Wu Yuanfang IOPP, Huazhong Normal University, Wuhan, China

2008.10.92008.10.9 SQM’08SQM’0811

An explorer for theAn explorer for the shear viscosityshear viscosity in the formed in the formed matter at relativistic heavy ion collisionsmatter at relativistic heavy ion collisions

Wu YuanfangWu YuanfangIOPP, Huazhong Normal University, Wuhan, ChinaIOPP, Huazhong Normal University, Wuhan, China

1.1. MotivationMotivation

2.2. Azimuthal bin-bin multiplicity corr. patternAzimuthal bin-bin multiplicity corr. pattern

3. The correlation pattern & shear viscosity3. The correlation pattern & shear viscosity

4. A rough estimation of 4. A rough estimation of ηη in AMPT in AMPT

5. Summary and outlook5. Summary and outlook

1.1. MotivationMotivation

2.2. Azimuthal bin-bin multiplicity corr. patternAzimuthal bin-bin multiplicity corr. pattern

3. The correlation pattern & shear viscosity3. The correlation pattern & shear viscosity

4. A rough estimation of 4. A rough estimation of ηη in AMPT in AMPT


Co-authers:Co-authers: Wang Meijuan, Li Lin, and Liu LianshouWang Meijuan, Li Lin, and Liu Lianshou

Acknowledgements:Acknowledgements: T. Hirano, Li Jiarong, Wang Fuqiang, Tang Aihong and Xu T. Hirano, Li Jiarong, Wang Fuqiang, Tang Aihong and Xu

NuNu

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1. Motivation:1. Motivation: 1. Motivation:1. Motivation:

★ ★ Why perfect Why perfect fluid fluid

★ ★ Why perfect Why perfect fluid fluid

► Large energy density achieved

► Jet energy loss in matter ► Collective behaviour observed

« Perfect liquid », « sQGP » !

The mass-dependenceThe mass-dependence

of vof v2 2 at pat pT T < 2 GeV< 2 GeV

shows shows qualitativelyqualitatively

agreement with agreement with idealideal

hydrodynamic flowhydrodynamic flow..

M. Gyulassy, L. McLerran, Nucl. Phys. A750, 30-63(2005); B. Muller, Annu. Rev. Nucl. and Part.

Phys.,1(2006). K. Adcox et al. (PHENIX Coll.), Nucl. Phys. A757, 184-283(2005); John Adams et al.

(STAR Coll.), Nucl. Phys. A757, 102-183(2005);

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★ ★ Why not perfect Why not perfect fluid ?fluid ?

★ ★ Why not perfect Why not perfect fluid ?fluid ?

Perfect liquidPerfect liquid Zero viscosityZero viscosity

S. Pratt, S. Pratt, arXiv: 0809.0089arXiv: 0809.0089; S. A. Voloshin, arXiv: 0805.1351.; S. A. Voloshin, arXiv: 0805.1351.

The result of leading order perturbative :The result of leading order perturbative :

for for / 0.8s 0.3s P. Arnold, G. D. Moore and L. G. Yaffe.P. Arnold, G. D. Moore and L. G. Yaffe.

The lower bound of shear viscosity: 1/ 0.08

4s

It reduces the flow values up to 10-30%.

P. Kovtun, D. T. Son, and A. O. Starinets, Phys. Rev. Lett. 94, 111601(2005) .P. Kovtun, D. T. Son, and A. O. Starinets, Phys. Rev. Lett. 94, 111601(2005) .

It is necessary to know the real value of shear viscosity!It is necessary to know the real value of shear viscosity!

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★ ★ Main difference between perfect and Main difference between perfect and viscous fluid.viscous fluid.

★ ★ Main difference between perfect and Main difference between perfect and viscous fluid.viscous fluid.

There are friction There are friction between two layers.between two layers.

→→

→→

→→→→→→

→→→→→→→→→→

Perfect liquid:Perfect liquid: →→→→→→→→→→

Viscous liquid:Viscous liquid:

No friction betweenNo friction between

two layers of flow.two layers of flow.

Velocity is const.Velocity is const.

Velocity is different Velocity is different

from layer to layer.from layer to layer.

→→

→→

→→→→→→

The The internal interactioninternal interaction and and velocity gradientvelocity gradient are are directly related to the viscous behavior of the fluid. directly related to the viscous behavior of the fluid.

