QGP viscosity at RHIC and LHC energies
New Results from Viscous Hydro + URQMD (VISHNU)
Huichao Song 宋慧超
International School for High Energy Nuclear Collisions ,
Wuhan, Oct 31- Nov.5, 2011
Supported by DOE
References:
H. Song , S. Bass and U. Heinz, Phys. Rev. C83, 024912 (2011)
H. Song, S. Bass, U. Heinz, T. Hirano and C. Shen, Phys. Rev. Lett. 106, 192301(2011)
H. Song, S. Bass, U. Heinz, T. Hirano and C. Shen, Phys. Rev. C83, 054910(2011)
1
H. Song, S. Bass, U. Heinz, Phys Rev. C83 054912(2011)
11/04/2011
QGP-the most perfect fluid in the world?
BNL News, 2005
How perfect the QGP fluid is?
2
viscous hydrodynamics
 T  ( x)  0
T    (e  p  )u  u  ( p  ) g     


1   T

    u 
2

 T

     (  u)  1  T      u 
 
 T

2 


           2   
Input: “EOS”
   ( p)
S.Bass
3
viscous hydrodynamics
T    (e  p  )u  u  ( p  ) g     
 T  ( x)  0


1   T

    u 
2

 T

     (  u)  1  T      u 
 
 T

2 


           2   

Input: “EOS”
   ( p)

4
viscous hydrodynamics
 T  ( x)  0
T    (e  p  )u  u  ( p  ) g     


1   T

    u 
2

 T

     (  u)  1  T      u 
 
 T

2 


           2   
Input: “EOS”
   ( p)
S.Bass
pre-equilibrium dynamics + viscous hydro + hadron cascade
Initial conditions + viscous hydro (QGP & HRG) + final conditions
Initial conditions + viscous hydro (QGP) + hadron cascade (HRG)
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Viscous hydro: Shear viscosity & elliptic flow V2
H. Song and U. Heinz,
PRC08
Elliptic flow v2
20-25% v2 suppression
-V2 can be used to extract the QGP shear viscosity
E

