# Presentation: 714593

## QCD Plasma Equilibration and Collective Flow Effects

- Zhe Xu

- with C. Greiner and H. Stöcker

**Quark Matter 2008, Jaipur, India, Feb. 6**

## Three body effects in parton cascades!

- Fast Thermalization from QCD: 3-2 important!
- Equilibr. time short in 2-3!
- Elliptic flow v2 high in 2-3!
- Viscosity small ~ 0.08!

- P.Huovinen et al., PLB 503, 58 (2001)

- from R. Bellwied

## Thermalization driven by plasma instabilities

- Thermalization driven by **plasma instabilities**

- Refs.:
**Mrowczynski;**
**Arnold, Lenaghan, ****Moore, Yaffe;**
**Rebhan, Romatschke, Strickland,**
**Bödeker, Rummukainen;**
**Dumitru, Nara;**
**Berges, Scheffler, Sexty**

**Dumitru, Nara, Strickland**, PRD 75, 025016 (2007)

**Dumitru, Nara, Schenke, Strickland**, arXiv:0710.1223

- talk by B. Schenke
- parallel session VIII

## QCD thermalization using

- parton cascade

- VNI/BMS:  K.Geiger and B.Müller, NPB 369, 600 (1992)
- 	     S.A.Bass, B.Müller and D.K.Srivastava, PLB 551, 277(2003)
- ZPC:  B. Zhang, Comput. Phys.Commun. 109, 193 (1998)
- MPC:  D.Molnar and M.Gyulassy, PRC 62, 054907 (2000)
- AMPT:  B. Zhang, C.M. Ko, B.A. Li, and Z.W. Lin,  PRC 61, 067901 (2000)
**BAMPS****: **Z. Xu and C. Greiner,**  **PRC 71, 064901 (2005); 76, 024911 (2007)

## BAMPS: Boltzmann Approach of MultiParton Scatterings

**BAMPS**: Boltzmann Approach of MultiParton Scatterings
- A transport algorithm solving the Boltzmann-Equations for on-shell partons with pQCD interactions

**new development ggg       gg**

- (Z)MPC, VNI/BMS, AMPT

- Elastic scatterings are ineffective in thermalization !
- Inelastic interactions are needed !

**Xiong, Shuryak, PRC 49, 2203 (1994)**
**Dumitru, Gyulassy, PLB 494, 215 (2000)**
**Serreau, Schiff, JHEP 0111, 039 (2001)**
**Baier, Mueller, Schiff, Son, PLB 502, 51 (2001)**

## screened partonic interactions in leading order pQCD

- J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982)
- T.S.Biro at el., PRC 48, 1275 (1993)
- S.M.Wong, NPA 607, 442 (1996)

- screening mass:

**LPM**** ****suppression**:  the formation time

- g: mean free path

## distribution of collision angles

- gg gg:        small-angle scatterings
**gg ********ggg: ****large-angle**** bremsstrahlung**

- at RHIC energies

##  3-2 + 2-3: thermalization! 

-  **3-2 ****+**** 2-3: ****thermalization! **
**Hydrodynamic behavior!**

** ****2-2:     NO** thermalization

**simulation pQCD 2-2 ****+ ****2-3 ****+ ****3-2**

- simulation pQCD, **only 2-2**

- at collision center: xT<1.5 fm,  z < 0.4 t fm of a central Au+Au at  s1/2=200 GeV
- Initial conditions: minijets pT>1.4 GeV;   coupling s=0.3

- pT spectra

## pT spectra

- A,El, ZX and C.Greiner, arXiv: 0712.3734 [hep-ph]

- talk by A. El
- parallel session VI

- ggg      gg !
- This 3-2 is missing in
- the Bottom-Up scenario
- (Baier et al.).

-      Initial conditions: Color Glass Condensate Qs=3 GeV;   coupling s=0.3

- pT spectra

## time scale of thermalization

-   = time scale of kinetic equilibration.

