Hard Probe - Medium Interactions in 3D-Hydrodynamics

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