Langevin + Hydrodynamics Langevin + Hydrodynamics Approach to Heavy Quark Approach to Heavy Quark Diffusion in the QGPDiffusion in the QGP

Yukinao Akamatsu

Tetsuo Hatsuda

Tetsufumi Hirano

(Univ. of Tokyo)

1

2009/05/09Heavy Ion Café @Tokyo

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

Outline

• Introduction• Langevin + Hydro Model for

Heavy Quark• Numerical Calculations• Conclusions and Outlook

2

Introduction0 0.6fm O(10) fm

CGC Glasma Hydrodynamics Hadron Rescattering Observed

Medium composed of light particles (u,d,s,g)

Others : jets, J/Psi, etc Heavy quarks (c,b) --- heavy compared to temperature tiny thermal pair creation　　　　　　　　　　　　　　　　　 no mutual interaction Good probe !

3

Local thermalization assumed

Strongly coupled QGP (sQGP) How can we probe ?

4

Langevin + Hydro Model for Heavy Quark

1) Our model of HQ in medium

Relativistic Langevin equation

the only input, dimensionless

Assume isotropic Gaussian white noise

in the (local) rest frame of matterin the (local) rest frame of matter

2) Energy loss of heavy quarks

Weak coupling (pQCD)Poor convergence (Caron-Huot ‘08)

Strong coupling (SYM by AdS/CFT sQGP)N=4 SYM theory

pM

T

v

vT

Ng

dt

pd YM 2

2

22

12

),( 2 NNgYM

[ for naïve perturbation]4YMg

(Gubser ’06, Herzog et al. ’06, Teaney ’06)

“Translation” to sQGP 5.01.2 (Gubser ‘07)

tpD

P)(2

exp)(2

Satisfy fluctuation-dissipationtheorem

2.0~ (leading order)

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)5

3) Heavy Quark Langevin + Hydro Model

O(10)fm…

generated by PYTHIA

(independent fragmentation)

6

Numerical Calculations

Experimental result γ=1-3 AdS/CFT γ=2.1±0.5

Different freezeouts at 1st order P.T.

Bottom dominant

1) Nuclear Modification Factor

・ Initial (LO pQCD): good only at high pT

・ CNM, quark coalescence : tiny at high pT

7

Poor statistics, but at least consistent with γ=1-3.(Still preliminary, PHENIX : v2~0.05-0.1 for pT~3-5GeV)

2) Elliptic Flow

8

22 6.7 2.272 21 7.2

thermalized

not thermalized

2T

MHQ

Degree of HQ Thermalization

Experimental result γ=1-3 charm : nearly thermalized, bottom : not thermalized

Relaxation time

Stay time ]fm[43~ St

9

3) Azimuthal Correlation

Observables : c, b D, B single electron, muon charged hadron

e-h, μ-h correlation : two peaks (near & away side)

e-μ correlation : one peak (away side only) no contribution from vector meson decay

Back to back correlation quenched & broadeneddiffusion

10

electron - (charged) hadron correlation(e - π, K, p) = (trigger - associate)

Quenching of backward (0.5π-1.5π) signal QBS

)0(

)()(

A

AQBS

・ More quenching & broadening with larger γ・ Mach cone : not included

ZYAMZYAM

11

electron - muon correlation(trigger - associate)

Quenching of backward (0-2π) signal QBS

・ High pT associate : energy loss・ Low pT associate : fluctuation

・ Energy loss quenching・ Fluctuation broadening

・ More quenching & broadening with larger γ

electron, muon : mid-rapidity (< 1.0)

12

electron - muon correlation

electron : mid pseudo-rapidity (< 0.35)muon : forward pseudo-rapidity (1.4~2.1)

(trigger - associate)

13

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

• V2 has large statistical error. But at least consistent.• Heavy quark correlations in terms of lepton-hadron,

electron-muon correlations are sensitive to drag parameter.

• Possible update forinitial distribution with FONLL pQCDquark coalescence, CNM effects, ・・・

Conclusions and OutlookY. Morino (PhD Thesis)arXiv:0903.3504 [nucl-ex](Fig.7.12)

14

Backup

15

Weak coupling calculations for HQ energy loss

RHIC, LHC

γ~0.2

γ~2.5

16

Fluctuation-dissipation theorem

Ito discretization Fokker Planck equation

tpppMTp

txpPpDp

ppp

txpPxE

p

t

)()(

),,()(2

1)(

),,(

2

TMpPeq22exp

)(2

)(

2

)(

)(

)()(

3

2

TEM

TpD

ET

pD

pd

pdDp

Generalized FD theorem

A Little More on Langevin HQ

tpD

P)(2

exp)(2

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 hadronization

Where to stop in mixed phase at 1st order P.T. 3 choices (no/half/full mixed phase)

Reliable at high pT

17f0=1.0/0.5/0.0

Notes in our model

18

Numerical calculations for HQ

Nuclear Modification Factor

19

γ=30 : Surface emission dominates at high pT

only at low pT

Elliptic Flow

20

Subtlety of outside production

proportion of ts=0 for pT>5GeV

Gamma=0.3_ccbar: 1.2% Gamma=0.3_bbbar: 0.70%Gamma=1_ccbar: 4.2% Gamma=1_bbbar: 0.93%Gamma=3_ccbar: 25% Gamma=3_bbbar: 2.2%Gamma=10_ccbar: 68% Gamma=10_bbbar: 15%Gamma=30_ccbar: 90% Gamma=30_bbbar: 46%

Gamma=0.3_eb: 0.75%Gamma=0.3_mb: 0.97%Gamma=1_eb: 1.7%Gamma=1_mb: 2.0%Gamma=3_eb: 5.3%Gamma=3_mb: 5.1%Gamma=10_eb: 31%Gamma=10_mb: 30%

21

DEFINITION VALUE

Stay time ts=Σ Δt|FRF 3-4 [fm]

Temperature T=Σ(TΔt|FRF) / ts ~210 [MeV]

22 6.7 2.272 21 7.2

For γ=0-30 and initial pT=0-10GeV

(T=210MeV)

thermalizednot thermalized

Time measured by a clock co-moving with fluid element

2T

MHQ

_

Degree of HQ Thermalization

Experimental result γ=1-3 charm : nearly thermalized, bottom : not thermalized

22

QQbar Correlation

23

Other numerical calculations

muon - (charged) hadron correlation

Quenching of backward (0.5π-1.5π) signal QBS