Wu Yuanfang IOPP, Huazhong Normal University, Wuhan, China

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

2. 1. Motivation: ★ Why perfect fluid ► Large energy density achieved ► Jet energy loss in matter ► Collective behaviour observed The mass-dependence of v2 at pT < 2 GeV shows qualitatively agreement with ideal hydrodynamic flow. « Perfect liquid », « sQGP » ! 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); SQM’08

3. 1. Motivation: Perfect liquid Zero viscosity ★ Why not perfect fluid ? The lower bound of shear viscosity: P. Kovtun, D. T. Son, and A. O. Starinets, Phys. Rev. Lett. 94, 111601(2005) . It reduces the flow values up to 10-30%. 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. It is necessary to know the real value of shear viscosity! SQM’08

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

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

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

7. 2. Azimuthal bin-bin multiplicity correlation pattern: ★ Influences of multiplicity (Nch) and elliplitic flow (v2) 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 ! SQM’08

8. 2. Azimuthal bin-bin multiplicity correlation pattern: ★ influences of the correlation between N and v2 . Case 5: Randomly produced particles but Φ dis. increase with N The correlation between N and v2 contributes to the pattern. It is necessary to study the pattern in fixed N or v2 sample. SQM’08

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

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

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

13. 4. A rough estimation of shear viscosity in AMPT: ★Velocity gradient: Velocity gradient is in-plane like too! If we fit it by: then: SQM’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. Hans-Joachim Drescher,1 Adrian Dumitru,2 Cl´ementGombeaud, and Jean-Yves Ollitrault, PRC 76, 024905(2007) 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) SQM’08

15. 5. Summary and outlook ☞azimuthal bin-bin multiplicity corr. pattern is suggested. ☞ Its relation with shear viscosity is demonstrated. ☞ The shear viscosity inAMPT with string melting is estimated. ☞ The correlation pattern from current and coming relativistic heavy ion collisions are looking forward! Thanks/谢 谢 ！ SQM’08