1. Yukinao Akamatsu Tetsuo Hatsuda Tetsufumi Hirano (Univ. of Tokyo)
2009/04/03
Quark Matter
@Knoxville
Langevin + Hydrodynamics Approach to Heavy Quark Propagation and Correlation in QGP
Yukinao Akamatsu
Tetsuo Hatsuda
Tetsufumi Hirano
(Univ. of Tokyo)
Ref : Y.A., T.Hatsuda and T.Hirano, arXiv: [hep-ph]

2. Outline Introduction Langevin + Hydro Model for Heavy Quark
Numerical Calculations
Conclusions and Outlook

3. Introduction
0.6fm
O(10) fm
CGC Glasma Hydrodynamics Hadron Rescattering Observed
Local thermalization assumed
Medium composed of light particles (u,d,s,g)
Strongly coupled QGP (sQGP)  How can we probe ?
Others : jets, J/Psi, etc
Heavy quarks (c,b) --- heavy compared to temperature
tiny thermal pair creation
　　　　　　　　　　　 no mutual interaction
Good probe !

4. Langevin + Hydro Model for Heavy Quark
1) Our model of HQ in medium
in the (local) rest
frame of matter
Relativistic Langevin equation
Assume isotropic Gaussian white noise
the only input,
dimensionless
Satisfy fluctuation-dissipation
theorem
2) Energy loss of heavy quarks
Weak coupling (pQCD)
(leading order)
Poor convergence
(Caron-Huot ‘08)
Strong coupling (SYM by AdS/CFT  sQGP)
[ for naïve perturbation]
N=4 SYM theory
(Gubser ’06, Herzog et al. ’06, Teaney ’06)
“Translation” to sQGP
(Gubser ‘07)

5. c(b)→D(B)→e- +νe+π etc
3) Heavy Quark Langevin + Hydro Model
0 fm….
Little Bang
generated by PYTHIA
0.6 fm…
Initial Condition
(pp + Glauber)
Local temperature and flow
Brownian Motion
Full 3D hydrodynamics
QGP
T(x), u(x)
(Hirano ’06)
Heavy Quark Spectra _
c(b)→D(B)→e- +νe+π etc
O(10)fm…
(independent fragmentation)
Electron Spectra + ….
Experiment
(PHENIX, STAR ’07)
time

6. Numerical Calculations
1) Nuclear Modification Factor
Experimental result  γ=1-3
・Initial (LO pQCD): good only at high pT
・CNM, quark coalescence : tiny at high pT
AdS/CFT γ=2.1±0.5
Different freezeouts
at 1st order P.T.
Bottom dominant

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

8. 22 6.7 2.2 72 21 7.2  Degree of HQ Thermalization Stay time
Relaxation time 22
6.7
2.2 72 21
7.2
thermalized
not thermalized
Experimental result γ=1-3  charm : nearly thermalized,
bottom : not thermalized

9. 3) Azimuthal Correlation
Back to back correlation
Quenched
diffusion
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

10. electron - (charged) hadron correlation
(e - π, K, p) = (trigger - associate)
・More quenching with larger γ
・Partial quenching predicted
Quenching of backward (0.5π-1.5π) signal QBS
ZYAM γ
QBS
0.3
1.01±0.16
1.0
0.88±0.11
3.0
0.55±0.09
10.0
0.21±0.07

11. electron - muon correlation (trigger - associate)
・More quenching with larger γ
・Partial quenching predicted
Quenching of backward (0-2π) signal QBS
ZYAM γ
QBS
0.3
1.01±0.02
1.0
0.98±0.02
3.0
0.79±0.02
10.0
0.31±0.03

12. V2 has large statistical error. But at least consistent.
Y. Morino (PhD Thesis)
arXiv: [nucl-ex]
(Fig.7.12)
Conclusions and Outlook
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 for
initial distribution with FONLL pQCD
quark coalescence, CNM effects,・・・

13. Backup

14. Weak coupling calculations for HQ energy loss
γ~2.5
γ~0.2
RHIC, LHC

15. A Little More on Langevin HQ
Fluctuation-dissipation theorem
Ito discretization  Fokker Planck equation
Generalized FD theorem

16. Notes in our model Initial condition <decayed electron in pp>
<HQ in pp>
available only spectral shape
above pT ~ 3GeV
Reliable at high pT
No nuclear matter effects in initial condition
No quark coalescence effects in hadronization
Where to stop in mixed phase at 1st order P.T.
 3 choices (no/half/full mixed phase)
f0=1.0/0.5/0.0

17. Numerical calculations for HQ
Nuclear Modification Factor

18. Elliptic Flow
γ=30 : Surface emission
dominates at high pT
only at low pT

19. 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: %
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%

20. 22 6.7 2.2 72 21 7.2 DEFINITION VALUE Stay time ts=Σ Δt|FRF 3-4 [fm]
 Degree of HQ Thermalization
Time measured by a clock co-moving with fluid element
For γ=0-30 and initial pT=0-10GeV
DEFINITION
VALUE
Stay time
ts=Σ Δt|FRF
3-4 [fm]
Temperature
T=Σ(TΔt|FRF) / ts
~210 [MeV] 22
6.7
2.2 72 21
7.2
thermalized
not thermalized _
(T=210MeV)
Experimental result γ=1-3  charm : nearly thermalized,
bottom : not thermalized

21. QQbar Correlation

22. Other numerical calculations
muon - (charged) hadron correlation
Quenching of backward (0.5π-1.5π) signal QBS γ
QBS
0.3
0.89±0.13
1.0
0.77±0.11
3.0
0.49±0.07
10.0
0.12±0.06

23. electron - muon correlation with higher associate pT
Quenching of backward (0-2π) signal QBS γ
QBS
0.3
1.00±0.02
1.0
0.97±0.02
3.0
0.92±0.03
10.0
0.95±0.06 γ
QBS
0.3
0.99±0.02
1.0
0.95±0.01
3.0
0.76±0.01
10.0
0.31±0.02

24. Summary of QBS