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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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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Relativistic Fluid Dynamics

C. Nonaka & S.A. Bass: PRC in print, nucl-th/0607018

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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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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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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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Hybrid Hydro+Micro Approaches

C. Nonaka & S.A. Bass: PRC in print, nucl-th/0607018

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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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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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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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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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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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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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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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Hard Probes II: Heavy-Quarks

S.A. Bass, M. Asakawa & B. Mueller: in preparation

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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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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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The End