1. 2008.10.9SQM’08 1 An explorer for the shear viscosity in the formed matter at relativistic heavy ion collisions Wu Yuanfang IOPP, Huazhong Normal University, Wuhan, China 1. Motivation 2. Azimuthal bin-bin multiplicity corr. pattern 3. The correlation pattern & shear viscosity 4. A rough estimation of η in AMPT 5. Summary and outlook Co-authers: Wang Meijuan, Li Lin, and Liu Lianshou Acknowledgements: T. Hirano, Li Jiarong, Wang Fuqiang, Tang Aihong and Xu Nu

2. 2008.10.9SQM’08 2 1. Motivation: ★ Why perfect fluid ► Large energy density achieved ► Jet energy loss in matter ► Collective behaviour observed « Perfect liquid », « sQGP » ! The mass-dependence of v 2 at p T < 2 GeV shows qualitatively agreement with ideal hydrodynamic 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);

3. 2008.10.9SQM’08 3 1. Motivation: ★ Why not perfect fluid ? Perfect liquid Zero viscosity S. Pratt, arXiv: 0809.0089 ; S. A. Voloshin, arXiv: 0805.1351. S. Pratt, arXiv: 0809.0089 ; S. A. Voloshin, arXiv: 0805.1351. The result of leading order perturbative : for P. Arnold, G. D. Moore and L. G. Yaffe. The lower bound of shear viscosity: It reduces the flow values up to 10-30%. 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!

4. 2008.10.9SQM’08 4 1. Motivation: ★ Main difference between perfect and viscous fluid. There are friction between two layers. →→→→→ →→→→→ Perfect liquid: →→→→→ Viscous liquid: No friction between two layers of flow. two layers of flow. Velocity is const. Velocity is different from layer to layer. →→→→→ The internal interaction and velocity gradient are directly related to the viscous behavior of the fluid. directly related to the viscous behavior of the fluid.

5. 2008.10.9SQM’08 5 2. Azimuthal bin-bin multiplicity correlation pattern: y x ★ Neighboring angular bin-bin N corr. pattern: Shear interaction : multiplicity in mth bin. : the direction of reaction plane. It measures azimuthal distribution of nearby particles correlation. Wu Yuanfang, Lianshou Liu, Yingdan Wang, Yuting Bai & Hongbo Liao, PRE71, 017103 (2005).

6. 2008.10.9SQM’08 6 2. Azimuthal bin-bin multiplicity correlation pattern: ★ Bin-bin correlations & 2-particle correlations 2-particle corr. : Case 1: Randomly produced particles produced particles with in-plane liked with in-plane liked Φ dis. Case 2 : RQMD w/o re-scattering N ab : no. of pairs with separated angle δφ. Bin-bin correlation is not sensitive to the trivial correlations in both cases !

7. 2008.10.9SQM’08 7 2. Azimuthal bin-bin multiplicity correlation pattern: ★ Influences of multiplicity (N ch ) and elliplitic flow (v 2 ) Case 3: Randomly produced particles with given Φ dis. for diff. N Case 4: Randomly produced particles with given N dis. for diff. Φ dis. Neither of them contributes to the pattern !

8. 2008.10.9SQM’08 8 2. Azimuthal bin-bin multiplicity correlation pattern: ★ influences of the correlation between N and v 2. Case 5: Randomly produced particles but Φ dis. increase with N The correlation between N and v 2 contributes to the pattern. It is necessary to study the pattern in fixed N or v 2 sample.

9. 2008.10.9SQM’08 9 3. The correlation pattern and shear viscosity : ★ Bin-bin correlation and interaction energy M. Stephanov, Int. J. Mod. Phys. A20, 4787(2005); M. Stephanov, Phys. Rev. D65, 096008(2002)., is the interaction energy. In the whole system, the total interaction energy is : If the interaction is small, in the leading order, the correlation is,

10. 2008.10.9SQM’08 10 3. The correlation pattern and shear viscosity : ★ Dissipative energy of the fluid In hydrodynamics, the viscous stress tensor : L. D. Landau & E. M. Lifshitz, Fluid Mechanics, Pergamon Press. η(p,T) and ξ(p,T) are shear and bulk viscosity respectively. For incompressible fluid, the dissipative energy is: Take the cylindrical coordinates, and assume,

11. 2008.10.9SQM’08 11 3. The correlation pattern and shear viscosity : ★ Shear viscosity and bin-bin correlation If the bin-bin correlation is only due to viscous interaction, Then, i.e., T → p T spectrum; → final velocity gradient.

12. 2008.10.9SQM’08 12 4. A rough estimation of shear viscosity in AMPT: ★ Correlation pattern from AMPT with string melting: Correlation pattern is in-plane like! is in-plane like! If we fit it by: then : For Au + Au collisions at 200 GeV with fixed N and b

13. 2008.10.9SQM’08 13 4. A rough estimation of shear viscosity in AMPT: ★ Velocity gradient: If we fit it by: then: Velocity gradient is in-plane like too! is in-plane like too!

14. 2008.10.9SQM’08 14 4. A rough estimation of shear viscosity in AMPT: ★ Shear viscosity in AMPT: Take the second harmonics in expansions of correlation pattern and velocity gradient, and approximate T=170MeV, It is very small, since the transportation in AMPT has a very large cross section of scattering. It is shown recently that the finite interaction range in transportation will contribute to the viscous coefficients and conductivity. S. Cheng & S. Pratt, PRC 65, 024901(2002) Hans-Joachim Drescher,1 Adrian Dumitru,2 Cl´ement Gombeaud, PRC 76, 024905(2007) and Jean-Yves Ollitrault, PRC 76, 024905(2007)

15. 2008.10.9SQM’08 15 5. Summary and outlook 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 in AMPT with string melting is estimated. estimated. ☞ The correlation pattern from current and coming relativistic heavy ion collisions are looking forward! relativistic heavy ion collisions are looking forward!