HEAVY QUARK AND CHARM PROPAGATION

IN QUARK-GLUON PLASMA

Yukinao Akamatsu

Tetsuo Hatsuda

Tetsufumi Hirano

(Univ. of Tokyo)

12009/11/25Discussion with Prof. Blaizot

Ref : Y.A., T.Hatsuda and T.Hirano, PRC79,054907 (2009)

Y.A., T.Hatsuda and T.Hirano, PRC80,031901(R) (2009)

Outline

• Introduction• Langevin + Hydro Model for

Heavy Quark• Numerical Calculations• Conclusions and Outlook• Discussion

2

Introduction0 0.6fm O(10) fm

initial thermalization hydrodynamics hadron scattering 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

Strongly coupled QGP (sQGP) How can we probe it?

4

Langevin + Hydro Model for Heavy Quark

1) Our model of HQ in mediumRelativistic Langevin equation

the only input, dimensionless

Assume isotropic Gaussian white noise

in 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

bottom dominant

1) Nuclear Modification Factor & Elliptic Flow

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

・ CNM, quark coalescence : tiny at high pT

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

Numerical Calculations

]fm[43~ St

c/bfor [fm] 20-7 / 6-2

/ 2

TMHQ

charm : nearly thermalized bottom : not thermalized

Different freezeouts at 1st order P.T.

γ=1-3 Much smaller elliptic flow than in experiment

7

2) Azimuthal CorrelationBack to back correlation of a heavy quark pair

Loss of correlation in decay products from D & B

e-μ azimuthal correlation: sensitive probe for heavy quark thermalization rate

ppAAAA

ZYAM

assoc

trigAA

/

1)(

max

min

I

d

dN

Nd

IAA : quantitative measure

diffusion

e(mid-pseudorapidity)-μ(fwd-pseudorapidity) correlation : one peak

no contribution from vector meson decay

8

Effects we ignore :

・ Hadronic interaction of associates・ Medium response to HQ propagation・ Fictitious correlation due to bulk v2Relative angle range for IAA

Near side : -0.5π Δφ 0.5π≦ ≦ Away side : 0.5π Δφ 1.5π≦ ≦

A sensitive probe but not clean …

e-h correlation (mid-pseudorapidity) : two peaks

9

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

• Drag parameter cannot explain RAA and v2 simultaneously.

• A proposal of electron-muon correlation as a new tool to probe the heavy quark drag parameter.

• Possible updates for initial distribution with FONLL pQCD

quark coalescence, CNM effects, ・・・ (but almost done by Dr. Morino)

Conclusions and Outlook

10

Backup

11

Weak coupling calculations for HQ energy loss

RHIC, LHC

γ~0.2

γ~2.5

12

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

13f0=1.0/0.5/0.0

Notes in our model