**Theoretical Result !**

## What determines

- Cross section does **not**** **determine !

- ZX and C.Greiner, arXiv: 0710.5719 [nucl-th]

- the equilibration time scale  ?

## BUT, this is not the full story !

- BUT, this is **not** the full story !

## 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.

## Transport Rates

**Large Effect of 2-3 !**

## Shear Viscosity 

- Shear Viscosity 

- D.Teaney, PRC 68, 034913 (2003)
- P.Arnold, G.D.Moore, L.G.Yaffe, JHEP 0011, 001 (2001); 0305, 051 (2003)
- T.Hirano, M.Gyulassy, NPA 769, 71 (2006)
- M.Asakawa, S.A.Bass, B.Müller, Prog.Theor.Phys. 116, 725 (2007)
- A.Muronga, PRC 76, 014910 (2007)
- ZX, C.Greiner, arXiv: 0710.5719 [nucl-th]

## From Navier-Stokes approximation

- From Boltzmann-Eq.

- relation between  and Rtr

## Ratio of shear viscosity to entropy density in 2-3

- AdS/CFT

**RHIC**

## Collective Effects

- transverse flow velocity of local cell in the
- transverse plane of central rapidity bin

- Au+Au b=8.6 fm
- using BAMPS

- =c

## Zhe Xu, Jaipur, Quark Matter 2008

## /s at RHIC > 0.08

**Elliptic Flow and Shear Viscosity in 2-3 at RHIC**

-              **2-3**** ****Parton cascade BAMPS**
- ZX, Greiner, Stöcker, arXiv: 0711.0961 [nucl-th]

- viscous hydro.
- Romatschke, PRL 99, 172301,2007

- /s at RHIC > 0.08

## Rapidity Dependence of v2: Importance of 2-3! BAMPS ZX,G,S

**Rapidity Dependence of v****2****: Importance of 2-3! BAMPS ZX,G,S**

- see also:
- L.W.Chen, et al., PLB 605, 95 (2005)
- C.Nonaka, et al., JPG 31, 429 (2005)
- T.Hirano, et al., PLB 636, 299 (2006)
- J.Bleibel, et al., PRC 76, 024912 (2007);
-                          PLB 659, 520 (2008)
- Hama, et al., arXiv: 0711.4544 [hep-ph]
- A.K.Chaudhuri, arXiv: 0801.3180
- Session XVI, Collectivity-theory
- Hirano, Molnar, Bhalerao, Song,
- Muronga, Csorgo

## Summary

**Inelastic pQCD interactions (23 + 32) explain:**
**Fast ****Thermalization**
**Large ****Collective Flow**
**Small**** shear Viscosity of QCD matter at RHIC**
**Initial conditions, hadronization and afterburning determine **
**how ****imperfect**** the QGP at RHIC & LHC can be.**

- further investigations in progress:
- H. Petersen, G. Burau, J. Steinheimer, M. Bleicher (University of Frankfurt)
- see Poster P68

## Zhe Xu, Jaipur, Quark Matter 2008

## Zhe Xu, Jaipur, Quark Matter 2008

## total transverse energy per rapidity at midrapidity

## Stochastic algorithm

- _Stochastic algorithm_

- P.Danielewicz, G.F.Bertsch, Nucl. Phys. A 533, 712(1991)
- A.Lang et al., J. Comp. Phys. 106, 391(1993)

- for particles in 3x with momentum **p**1,**p**2,**p**3 ...

- interaction probability:

- cell configuration in space

- 3x

## Initial conditions

- _Initial conditions_

- Glauber-type: Woods-Saxon profile, binary nucleon-nucleon collision

- for a central Au+Au collision at **RHIC**
- at 200 AGeV using **p****0****=1.4 GeV**

- minijets production with pt > p0

## ggggg interactions are essential for kinetic equilibration!

- The drift term is large.

- ggggg interactions are essential for kinetic equilibration!

## due to the fact that a 2->3 process brings one more particle

- toward isotropy than a gg->gg process.