1. Shear Viscosity and Collective Flow in Heavy Ion Collisions within Parton Cascade Calculations Zhe Xu, Carsten Greiner Trento, Sept. 17, 2009 Institut für Theoretische Physik Goethe-Universität Frankfurt, Germany

2. Zhe Xu, Trento 20092/23 Y X Motivation: how small is the QGP viscosity at RHIC? P.Huovinen et al., PLB 503, 58 (2001) Viscous Hydrodynamics Muronga Luzum / Romatschke Song / Heinz Teaney / Dusling Molnar / Niemi / Rischke Kinetic Transport Model (Z)MPC: Zhang / Molnar / Gyulassy AMPT: Lin / Chen / Ma / Ko UrQMD: Petersen, Bleicher et al. BAMPS: Xu, Greiner et al.

3. Zhe Xu, Trento 20093/23 Outline Parton Cascade BAMPS Elliptic Flow at RHIC Extracting  /s v 2 (p T ) Summary

4. Zhe Xu, Trento 20094/23 BAMPS: B oltzmann A pproach of M ulti P arton S catterings A transport algorithm solving the Boltzmann-Equations for on-shell partons with pQCD interactions new development ggg gg (Z)MPC, VNI/BMS, AMPT, PACIAE Elastic scatterings are ineffective in thermalization ! Inelastic interactions are needed ! Transport Model

5. Zhe Xu, Trento 20095/23 Stochastic algorithm 3x3x collision probability -- stochastic Space is divided into small cells ! ZX and C. Greiner, PRC 71, 064901 (2005) x y

6. Zhe Xu, Trento 20096/23 J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982) screened pQCD based partonic interactions treatment for incoherent interactions: the formation time  g : mean free path LPM suppression :

7. Zhe Xu, Trento 20097/23 Results: Transverse Energy in Au+Au at RHIC Initial conditions: gluon minijets production in independent binary NN collisions

8. Zhe Xu, Trento 20098/23 Elliptic Flow at RHIC using BAMPS ZX, Greiner, Stöcker, PRL 101, 2008 gg ggg processes generate large elliptic flow !

9. Zhe Xu, Trento 20099/23

10. Zhe Xu, Trento 200910/23 Navier-Stokes approximation Boltzmann-Eq. Shear Viscosity  AMY, JHEP 11 (2000) solve f 1 (x,p) using the variational method, which determines the coefficients of the functions of p in f 1 (x,p)

11. Zhe Xu, Trento 200911/23 ZX and C.Greiner, PRL 100, 172301, (2008) transport rate ZX and C. Greiner, PRC 76, 024911 (2007)

12. Zhe Xu, Trento 200912/23 Transport Rates

13. Zhe Xu, Trento 200913/23 gg  gg: small-angle scatterings gg  ggg: large-angle bremsstrahlung distribution of collision angles at RHIC energies central plateau

14. Zhe Xu, Trento 200914/23 Elliptic Flow and Shear Viscosity at RHIC 2-3 Parton cascade BAMPS ZX, Greiner, Stöcker, PRL 101, 2008 viscous hydro. Romatschke, PRL 99, 2007  /s > 0.08  /s at the collision center

15. Zhe Xu, Trento 200915/23 A. El, A. Muronga, ZX and C. Greiner, PRC 79, 044914 (2009) Shear Viscosity  Grad´s method

16. Zhe Xu, Trento 200916/23

17. Zhe Xu, Trento 200917/23 comparison = 0 in chemical equilibration For minijets initial conditions: No kinetic equilibrium No chemical equilibrium

18. Zhe Xu, Trento 200918/23 Uncertainty: dependence of v2 on freeze-out condition generate the same elliptic flow. Therefore,  /s  between 0.08 and 0.16.

19. Zhe Xu, Trento 200919/23 V 2 (p T ) lower than data ZX and C. Greiner, PRC 79, 014904 (2009)

20. Zhe Xu, Trento 200920/23 e does not depend on N d. If changing N d from 16 to 40 (gluons+quarks with 2 flavors), ~ e/n decreases by a factor of 1.26.

21. Zhe Xu, Trento 200921/23 Including `quarks´ in BAMPS Assume: Quark dynamics is as same as the gluon one. Changing the degrees of freedom of gluons 16 to 40 (gluons+quarks with 2 flavors)

22. Zhe Xu, Trento 200922/23 Including `quarks´ 15% effect instead of 26% due to imcomplete chemical equilibration

23. Zhe Xu, Trento 200923/23 Summary Inelastic pQCD based interactions (23 + 32) explain: Large Collective Flow Small shear Viscosity of QCD matter at RHIC  /s: 0.08 ~ 0.2 Uncertainties of  /s: freezeout conditions, initial conditions, quark dynamics, hadronization, hadron cascade v2(pt) and v2 do not match data simultanously: need better understanding of quark dynamics and hadronization

24. Zhe Xu, Trento 200924/23 Variational method: AMY, JHEP 11 (2000) f1 to be solved.

25. Zhe Xu, Trento 200925/23 The maximun value of  S) –( ,C  )/2 occurs when  satisfied the linearized BE.

26. Zhe Xu, Trento 200926/23 Transport Rates ZX and C. Greiner, PRC 76, 024911 (2007) Transport rate is the correct quantity describing kinetic equilibration. Transport collision rates have an indirect relationship to the collision-angle distribution.

27. Zhe Xu, Trento 200927/23

28. Zhe Xu, Trento 200928/23 De Broglie length over mean free path Changing the mean free path by the inverse of the transport rate will lower the ratios.