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
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