2008.10.92008.10.9 SQM’08SQM’0855

2. Azimuthal bin-bin multiplicity correlation pattern:2. Azimuthal bin-bin multiplicity correlation pattern: 2. Azimuthal bin-bin multiplicity correlation pattern:2. Azimuthal bin-bin multiplicity correlation pattern:

y

x

★★ Neighboring angular bin-bin N corr. pattern:Neighboring angular bin-bin N corr. pattern:★★ Neighboring angular bin-bin N corr. pattern:Neighboring angular bin-bin N corr. pattern:

11

1

1,

mm

mm

mm nn

nnC

Shear interactionShear interaction

mn : multiplicity in : multiplicity in mmth bin.th bin.

MmM

,,1,2

0 : the direction of reaction plane.: the direction of reaction plane.

It measures azimuthalIt measures azimuthal distribution of nearby particles correlation .distribution of nearby particles correlation .

Wu Yuanfang, Lianshou Liu, Yingdan Wang, Yuting Bai & Hongbo Liao, PRE71, 017103 Wu Yuanfang, Lianshou Liu, Yingdan Wang, Yuting Bai & Hongbo Liao, PRE71, 017103 (2005).(2005).

2008.10.92008.10.9 SQM’08SQM’0866

2. Azimuthal bin-bin multiplicity correlation pattern:2. Azimuthal bin-bin multiplicity correlation pattern:2. Azimuthal bin-bin multiplicity correlation pattern:2. Azimuthal bin-bin multiplicity correlation pattern:

★★ Bin-bin correlations & 2-particle correlationsBin-bin correlations & 2-particle correlations★★ Bin-bin correlations & 2-particle correlationsBin-bin correlations & 2-particle correlations

( )( ) ab

ab

NC

N

2-particle corr. :2-particle corr. :

Case 1: Case 1: RandomlyRandomly

produced particlesproduced particles

with in-plane liked with in-plane liked

ΦΦ dis. dis.

Case 2 : Case 2 : RQMDRQMD

w/o re-scatteringw/o re-scattering

Nab: no. of pairs with separated angle δφ.

Bin-bin correlation is not sensitive to

the trivial correlations in both cases !

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2. Azimuthal bin-bin multiplicity correlation pattern:2. Azimuthal bin-bin multiplicity correlation pattern:2. Azimuthal bin-bin multiplicity correlation pattern:2. Azimuthal bin-bin multiplicity correlation pattern:★ ★ Influences of multiplicity (NInfluences of multiplicity (Nchch) and elliplitic ) and elliplitic

flow (vflow (v22))Case 3:Case 3:

Randomly produced Randomly produced

particles with givenparticles with given

ΦΦ dis. for diff. N dis. for diff. N

Case 4:Case 4:

Randomly produced Randomly produced

particles with givenparticles with given

N dis. for diff. N dis. for diff. ΦΦ dis. dis.

Neither of them contributes to the pattern !Neither of them contributes to the pattern !

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2. Azimuthal bin-bin multiplicity correlation pattern:2. Azimuthal bin-bin multiplicity correlation pattern:2. Azimuthal bin-bin multiplicity correlation pattern:2. Azimuthal bin-bin multiplicity correlation pattern:

★ ★ influences of the correlation between N and influences of the correlation between N and vv2 .2 .

Case 5: Randomly produced particles but Case 5: Randomly produced particles but ΦΦ dis. increase with N dis. increase with N

The correlation between N and vThe correlation between N and v22 contributes to the pattern. contributes to the pattern.

It is necessary to study the pattern in fixed N or vIt is necessary to study the pattern in fixed N or v2 2 sample.sample.

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3. The correlation pattern and shear viscosity :3. The correlation pattern and shear viscosity : 3. The correlation pattern and shear viscosity :3. The correlation pattern and shear viscosity :

★★ Bin-bin correlation and interaction energyBin-bin correlation and interaction energy★★ Bin-bin correlation and interaction energyBin-bin correlation and interaction energy

( ), 1 ( )IE

IC e E

M. Stephanov, Int. J. Mod. Phys. A20, 4787(2005);M. Stephanov, Int. J. Mod. Phys. A20, 4787(2005);

M. Stephanov, Phys. Rev. D65, 096008(2002).M. Stephanov, Phys. Rev. D65, 096008(2002).

, is the , is the interaction energyinteraction energy..1

T ( )IE

,,( )Corr I

CE E d d TC d

In the whole system, the total interaction energy is :In the whole system, the total interaction energy is :

If the interaction is small, in the leading order, the correlation is,If the interaction is small, in the leading order, the correlation is,

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★★ Dissipative energy of the fluidDissipative energy of the fluid★★ Dissipative energy of the fluidDissipative energy of the fluid

' 2( )

3i k l l

ik ik ikk i l l

v v v v

x x x x

In hydrodynamics, the viscous stress tensor :In hydrodynamics, the viscous stress tensor :

L. D. Landau & E. M. Lifshitz, Fluid Mechanics, Pergamon Press.L. D. Landau & E. M. Lifshitz, Fluid Mechanics, Pergamon Press.

