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2009/11/25 Discussion with Prof. Blaizot. Heavy Quark and charm propagation in Quark-Gluon plasma. Ref : Y.A., T.Hatsuda and T.Hirano, PRC79,054907 (2009) Y.A., T.Hatsuda and T.Hirano, PRC80,031901(R) (2009). Yukinao Akamatsu T etsuo Hatsuda Tetsufumi Hirano

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heavy quark and charm propagation in quark gluon plasma


Discussion with Prof. Blaizot

Heavy Quark and charm propagationin Quark-Gluon plasma

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

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

Yukinao Akamatsu

Tetsuo Hatsuda

Tetsufumi Hirano

(Univ. of Tokyo)

  • Introduction
  • Langevin + Hydro Modelfor Heavy Quark
  • Numerical Calculations
  • Conclusions and Outlook
  • Discussion




O(10) fm

initial thermalization hydrodynamics hadron scattering observed

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

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

Others : jets, J/Psi, etc

Heavy quarks (c,b) --- heavy compared to temperature

tiny thermal pair creation

no mutual interaction

 Good probe !


Langevin + Hydro Model for Heavy Quark

1) Our model of HQ in medium

in the (local) rest

frame of matter

Relativistic Langevin equation

Assumeisotropic Gaussian white noise

the only input,


Satisfy fluctuation-dissipation


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)


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


T(x), u(x)

(Hirano ’06)

Heavy Quark Spectra


c(b)→D(B)→e- +νe+π etc


(independent fragmentation)

Electron Spectra+ ….





Numerical Calculations

1) Nuclear Modification Factor & Elliptic Flow

Experimental result  γ=1-3

(AdS/CFT γ=2.1±0.5)

charm : nearly thermalized

bottom : not thermalized

Different freezeouts at 1st order P.T.

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

bottom dominant

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

・CNM, quark coalescence : tiny at high pT


2) Azimuthal Correlation

Back to back correlation of a heavy quark pair


Loss of correlation in decay products from D & B


correlation : one peak

no contribution from vector meson decay

IAA : quantitative measure

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


e-h correlation (mid-pseudorapidity)

: two peaks

A sensitive probe but not clean …

Effects we ignore :

・Hadronic interaction of associates

・Medium response to HQ propagation

・Fictitious correlation due to bulk v2

Relative angle range for IAA

Near side : -0.5π≦Δφ≦0.5π

Away side : 0.5π≦Δφ≦1.5π


Conclusions and Outlook

  • 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 anew 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)

A Little More on Langevin HQ

Fluctuation-dissipation theorem

Ito discretization  Fokker Planck equation

Generalized FD theorem


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)