s

1
4
dN
dN

d 3 p dypT dpT d
1 dN
-For an accurate extraction of QGP viscosity, one

[1  2v 2 ( pT , b) cos(2 )  ...]
2

dyp
dp
needs to control the theoretical uncertainties as well
T
T
6
as precise exp data.
Hadronic effects on elliptic flow V2
Partially Chemical equil.
hadronic dissipative effects
Ideal hydro
~30%
~30-50%
P. Huovinen 07
0
1
T. Hirano 06
pT (GeV)
-These two HRG effects are not included in early viscous hydro calculations
viscous hydro + hadron cascade (URQMD) hybrid approach
7
URQMD includes the partially chemical equilibrium nature & hadronic dissipative effects
viscous hydro vs.
viscous hydro + hadron cascade
8
viscous v suppression
2
H. Song, S. Bass & U. Heinz, PRC11
ideal hydro (QGP & HRG)
20% 30% viscous hydro
(QGP & HRG)
viscous hydro (QGP)
+ URQMD (HRG)
s95p-PCE
v2 suppression increases from ~20% (min visc hydro)
to ~30% (min visc hydro + URQMD)
9
Extracting QGP viscosity from RHIC data
EXP.
from different exp methods
are affected by non-flow and
fluctuations
V2
~20%
STAR DATA
~20% uncertainties in EXP V2
~100% uncertainties for the
extracted QGP viscosity
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Extracting QGP viscosity from RHIC data
EXP.
Corrected v2:
Ollitrault, Poskanzer & Voloshin, PRC09
with assumptions on fluctuations and non
flow, all corrected v2 in participant /
reaction plan converge to unique curves
Corrected V2
greatly reduces uncertainties from
EXP data for the extracted  / s
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Extracting QGP viscosity from RHIC data
Theoretical Modeling
Viscous Hydro + URQMD
-initial conditions
-EoS: s95p-PCE
Huovinen & Petreczky10
-chemical composition of HRG
Song, Bass
& Heinz, PRC2011
-viscosity of HRG
Song & Heinz,
-bulk viscosity: <20%
PRC 09
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Extracting QGP viscosity from RHIC data
initial conditions
Viscous Hydro + URQMD
-initial conditions
-EoS: s95p-PCE
Huovinen & Petreczky10
-chemical composition of HRG
Song, Bass
& Heinz, PRC2011
-viscosity of HRG
Song & Heinz,
-bulk viscosity: <20%
- Glauber / KLN initializations
- Fluctuation effects
 0 , s( x, y, 0 )
Constrained from dN/dy and spectra
- initial flow
PRC 09
v2 is sensitive to the initial conditions
v2 /   (1 / S )dN / dy
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v2 /   (1 / S ):dN / dy:
QGP viscosity
H. Song, S. Bass, U. Heinz, T. Hirano, and C. Shen, PRL2011
v2 /   (1 / S )dN / dy is insensitive to initial conditions, but sensitive to the QGP
viscosity in viscous hydro +URQMD calculations
14
theoretical vs. experimental v2 /   (1 / S )dN / dy
---QGP viscosity
Ollitrault, Poskanzer & Voloshin, PRC09
Exp.
v2 /   (1 / S )dN / dy
Corrected V2
in part. plan
- Corrected V2 in participant plan
- dN/dy : STAR data 08
-  , S Glauber / fKLN (part. plan)
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QGP viscosity from v2 /   (1 / S )dN / dy
MC-KLN
(Part. Plan)
MC-Glauber
(Part. Plan)
 / s  0.16  0.24 for MC-KLN initial conditions
 / s  0.08  0.16 for MC-Glauber initial conditions
H. Song, S. Bass, U. Heinz, T. Hirano, and C. Shen, PRL2011
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QGP viscosity from v2 /   (1 / S )dN / dy
MC-KLN
MC-Glauber
(Part. Plan)
(Part. Plan)
effects from initial flow
 / s  0.16  0.24
 / s  0.08  0.16
effects from bulk viscosity
for MC-KLN initial conditions
for MC-Glauber initial conditions
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H. Song, S. Bass, U. Heinz, T. Hirano, and C. Shen, PRC2011
-a nice fit for both pion and proton spectra, insensitive to QGP viscosity
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H.Song, S. Bass , U. Heinz, T. Hirano, and C. Shen, PRC2011
5-10%
 / s  0.08
20-30%
20-30%
30-40%
30-40%
40-50%
40-50%
Glauber
Glauber
5-10%
 / s  0.16
20-30%
20-30%
30-40%
30-40%
40-50%
40-50%
KLN
KLN
-fluctuating effects is reduced by comparing theory v2 /  & EXP. v2 {2} /  2
-hit the lower-bound of  / s extracted from v2 /   (1 / S )dN / dy (non flow effects)
 / s  0.08  0.16 for Glauber initial condi.
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 / s  0.16  0.24 for KLN initial condi.
QGP viscosity at RHIC & LHC energies
-- H. Song, S. Bass, U. Heinz, PRC2011
ALICE collaboration arXiv:1011.3914[nucl-ex]
20
V2(PT) at RHIC and LHC
Song, Bass & Heinz, PRC2011
Assuming const.
/s
This is not aim for extracting QGP
viscosity at LHC energy with
reliable uncertainty estimates
 / s  0.16
Approximately fit STAR v2{4}, but over predict ALICE v2{4}
21
V2(PT) at RHIC and LHC
Song, Bass & Heinz, PRC2011
Assuming const.
RHIC:
LHC:
/s
 / s  0.16
 / s  0.20  0.24
This is not aim for extracting QGP
viscosity at LHC energy with
reliable uncertainty estimates
 / s  0.16
Approximately fit STAR v2{4}, but over predict ALICE v2{4}
22
Is QGP fluid more viscous at LHC ?
Song, Bass & Heinz, PRC2011
Assuming const.
/s
RHIC:  / s  0.16(Tc
LHC:  / s  0.24(Tc
 2Tc )
?
 3Tc )
Weakly coupled QGP
Lattice results
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Is QGP fluid more viscous at LHC ?
Song, Bass & Heinz, PRC2011
We do not have enough
evidence from v2 and
spectra alone
At this moment, it is an open issue on
whether QGP fluid is more viscous or perfect
in temperature region covered by LHC !
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A short summary
- v 2 is sensitive to  / s
Extraction
/s
from elliptic flow data using viscous hydro + UrQMD indicates:
1  (1 4  )   / s  3  (1 4  )
Similar averaged QGP viscosity at RHIC and LHC energies
-Relatively larger uncertainties are from initial geometry
MC-Glauber:  / s  (1  2)  (1 / 4 )
MC-KLN:
 / s  (2  3)  (1 / 4 )
-Relatively smaller uncertainties are from
initial flow, bulk viscosity, single short hydro vs. e-by-e simulations …
-other possible observables may help to reduce these uncertainties ,
photons, HBT radii, triangular flow …
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Photons
HBT
/s
V2
Spectra
Other free inputs in the hybrid model
26
e-b-e hydro vs. single shot hydro
Zhi & Heinz, preliminary results
Event-by-event hydro produces
5% less v2/ecc than singleshot hydro with smooth
averaged initial profile
initial flow, bulk viscosity and e-b-e hydro:
 / s  0.16  0.24
 / s  0.08  0.16
each of them shifts v2 by a few percent
cancelation among them
for MC-KLN initial conditions
for MC-Glauber initial conditions
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30
31
Thank You
32
Thank You
33
HBT radii
S. Pratt QM09
without viscosity
with viscosity
- Rout / Rside is sensitive to the QGP viscosity
- However, viscosity is only one of the many ingredients that affect HBT radii (Pratt QM09)
- HBT HELPS to constrain the QGP viscosity, together with other observables (V2 …)
34
EM probes: Photons
Photon spectra
Pion spectra
K. Dusling, 0903
-Viscous hardening of PT-spectra is stronger for photons than hadrons
f / f 0 ~
   p  p
e p
T2
 
