Transcript Heavy Quark Diffusion in the Quark

2009/05/09
Heavy Ion Café
@Tokyo
Langevin + Hydrodynamics Approach
to Heavy Quark Diffusion in the QGP
Yukinao Akamatsu
Tetsuo Hatsuda
Tetsufumi Hirano
(Univ. of Tokyo)
Ref : Y.A., T.Hatsuda and T.Hirano, arXiv:0809.1499[hep-ph]
1
Outline
•
•
•
•
Introduction
Langevin + Hydro Model for Heavy Quark
Numerical Calculations
Conclusions and Outlook
2
Introduction
0
CGC
0.6fm
Glasma
O(10) fm
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 !
3
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



2
P( )  exp

 2 D( p)t 

the only input,
dimensionless
Satisfy fluctuation-dissipation
theorem
2) Energy loss of heavy quarks
Weak coupling (pQCD)
 ~ 0.2
(leading order)
Poor convergence (Caron-Huot ‘08)
4
Strong coupling (SYM by AdS/CFT  sQGP) [  gYM
for naïve perturbation]


2
 gYM
N 2 v
N=4 SYM theory dp
T2 

T
 
p ( g 2 N , N  )
YM
2
dt
“Translation” to sQGP
M
1 v
(Gubser ’06, Herzog et al. ’06, Teaney ’06)
2
  2.1  0.5
(Gubser ‘07)
4
3) Heavy Quark Langevin + Hydro Model
0 fm….
Little Bang
generated by PYTHIA
QGP
0.6 fm…
Initial Condition
Brownian Motion
(pp + Glauber)
Local temperature
and flow
T(x), u(x)
Full 3D hydrodynamics
(Hirano ’06)
Heavy Quark Spectra
O(10)fm…
_
c(b)→D(B)→e- +νe+π etc
(independent fragmentation)
Electron Spectra + ….
time
Experiment
(PHENIX, STAR ’07)
5
Numerical Calculations
1) Nuclear Modification Factor
Experimental result  γ=1-3
AdS/CFT γ=2.1±0.5
・Initial (LO pQCD): good only at high pT
・CNM, quark coalescence : tiny at high pT
Different
freezeouts
at 1st order
P.T.
Bottom dominant
6
2) Elliptic Flow
Poor statistics, but at least consistent with γ=1-3.
(Still preliminary, PHENIX : v2~0.05-0.1 for pT~3-5GeV)
7
 Degree of HQ Thermalization
tS ~ 3  4[fm]
M
Relaxation time  HQ 
T 2
Stay time
22
72
6.7 2.2
21 7.2
thermalized
not thermalized
Experimental result γ=1-3  charm : nearly thermalized,
bottom : not thermalized
8
3) Azimuthal Correlation
Back to back correlation
diffusion
quenched & broadened
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
9
electron - (charged) hadron correlation
(e - π, K, p) = (trigger - associate)
・More quenching & broadening
with larger γ
・Mach cone : not included
Quenching of backward
(0.5π-1.5π) signal QBS
QBS ( ) 
A( )
A(  0)
ZYAM
10
electron - muon correlation
(trigger - associate)
electron, muon : mid-rapidity (< 1.0)
・More quenching & broadening
with larger γ
・High pT associate : energy loss
・Low pT associate : fluctuation
・Energy loss  quenching
・Fluctuation  broadening
Quenching of backward
(0-2π) signal QBS
11
electron - muon correlation
(trigger - associate)
electron : mid pseudo-rapidity (< 0.35)
muon : forward pseudo-rapidity (1.4~2.1)
12
Conclusions and Outlook
Y. Morino (PhD Thesis)
arXiv:0903.3504 [nucl-ex]
(Fig.7.12)
• 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

p    

     P ( p, x , t )
 t E x 
  
 1 
 
   ( p ) p    D( p )  P( p, x , t )
p 
2 p

( p)  T
2



M  p  ( p ) pt  



2
P( )  exp

 2 D( p)t 


Peq  exp 
p2  M 2 T


( p ) 
dD( p ) D( p )
 
d ( p2 )
2 ET
2T 3
D( p)  
(E  T )
M
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:
Gamma=1_ccbar:
Gamma=3_ccbar:
Gamma=10_ccbar:
Gamma=30_ccbar:
1.2%
4.2%
25%
68%
90%
Gamma=0.3_eb:
Gamma=0.3_mb:
Gamma=1_eb:
Gamma=1_mb:
Gamma=3_eb:
Gamma=3_mb:
Gamma=10_eb:
Gamma=10_mb:
0.75%
0.97%
1.7%
2.0%
5.3%
5.1%
31%
30%
Gamma=0.3_bbbar:
Gamma=1_bbbar:
Gamma=3_bbbar:
Gamma=10_bbbar:
Gamma=30_bbbar:
0.70%
0.93%
2.2%
15%
46%
20
 Degree of HQ Thermalization
Time measured by a clock comoving with fluid element
For γ=0-30 and initial pT=0-10GeV
Stay time
DEFINITION
VALUE
ts=Σ Δt|FRF
3-4 [fm]
Temperature T=Σ(TΔt|FRF) / ts
 HQ
M

T 2
22
72
_
~210 [MeV]
6.7 2.2
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
23