Heavy Quark Diffusion with Relativistic Langevin Dynamics in the Quark-

Gluon Fluid

Yukinao Akamatsu 赤松 幸尚(Univ. of Tokyo)

ATHIC 2008 Tsukuba

Ref : YA, T. Hatsuda, and T. Hirano, arXiv:0809.1499[hep-ph]

Outline

• Introduction• Langevin Dynamics of Heavy Quarks• Hydro + HQ Model• Numerical Results• Conclusions and Outlook

relativistic ideal hydrodynamics

Light (m << T~200MeV) components (g, u, d, s)

• Relativistic Heavy Ion Collision

1. Introduction

Heavy (M >> T~200MeV) components (c, b)long time scale not thermalized in fluid impurity

HQ

g,u,d,s

Other impurities : J/Ψ (color singlet), Jet (too energetic)

strongly coupled matter

2. Langevin Dynamics of Heavy Quarks

• Heavy Quarks in Medium

1. weak coupling (pQCD)

2. strong coupling (AdS/CFT)

drag force

Energy loss of heavy quarks

energy of HQ dominant mechanism

low energy collision

high energy radiation

<Energy loss of HQ>

HQ q-hats > LQ q-hats indicates collision

but poor convergence

(Armesto ’06, Wicks ‘07)

(Caron-Huot ‘08)

(Gubser ’06,’07, HKKKY ’06, Teaney ‘06)

,

relativistic Langevin equation

Model of HQ in medium

the only input,dimensionless

in the rest frame of matter

22 6.7 2.2

72 21 7.2

assume isotropic noise

relaxation time of HQ

(at T=210MeV)

3. Hydro + HQ Model

• Flowchart

0 fm….

0.6 fm…

Little Bang

Initial Condition

Brownian Motion

Heavy Quark Spectra

Full 3D hydrodynamics

Electron Spectra

T(x), u(x)

Local temperature and flow

(pp + Glauber)

(Hirano ’06)

c(b)→D(B)→e- +νe+π etc_

time

QG

P

Experiment

(PHENIX, STAR ’07)

• Comments

Initial condition

available only spectral shape above pT~3GeV

<HQ in pp>

<decayed electron in pp>

No nuclear matter effects in initial conditionNo quark coalescence effects in hadronizationWhere to stop in coexisting phase at 1st order P.T. 3 choices (no/half/full coexisting phase)

Reliable at high pT

4. Numerical Results

• Profile of HQ Diffusion

2 time scales

22 6.7 2.2

72 21 7.2

Charm ~ not yet fully thermalizedBottom ~ not thermalized at all

: stay time and relaxation time

<relaxation times>

<stay times>

stay time :~3-4fm

• HQ Spectra

Nuclear modification factor

Large pT, γ large momentum loss large suppression

Elliptic flow

High pT (almost) no anisotropyAt low pT, large γ large anisotropy

• Electron Spectra

Bottom ratio

At pT above 3GeV, bottom origin electrons dominate.

Nuclear modification factor

Elliptic flow

Poor statistics for both simulation and experiment at high pT.But at least consistent.(Still preliminary, PHENIX : v2~0.05-0.1 for pT~3-5GeV)

Quite Large v2

5. Conclusions and Outlook

• Heavy quark can be described by relativistic Langevin dynamics with a parameter predicted by AdS/CFT.

• Prediction for heavy quark correlations.

• Latest experimental data for v2 seems to have larger elliptic flow.

• Theoretically, heavy quark energy loss at strong coupling (based more on field theory) should be reconsidered.

Back Up Slides

Average Temperature

charm bottom

Momentum Loss

charm bottom

RAA of Electrons from Charm/Bottom

charm bottom