e p
~
 1
sT 
-However, earlier thermalization also leads to harder photon spectra (Dusling 0903)
-Photon spectra MAY HELP to constrain the 2-d range of QGP viscosity &
thermalization time, together with other observables (V2 …)
35
Triangular flow & QGP viscosity
Schenke, Jeon & Gale,
arXiv:1009.3244 [hep-ph]
-triangular flow is sensitive to QGP shear viscosity
36
Triangular flow & QGP viscosity
2
Schenke, Jeon & Gale,
arXiv:1009.3244 [hep-ph]
MC-KLN
MC-Glauber
3
Zhi & Heinz, preliminary results
-triangular flow is sensitive to QGP shear viscosity
37
-triangular flow may help us to eliminate the uncertainties from KLN and Glauber
LHC
38
v2 /   (1 / S )dN / dy
& initialization models
Glauber
 , S from MC- glauber
(smearing) with finite
nucleon size
(used by our theoretical Cal)
 , S from MC- glauber
with very small nucleon
size (delta function)
(used by some EXP. Group )
The slope of theoretical
model (with delta fun. )
v2 /   (1 / S )dN / dy curves is un-favor the early MC-Glauber
39
Uncertainties from bulk viscosity
N-S initialization
   ( / s)  120fm/c
Zero initialization
   ( / s)  120fm/c
C 1
 /s
C  1.3
C 1  /s
C  100
Song & Heinz, 0909
-with a critical slowing down   , effects from bulk viscosity effects are much
smaller than from shear viscosity
bulk viscosity influences V2 ~5% (N-S initial.)
uncertainties to  / s ~20% (N-S initial.)
<4% (zero initial.)
<15% (zero initial.)
40