1. Yukinao Akamatsu 赤松 幸尚 (Univ. of Tokyo)
ATHIC 2008 Tsukuba
Heavy Quark Diffusion with Relativistic Langevin Dynamics in the Quark-Gluon Fluid
Yukinao Akamatsu 赤松 幸尚
(Univ. of Tokyo)
Ref : YA, T. Hatsuda, and T. Hirano, arXiv: [hep-ph]

2. Outline Introduction Langevin Dynamics of Heavy Quarks
Hydro + HQ Model
Numerical Results
Conclusions and Outlook

3. 1. Introduction Relativistic Heavy Ion Collision
Light (m << T~200MeV) components
(g, u, d, s) HQ
relativistic ideal hydrodynamics
g,u,d,s
strongly coupled matter
Heavy (M >> T~200MeV) components (c, b)
long time scale  not thermalized in fluid  impurity
Other impurities : J/Ψ (color singlet), Jet (too energetic)

4. 2. Langevin Dynamics of Heavy Quarks
<Energy loss of HQ>
Heavy Quarks in Medium
energy of HQ
dominant mechanism
low energy
collision
high energy
radiation
Energy loss of heavy quarks
1. weak coupling (pQCD)
HQ q-hats > LQ q-hats
 indicates collision
(Armesto ’06, Wicks ‘07)
but poor convergence
(Caron-Huot ‘08)
2. strong coupling (AdS/CFT)
drag force
(Gubser ’06,’07, HKKKY ’06, Teaney ‘06) ,

5. Model of HQ in medium
relativistic Langevin equation
in the rest frame of matter
assume isotropic noise
the only input,
dimensionless
relaxation time of HQ 22
6.7
2.2 72 21
7.2
(at T=210MeV)

6. c(b)→D(B)→e- +νe+π etc
3. Hydro + HQ Model
Flowchart
0 fm….
Little Bang
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
Electron Spectra
Experiment
(PHENIX, STAR ’07)
time

7. Comments <decayed electron in pp> Initial condition
<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 coexisting phase at 1st order P.T.
 3 choices (no/half/full coexisting phase)

8. 4. Numerical Results 22 6.7 2.2 72 21 7.2 Profile of HQ Diffusion
2 time scales
: stay time and relaxation time
stay time :
~3-4fm
<relaxation times> 22
6.7
2.2 72 21
7.2
Charm ~ not yet fully thermalized
Bottom ~ not thermalized at all
<stay times>

9. HQ Spectra Nuclear modification factor
Large pT, γ large momentum loss
 large suppression

10. Elliptic flow
High pT  (almost) no anisotropy
At low pT, large γ large anisotropy

11. Electron Spectra Bottom ratio
At pT above 3GeV, bottom origin electrons dominate.

12. Nuclear modification factor

13. Poor statistics for both simulation and experiment at high pT.
Elliptic flow
Poor statistics for both simulation and experiment at high pT.
But at least consistent.
(Still preliminary, PHENIX : v2~ for pT~3-5GeV)
Quite Large v2

14. 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.

15. Back Up Slides

16. Average Temperature
charm
bottom

17. Momentum Loss
charm
bottom

18. RAA of Electrons from Charm/Bottom