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Viscous Hydro +URQMD
Huichao Song
The Ohio State University
Lawrence Berkeley National Lab
Quantifying the Properties of Hot QCD Matter
May24- July 16, INT Seattle, WA
In collaboration with S.Bass, U.Heinz,
C.Shen, P.Huovinen & T.Hirano (?)
Supported by DOE
06/14/2004
Viscous hydrodynamics
S.Bass
Conservation laws:
 T  ( x)  0
T    (e  p  )u  u  ( p  ) g     


1   T

    u 
2

 T

     (  u)  1  T      u 
 
 T

2 


           2   
- Israel-Stewart eqns.
 S  0
Viscous hydrodynamics
S.Bass
Conservation laws:
 T  ( x)  0
T    (e  p  )u  u  ( p  ) g     


1   T

    u 
2

 T

     (  u)  1  T      u 
 
 T

2 


           2   
- Israel-Stewart eqns.
 S  0
viscous hydro: near-equilibrium system
pre-equilibrium dynamics + viscous hydro + hadron cascade
Initial conditions
viscous hydro + final conditions
Ideal/ViscousHydro + URQMD
2+1 Ideal/Viscous Hydro
Hadron Cascade
MC- Particle
Generator
S.Bass
Tsw
Convertor:
MC particle generator
p  d 3 i ( x )
dN
E 3

