Yukinao AkamatsuUniv. of Tokyo

Heavy Quark Diffusionin the Quark-Gluon Fluid

2008/11/26Komaba Seminar

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

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Outline

• Introduction• HQ Energy Loss• Langevin HQ + Hydro Model• Numerical Results : HQ• Numerical Results : e±

• Conclusions and Outlook

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Introduction

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Relativistic Heavy Ion Collision0 0.6fm O(10) fm

CGC Glasma Hydrodynamics Hadron Rescattering Observed

What ? --- medium composed of light particles (u,d,s,g)

Others : jets --- very energetic light quarks and gluons : heavy quarks (c,b) --- very heavy compared to temperature : J/Psi --- almost colorless : photons --- electromagnetic interaction

Hard Probes

EM ProbeDynamical Probe?

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Hard Probes

From slides of X.-N. Wang @Hard Probe ’081) Jet Quenching

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q-hat ~ 4-14 [GeV2/fm]

2) Heavy Quark

From slides of R. Rapp @SQM ’08

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• pQCD radiative E-loss with upscaled transport coeff. • Langevin with elastic pQCD + resonances + coalescence• Langevin with upscaled pQCD elastic

Radiation vs. Collision

q-hat ~ >14 [GeV2/fm] (line) for rad.non-perturbative for coll.

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Dynamical Probes?

EM Probe

Hydro + J/yT. Gunji et al. PRC 76:051901,2007

From slides of T. Gunji @SQM ’08

From slides of F.-M. Liu @SQM ’08

Survival of J/Psi ~ 2Tc ?

HQ Energy Loss

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Collisional Energy Loss (E>>M>>T)

(ET>>M2)

(ET<<M2)

(Braaten ‘91)

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Radiative Energy Loss

Energy Loss 2ˆ2

LqCE RS

(E>>M)

(BDMPS)

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~ˆ Tq S

μ : Debye mass

λ : mean free path

Langevin HQ + Hydro Model

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weak coupling (pQCD)1) Energy loss of heavy quarks

HQ q-hats > LQ q-hatsindicates collision

(Armesto ’06, Wicks ’07)

(Caron-Huot ‘08)

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Heavy Quarks in Medium

Dominance Experiment Higher order

Radiation (g=g(T)) Fast (v ~ c) Not alone ×

Radiation (g=g(mD)) Fast (v ~ c) ? ?

Collision (g=g(T)) Slow (v ~ 0) Not alone ×

Collision (g=g(mD)) Slow (v ~ 0) OK by alone ?

(Moore ’05, van Hees ‘05)(Aichelin ’08)

(Djordjevic ’06)But even rad+coll cannot Non-Perturbative

method is required

relativistic Langevin equation

2) Model of HQ in medium

the only input,dimensionless

in the rest frame of matter

22 6.7 2.272 21 7.2

assume isotropic noise

relaxation time of HQ

(at T=210MeV) 13

strong coupling (AdS/CFT)drag force (= enegy loss dE/dx)

By comparing energy density & HQ pot.

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

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

QGP

Experiment(PHENIX, STAR ’07)14

HQs in Dynamical Medium

1) Flowchart

O(10)fm…

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

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2) Comments

f0=1.0/0.5/0.0

Numerical Results : HQ

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Profile of HQ Diffusion2 time scales : stay time and relaxation time

1) stay time 3-4 fm

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2) relaxation time steps

FRFS txTtT )()/1(_

T ~ 0.21GeV_

22 6.7 2.272 21 7.2

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3) pt loss

MpdtTdp /2

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Nuclear Modification Factor : RAA

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Elliptic Flow : v2

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HQ Correlation

pT1>pT2 & pT1>pTtrig 1:trigger, 2:associateGamma 0.0 0.3 1.0 3.0 30.0

<Ts1+Ts2> 7.2fm 7.1fm 6.8fm 6.0fm 6.3fm

Gamma 0.0 0.3 1.0 3.0 30.0

<Ts1+Ts2> 7.0fm 6.7fm 6.0fm 4.0fm 0.6fm

Gamma 0.0 0.3 1.0 3.0 30.0

<Ts1+Ts2> 7.7fm 7.7fm 7.8fm 7.7fm 7.3fm

Gamma 0.0 0.3 1.0 3.0 30.0

<Ts1+Ts2> 7.5fm 7.4fm 7.4fm 7.1fm 4.8fm

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Numerical Results : e±

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Nuclear Modification Factor : RAA

Experimental result γ=1-3

AdS/CFT γ=2.1±0.5

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Elliptic Flow : v2

Poor statistics, but at least consistent.(Still preliminary, PHENIX : v2~0.05-0.1 for pT~3-5GeV)

Conclusions and Outlook

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

• Prediction for heavy quark correlations More effort needed for e-h correlations

• Latest experimental data for v2 seems to have larger elliptic flow Within our model, coalescence even at high pT is necessary ?

• Theoretically, heavy quark energy loss at strong coupling should be reconsidered.

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To Be Continued…