Huichao Song

The Ohio State University

Lawrence Berkeley National Lab

Viscous Hydro +URQMD

In collaboration with S.Bass, U.Heinz, C.Shen, P.Huovinen & T.Hirano (?)

06/14/2004

May24- July 16, INT Seattle, WA

Quantifying the Properties of Hot QCD Matter

Supported by DOE

Viscous hydrodynamics

0)( xT

S.Bass

Conservation laws:

gpuupeT )()(

u

T

T

2

12 - Israel-Stewart

eqns.

u

T

Tu

2

1)( 0

S

Viscous hydrodynamics

0)( xT

S.Bass

Conservation laws:

gpuupeT )()(

u

T

T

2

12 - Israel-Stewart

eqns.

u

T

Tu

2

1)( 0

S

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

S.Bass

MC- Particle Generator

Tsw

Convertor: MC particle generator

)],(),([2

)(3

3

3 pxfpxfxdp

pd

dNE eq

i

i

))((

)(

)(2

1),( 2 xpe

x

xT

pppxf

VIS -MC

extracting QGP viscosity from data Luzum & Romatschke, PRC 2008 Glauber CGC

2v

-Effects from highly viscous & non-chemical equilibrium hadronic stage, bulk viscosity …

?16.0/ s NOT so fast !

Effects of viscosity & chemical composition of HRG

(GeV)Tp0 1

~30%

PCE vs.CE (HRG)

Ideal hydro

P. Huovinen 07

- 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 hydro vs ideal hydro +hadron cascade

~30%

Ideal / viscous hydro+URQMD

SM-EOS Q (CE) vs. EOSL-PCE

ideal hydro vs. ideal hydro+URQMD (EOSL-PCE)

- EOS L-PCE : Hadronic viscosity (URQMD) leads to ~20% viscous v2 suppression

EOS L-PCE

ideal hydro +URQMD: SM-EOSQ(CE) vs. EOSL-PCE

- 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)

0/ s0/ s

SM-EOS Q (CE)

EOS L-PCE

SM-EOSQ(CE): viscous vs. ideal hydro +URQMD

- 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

08.0/ s 0/ s

SM-EOS Q (CE)

SM-EOS Q (CE)

ppf ~

EOSL-PCE: ideal vs. viscous hydro + URQMD

-EOS L-PCE: additional v2 suppression by URQMD (ideal/viscous hydro + URQMD behave similarly)

-Larger URQMD viscous v2 suppression in ideal hydro +URQMD

08.0/ s 0/ s

EOS L-PCE EOS L-PCE

Spectra: SM-EOS Q(CE) vs. EOSL-PCE

-EOS L-PCE (correct chemistry below Tch) is preferable

EOS L-PCE

EOS L-PCESM-EOS Q (CE)

SM-EOS Q (CE)

viscous v2 suppression

EOS L-PCE

-EOS L-PCE: v2 suppression increases from ~20% (min visc hydro) to ~30% (min visc hydro + URQMD)

viscous v2 suppression

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

-Radial flow increases the mass splitting between pion and proton; similar behavior in ideal/ viscous hydro +URQMD

EOS L-PCE EOS L-PCE

08.0/ s0/ s

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

-larger URQMD viscous v2 suppression for smaller systems

-viscous hydro + URQMD: smaller URQMD viscous v2 suppression, comparing with ideal hydro + URQMD

ideal vs viscous hydro & ideal vs viscous hydro +URQMD

-Viscous v2 suppressions are significantly reduced after a proper treatment of hadronic matter (URQMD)

: ideal Hydro + URQMD

-Hadronic viscosity from URQMD increase the slope of dydNSv /)/1(/2

dydNSv /)/1(/2

: ideal /Viscous Hydro + URQMD (I)

-hadronic viscosity from URQMD increases the slope of dydNSv /)/1(/2

dydNSv /)/1(/2

-hadronic viscosity from URQMD increase the slope of

- v2 is not fully saturated at Tsw the increase of the slope

dydNSv /)/1(/2

: ideal /Viscous Hydro + URQMD (II) dydNSv /)/1(/2

: experimental data Thanks for A. Tang for Exp data

dydNSv /)/1(/2

-Experimental data: v2 , dN/dy ; theoretical estimations: ecc. S (Glauber/CGC) -larger slope and magnitude for v2/ecc. for glauber initial profile

Glauber CGC

A hint for min vis. liquid with CGC initializationThanks for A. Tang for Exp data

- v2/ecc from hydro +URQMD is not sensitive to Glauber /CGC or optical/ fluctuation initializations (need some further calculations)

Glauber CGC

-Theoretical curves are all from Glauber initialization (add cures in the future )

-Overlap area are different for CGC and Glauber initializations

viscous hydro+URQMD

-- a try to extract the hadronic viscosity

vs. viscous hydro with )(/ Ts

EOSL-PCE is an essential input for the calculations here

inte v2 from hydro +URQMD with diff. Tsw

)(/ Ts-with a “perfect” and “correct” chemical components (PCE) for hadrons phase, final results from hydro +URQMD should not be sensitive to Tsw

- is not enough for hadronic viscosity 08.0/ s

inte v2 from hydro +URQMD with diff. Tsw

- is not enough for hadronic viscosity 08.0/ s - over suppresses v2 for T=165-150 MeV, but not enough for T<130 MeV 24.0/ s

inte v2 from hydro +URQMD with diff. Tsw

- is not enough for hadronic viscosity 08.0/ s - over suppresses v2 for T=165-150 MeV, but not enough for T<130 MeV 24.0/ s

extract from URQMD (a first try)

a hint?

24.0~/ s

- is not enough for hadronic viscosity 08.0/ s - over suppresses v2 for T=165-150 MeV, but not enough for T<130 MeV 24.0/ s

)(/ Ts

inte v2 from hydro +URQMD with diff. &Tsw s/

inte v2 from hydro +URQMD with diff. &Tsw s/

extract from URQMD (a first try)

?16.0/08.0 s?24.0/16.0 s

?48.0/24.0 s

-please do NOT take the above number too seriously -need further detailed extraction - such extraction gives a special trajectory of URQMD dynamic )(/ Ts

)(/ Ts

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 and hydro+URQMD)(/ Ts

Thank You