[ f eq ( x , p)  f ( x , p)]
3
d pi
2
VIS -MC
1 p p     ( x )
f ( x , p) 
2 T 2 ( x ) (e  p)( x )
extracting QGP viscosity from v2 data
Glauber
Luzum & Romatschke, PRC 2008
 / s  0.16?
CGC
NOT so fast !
-Effects from highly viscous & non-chemical equilibrium hadronic stage, bulk viscosity …
Effects of viscosity & chemical composition of HRG
PCE vs.CE (HRG)
Ideal hydro
vs
ideal hydro +hadron cascade
Ideal hydro
~30%
~30%
P. Huovinen 07
0
1
pT (GeV)
- Does hadronic viscosity and partially equilibrium chemistry balance each other in
elliptic flow? Is it safe to neglect both of them, when extracting QGP viscosity?
Ideal / viscous hydro+URQMD
SM-EOS Q (CE) vs. EOSL-PCE
ideal hydro vs. ideal hydro+URQMD (EOSL-PCE)
EOS L-PCE
- EOS L-PCE : Hadronic viscosity (URQMD) leads to ~20% viscous v2 suppression
ideal hydro +URQMD: SM-EOSQ(CE) vs. EOSL-PCE
/s0
/s0
EOS L-PCE
SM-EOS Q (CE)
- EOS L-PCE: Hadronic viscosity (URQMD) leads to ~20% viscous v2 suppression
- SM-EOS Q (CE): effects from hadronic viscosity and PCE (in URQMD) cancel each
other in elliptic flow v2 (Ideal hydro+URQMD)
SM-EOSQ(CE): viscous vs. ideal hydro +URQMD
/s0
 / s  0.08
f ~ p p   
SM-EOS Q (CE)
SM-EOS Q (CE)
- SM-EOS Q (CE): effects from hadronic viscosity and PCE (URQMD) cancel each
other in elliptic flow v2 (ideal hydro+URQMD)
-This is no longer true in viscous hydro+URQMD
-much larger v2 suppression for PT>1GeV: effects from shear viscous correction / EOS
EOSL-PCE: ideal vs. viscous hydro + URQMD
/s0
 / s  0.08
EOS L-PCE
EOS L-PCE
-EOS L-PCE: additional v2 suppression by URQMD (ideal/viscous hydro + URQMD
behave similarly)
-Larger URQMD viscous v2 suppression in ideal hydro +URQMD
Spectra: SM-EOS Q(CE) vs. EOSL-PCE
SM-EOS Q (CE)
EOS L-PCE
SM-EOS Q (CE)
EOS L-PCE
-EOS L-PCE (correct chemistry below Tch) is preferable
viscous v suppression
2
EOS L-PCE
-EOS L-PCE: v2 suppression increases from ~20% (min visc hydro)
to ~30% (min visc hydro + URQMD)
viscous v suppression
2
EOS L-PCE
-EOS L-PCE: v2 suppression increases from ~20% (min visc hydro)
to ~30% (min visc hydro + URQMD)
---> significantly reduces the extracted QGP viscosity
ideal/viscous hydro +URQMD: mass splitting
/s0
 / s  0.08
EOS L-PCE
EOS L-PCE
-Radial flow increases the mass splitting between pion and proton; similar behavior in
ideal/ viscous hydro +URQMD
More Systematic study
Inte v2: hydro decouple at Tsw vs. hydro+URQMD
-v2 is not fully developed at Tsw;
-positive ecc. at Tsw  additionally increase of v2 in URQMD
Inte v2: ideal hydro, vis hydro, vis hydro+URQMD
-Additional v2 suppression in URQMD (hadronic stage is highly viscous)
viscous v2 suppression: hydro vs. hydro+URQMD
-viscous hydro + URQMD: smaller URQMD viscous v2 suppression,
comparing with ideal hydro + URQMD
-larger URQMD viscous v2 suppression for smaller systems
ideal vs viscous hydro & ideal vs viscous hydro +URQMD
-Viscous v2 suppressions are significantly reduced after a proper treatment
of hadronic matter (URQMD)
v2 /   (1 / S )dN / dy:
ideal Hydro + URQMD
-Hadronic viscosity from URQMD increase the slope of v2 /   (1 / S )dN / dy
v2 /   (1 / S )dN / dy :
ideal /Viscous Hydro + URQMD (I)
-hadronic viscosity from URQMD increases the slope of v2 /   (1 / S )dN / dy
v2 /   (1 / S )dN / dy :
ideal /Viscous Hydro + URQMD (II)
-hadronic viscosity from URQMD increase the slope of v2 /   (1 / S )dN / dy
- v2 is not fully saturated at Tsw  the increase of the slope
v2 /   (1 / S )dN / dy :
Glauber
-Experimental data:
experimental data
CGC
v2 ,
dN/dy ;
Thanks for A. Tang for Exp data
theoretical estimations: ecc. S (Glauber/CGC)
-larger slope and magnitude for v2/ecc. for glauber initial profile
A hint for min vis. liquid with CGC initialization
Glauber
CGC
Thanks for A. Tang for Exp data
-Theoretical curves are all from Glauber initialization (add cures in the future )
- v2/ecc from hydro +URQMD is not sensitive to Glauber /CGC or optical/ fluctuation
initializations (need some further calculations)
-Overlap area are different for CGC and Glauber initializations
viscous hydro+URQMD
vs. viscous hydro with  / s(T )
-- a try to extract the hadronic viscosity
EOSL-PCE is an essential input for the calculations here
inte v2 from hydro +URQMD with diff. Tsw
-with a “perfect”  / s(T ) and “correct” chemical components (PCE) for hadrons phase,
final results from hydro +URQMD should not be sensitive to Tsw
- / s  0.08 is not enough for hadronic viscosity
inte v2 from hydro +URQMD with diff. Tsw
- / s  0.08 is not enough for hadronic viscosity
-  / s  0.24 over suppresses v2 for T=165-150 MeV, but not enough for T<130 MeV
inte v2 from hydro +URQMD with diff. Tsw
- / s  0.08 is not enough for hadronic viscosity
-  / s  0.24 over suppresses v2 for T=165-150 MeV, but not enough for T<130 MeV
extract  / s(T ) from URQMD (a first try)
 / s ~ 0.24
a hint?
- / s  0.08 is not enough for hadronic viscosity
-  / s  0.24 over suppresses v2 for T=165-150 MeV, but not enough for T<130 MeV
inte v2 from hydro +URQMD with diff.  / s &Tsw
inte v2 from hydro +URQMD with diff.  / s &Tsw
extract  / s(T ) from URQMD (a first try)
0.08   / s  0.16 ?
0.16   / s  0.24 ?
0.24   / s  0.48 ?
-please do NOT take the above number too seriously
-need further detailed extraction
- such extraction gives a special trajectory of URQMD dynamic
 / s(T )
A Short Summary
-when extracting the QGP viscosity, one need to consider the effects of
hadronic viscosity and the hadronic chemical components
-with viscous hydro+URQMD become available, these two above
uncertainties are naturally eliminated
-with a EOS correctly describe PCE HG, it is “somewhat” safe to swtich
hydro to URQMD at lower temperature
---> extract the effective URQMD viscosity at some specific dynamical
trajectory by comparing hydro with  / s(T ) and hydro+URQMD
Thank You