBmax=0.15 fm-3 0=0.5 =1.5 EOS (entropy density) =0 3D-Hydro: Parameters Initial Conditions: • Energy Density: • Baryon Number Density: Parameters: • Initial Flow: vL=Bjorken’s solution); vT=0 Equation of State: • Bag Model + excluded volume • 1st order phase transition (to be replaced by Lattice EoS) transverse profile: longitudinal profile: Steffen A. Bass

  6. b=6.3 fm 3D-Hydro: Results separate chemical f.o. simulated by rescaling p,K • 1st attempt to address all data w/ 1 calculation • decent agreement • centrality dependence of v2 problematic Nonaka & Bass, PRC in print (nucl-th/0607018) See also Hirano; Kodama et al. Steffen A. Bass

  7. Hybrid Hydro+Micro Approaches C. Nonaka & S.A. Bass: PRC in print, nucl-th/0607018 Steffen A. Bass

  8. ideally suited for dense systems model early QGP reaction stage well defined Equation of State parameters: initial conditions Equation of State 3D-Hydro + UrQMD Model Full 3-d Hydrodynamics QGP evolution UrQMD Hadronization Cooper-Frye formula hadronic rescattering Monte Carlo TC TSW t fm/c Hydrodynamics+micro. transport (UrQMD) • no equilibrium assumptions • model break-up stage • calculate freeze-out • includes viscosity in hadronic phase • parameters: • (total/partial) cross sections Bass & Dumitru, PRC61,064909(2000) Teaney et al, nucl-th/0110037 Nonaka & Bass, PRC & nucl-th/0607018 Hirano et al. PLB & nucl-th/0511046 matching condition: • use same set of hadronic states for EoS as in UrQMD • generate hadrons in each cell using local T and μB Steffen A. Bass

  9. 3D-Hydro+UrQMD: Results • good description of cross section dependent features & non-equilibrium features of hadronic phase Steffen A. Bass

  10. 3D-Hydro+UrQMD: Reaction Dynamics Hadronic Phase: • significant rescattering ±3 units in y • moderate increase in v2 • rescattering of multi-strange baryons strongly suppressed • rescattering narrows v2 vs. η distribution Steffen A. Bass

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

  12. Hard Probes I: Jet-Quenching T. Renk, J. Ruppert, C. Nonaka & S.A. Bass: nucl-th/0611027 A. Majumder & S.A. Bass: in preparation Steffen A. Bass

  13. Jet-Quenching in a Realistic Medium • use BDMPS jet energy loss formalism (Salgado & Wiedemann: PRD68: 014008) • define local transport coefficient along trajectory ξ: • connect to characteristic gluon frenqency: • medium modeled via: • 2+1D Hydro (Eskola et al.) • parameterized evolution (Renk) • 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 Steffen A. Bass see talk by T. Renk for details

  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. Bass

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

  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 vflow 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, 064904 (2005) Van Hees, Greco & Rapp: PRC73, 034913 (’06) Bass, Asakawa & Mueller in preparation Steffen A. Bass

  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. Bass

  18. The End Steffen A. Bass

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