ηη(p,T) and (p,T) and ξξ(p,T) are shear and bulk viscosity respectively.(p,T) are shear and bulk viscosity respectively.

For incompressible fluid, the dissipative energy is:For incompressible fluid, the dissipative energy is: 2

1

2i k

Dissk i

v vE dVdt

x x

Take the cylindrical coordinates, and assume , Take the cylindrical coordinates, and assume ,

0, 0v

vz

2 2

21 1 1 1

2 2 4T T

Diss

v vE r d dzdt d dzdt

r

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★★ Shear viscosity andShear viscosity and bin-bin correlationbin-bin correlation★★ Shear viscosity andShear viscosity and bin-bin correlationbin-bin correlation

If the bin-bin correlation is only due to viscous interaction, If the bin-bin correlation is only due to viscous interaction,

Then,Then,

Corr DissE Ei.e.,i.e.,

2

,

1

4TvTC d d dzdt

,2

4

T

TC

vdzdt

T T → p→ pTT spectrum; spectrum; → → final velocity gradient.final velocity gradient.2

Tv dzdt

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4. A rough estimation of shear viscosity in AMPT:4. A rough estimation of shear viscosity in AMPT: 4. A rough estimation of shear viscosity in AMPT:4. A rough estimation of shear viscosity in AMPT:

★★ Correlation pattern from AMPT with string Correlation pattern from AMPT with string melting:melting:

★★ Correlation pattern from AMPT with string Correlation pattern from AMPT with string melting:melting:

Correlation patternCorrelation pattern

is in-plane like!is in-plane like!

, 0 1 2cos cos(2 )C u u u If we fit it by:If we fit it by:

then :then :5

, 0.0035 6.23*10 cos 0.00049cos(2 )C

For Au + Au collisions at 200 GeV with fixed N and bFor Au + Au collisions at 200 GeV with fixed N and b

2008.10.92008.10.9 SQM’08SQM’081313


★★ Velocity Velocity gradient:gradient:

★★ Velocity Velocity gradient:gradient:

If we fit it by:If we fit it by:

then:then:

Velocity gradient Velocity gradient

is in-plane like is in-plane like too!too!

)2cos(cos)( 2102

www

vT

2( ) 4.468 0.0233cos 0.458cos(2 )Tv

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★★ Shear viscosity in Shear viscosity in AMPT:AMPT:

★★ Shear viscosity in Shear viscosity in AMPT:AMPT:

Take the second harmonics in expansions of correlation Take the second harmonics in expansions of correlation

pattern and velocity gradient, and approximate T=170MeV,pattern and velocity gradient, and approximate T=170MeV,

2 2

2 2

4 cos(2 ) 40.000725

cos(2 )

Tu Tu

w w

It is very small, since the transportation in AMPT It is very small, since the transportation in AMPT

has a very large cross section of scattering.has a very large cross section of scattering.

It is shown recently that the finite interaction range in transportationIt is shown recently that the finite interaction range in transportation

will contribute to the viscous coefficients and conductivity.will contribute to the viscous coefficients and conductivity.S. Cheng & S. Pratt, PRC 65, 024901(2002)S. Cheng & S. Pratt, PRC 65, 024901(2002)

Hans-Joachim Drescher,1 Adrian Dumitru,2 Cl´ement Gombeaud,

and Jean-Yves Ollitrault, PRC 76, 024905(2007)PRC 76, 024905(2007)

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☞ azimuthal bin-bin multiplicity corr. pattern is azimuthal bin-bin multiplicity corr. pattern is suggested.suggested.

☞ Its relation with shear viscosity is demonstrated. Its relation with shear viscosity is demonstrated.

☞ ☞ The shear viscosity inThe shear viscosity in AMPT with string melting isAMPT with string melting is estimated.estimated.

☞☞ The correlation pattern from current and comingThe correlation pattern from current and coming

relativistic heavy ion collisions are looking forward! relativistic heavy ion collisions are looking forward!

Wu Yuanfang IOPP, Huazhong Normal University, Wuhan, China

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