hard probe - medium interactions in 3d-hydrodynamics
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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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
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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!
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Steffen A. Bass Modeling of RHIC Collisions #3
Relativistic Fluid Dynamics
C. Nonaka & S.A. Bass: PRC in print, nucl-th/0607018
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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
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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)
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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.
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Steffen A. Bass Modeling of RHIC Collisions #7
Hybrid Hydro+Micro Approaches
C. Nonaka & S.A. Bass: PRC in print, nucl-th/0607018
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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
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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
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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
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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
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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
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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
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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)
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Steffen A. Bass Modeling of RHIC Collisions #15
Hard Probes II: Heavy-Quarks
S.A. Bass, M. Asakawa & B. Mueller: in preparation
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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
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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
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Steffen A. Bass Modeling of RHIC Collisions #18
The End