Heavy Quark Diffusion with Relativistic Langevin Dynamics in the Quark-Gluon Fluid

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Heavy Quark Diffusion with Relativistic Langevin
Dynamics in the Quark-Gluon Fluid
ATHIC 2008 Tsukuba

• Yukinao Akamatsu ?? ??
• (Univ. of Tokyo)

Ref YA, T. Hatsuda, and T. Hirano,
arXiv0809.1499hep-ph
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Outline

• Introduction
• Langevin Dynamics of Heavy Quarks
• Hydro HQ Model
• Numerical Results
• Conclusions and Outlook

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1. Introduction

• Relativistic Heavy Ion Collision

Light (m ltlt T200MeV) components (g, u, d, s)
HQ
relativistic ideal hydrodynamics
g,u,d,s
?strongly coupled matter
Heavy (M gtgt T200MeV) components (c, b)
long time scale ? not thermalized in fluid ?
impurity
Other impurities J/? (color singlet), Jet (too
energetic)
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2. Langevin Dynamics of Heavy Quarks
ltEnergy loss of HQgt

• 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 gt 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)
,
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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 T210MeV)
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3. Hydro HQ Model

• Flowchart

Little Bang
0 fm.
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- ?ep etc
Electron Spectra
Experiment
(PHENIX, STAR 07)
time
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• Comments

ltdecayed electron in ppgt
Initial condition
ltHQ in ppgt
available only spectral shape above pT3GeV
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)
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4. Numerical Results

• Profile of HQ Diffusion

2 time scales
stay time and relaxation time
stay time
3-4fm
ltrelaxation timesgt

22 6.7 2.2
72 21 7.2
Charm not yet fully thermalized Bottom not
thermalized at all
ltstay timesgt
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• HQ Spectra

Nuclear modification factor
Large pT, ?? large momentum loss ? large
suppression
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Elliptic flow
High pT ? (almost) no anisotropy At low pT,
large ?? large anisotropy
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• Electron Spectra

Bottom ratio
At pT above 3GeV, bottom origin electrons
dominate.
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Nuclear modification factor
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Elliptic flow
Poor statistics for both simulation and
experiment at high pT. But at least
consistent. (Still preliminary, PHENIX
v20.05-0.1 for pT3-5GeV)
Quite Large v2
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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.

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Back Up Slides
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Average Temperature
charm
bottom
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Momentum Loss
charm
bottom
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RAA of Electrons from Charm/Bottom
charm
bottom