Steffen A. Bass Modeling of RHIC Collisions #1
Steffen A. BassDuke 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
Hard Probe - Medium Interactions in 3D-Hydrodynamics
in collaboration with:• M. Asakawa• B. Mueller• C. Nonaka• T. Renk• J. Ruppert
Steffen A. Bass Modeling of RHIC Collisions #2
The Great WallThe 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 Modeling of RHIC Collisions #3
Relativistic Fluid Dynamics
C. Nonaka & S.A. Bass: PRC in print, nucl-th/0607018
Steffen A. Bass Modeling of RHIC Collisions #4
Relativistic Fluid Dynamics
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 Modeling of RHIC Collisions #5
3D-Hydro: Parameters3D-Hydro:
Parameters
max( , , ) ( , ; ) ( )x y W x y b H
max( , , ) ( , ; ) ( )BBn x y W x y bn H
EOS (entropy density)
=0
B1
4 233 [MeV]0=0.5 =1.5
max=55 GeV/fm3, nBmax=0.15 fm-3
0=0.6 fm/c
longitudinal profile:longitudinal profile: transverse profile:transverse profile: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)
Steffen A. Bass Modeling of RHIC Collisions #6
3D-Hydro: Results
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
b=6.3 fmNonaka & Bass, PRC in print(nucl-th/0607018)See also Hirano; Kodama et al.
Steffen A. Bass Modeling of RHIC Collisions #7
Hybrid Hydro+Micro Approaches
C. Nonaka & S.A. Bass: PRC in print, nucl-th/0607018
Steffen A. Bass Modeling of RHIC Collisions #8
Full 3-d Hydrodynamics
QGP evolution Cooper-Fryeformula
UrQMD
t fm/c
hadronic rescattering
Monte Carlo
Hadronization
TC TSW
Bass & Dumitru, PRC61,064909(2000)Teaney et al, nucl-th/0110037Nonaka & Bass, PRC & nucl-th/0607018Hirano et al. PLB & nucl-th/0511046
3D-Hydro + UrQMD Model
3D-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 μB
Steffen A. Bass Modeling of RHIC Collisions #9
3D-Hydro+UrQMD: Results
3D-Hydro+UrQMD: Results
good description of cross section dependent features & non-equilibrium features of hadronic phase
Steffen A. Bass Modeling of RHIC Collisions #10
3D-Hydro+UrQMD: Reaction Dynamics
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 Modeling of RHIC Collisions #11
3D-Hydro+UrQMD: Freeze-Out
3D-Hydro+UrQMD: Freeze-Out
• full 3+1 dimensional description of hadronic freeze-out; relevant for HBT
Steffen A. Bass Modeling of RHIC Collisions #12
Hard Probes I: Jet-Quenching
T. Renk, J. Ruppert, C. Nonaka & S.A. Bass: nucl-th/0611027A. Majumder & S.A. Bass: in preparation
Steffen A. Bass Modeling of RHIC Collisions #13
Jet-Quenching in a Realistic Medium
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: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
34ˆ 2q K
0
0
ˆ,c r d q
see talk by T. Renk for details
Steffen A. Bass Modeling of RHIC Collisions #14
Azimuthal Dependence of Energy-Loss
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
ˆ ˆ' cosh sinh cosq q (ρ: flow rapidity; α: angle of trajectory wrt flow)
Steffen A. Bass Modeling of RHIC Collisions #15
Hard Probes II: Heavy-Quarks
S.A. Bass, M. Asakawa & B. Mueller: in preparation
Steffen A. Bass Modeling of RHIC Collisions #16
Diffusion of Heavy Quarks in a Hydrodynamic MediumDiffusion 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
( ) (2
)p tT
t p t v t t t
• Teaney & Moore: PRC 71, 064904 (2005)• Van Hees, Greco & Rapp: PRC73, 034913 (’06)• Bass, Asakawa & Mueller in preparation
Steffen A. Bass Modeling of RHIC Collisions #17
Summary and OutlookSummary 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 Modeling of RHIC Collisions #18
The End
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