# Presentation: 000323

## Collectivity in a Parton Cascade 

- Collectivity in a Parton Cascade

- Zhe Xu

**BNL,  April 30, 2008**

- with A. El, O. Fochler, C. Greiner and H. Stöcker

## Motivation and Summary

- Fast Thermalization from pQCD: 2-3 important
-     Equilibr. time: 1 fm/c
- Elliptic flow v2: high in 2-3
-     Viscosity: small ~ 0.08
- Hard probe: RAA ~ 0.1
-    collisional 2-2 vs. radiational 2-3 energy loss

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

- Zhe Xu

## Outline

-    Transport model
-    Results from simulations
-    Analytical calculations

- Zhe Xu

## Transport Model

- 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 !

- Zhe Xu

## Old collision algorithm

- BUT,  difficult to 3  2 !

- collision criterion:

- (ZPC, MPC, VNI/BMS, AMPT)

- Zhe Xu

## Stochastic algorithm

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

- 3x

- collision rate per unit phase space for incoming
- particles p1 and p2 with 3p1 and 3p2:

- collision probability (Monte Carlo)

- Space has to be divided
- into small cells !

- Zhe Xu

## Interaction Probability

- Zhe Xu

## screened partonic interactions in leading order pQCD

- 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

- Gluons freeze out at local energy density = 1 GeV/fm3.

- Zhe Xu

## Results from 

- the parton cascade BAMPS
- thermalization
- transverse energy
- elliptic flow
- shear viscosity
- jet quenching

- Zhe Xu

##  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

- Zhe Xu

## pT spectra

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

- 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

- Zhe Xu

## time scale of thermalization

-   = time scale of kinetic equilibration.

**Theoretical Result !**

- Zhe Xu

## total transverse energy per rapidity at midrapidity y=0

- Zhe Xu

## Rapidity dependence of total transverse energy

- Zhe Xu

## /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

- Zhe Xu

## 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**

- Zhe Xu

## first realistic 3d results on jet-quenching with BAMPS

**first realistic 3d results on jet-quenching with BAMPS**

- dE/dx, static medium (T = 400 MeV)

- RAA ~ 0.1

- cf. S. Wicks et al.
- Nucl.Phys.A784, 426

**nuclear modification factor**
- central (*b=0* fm) Au-Au at 200 AGeV

**O. Fochler**

- 2-3

- 2-2

- Zhe Xu

## Inelastic pQCD interactions (23+32) explain:

**Fast ****Thermalization**
**Large ****Collective Flow**
**Small**** shear Viscosity of QCD matter at RHIC**
**Part**** of energy loss (for very high energy parton collisional energy loss due to 2-2 dominates.) **
**Initial conditions, hadronization and afterburning determine **
**how ****imperfect**** the QGP at RHIC & LHC can be.**

- Zhe Xu

## Analytical Calculations for a Gluon Gas

- Zhe Xu

## screened partonic interactions in leading order pQCD

- 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

- Zhe Xu

## Collision Rate

- Zhe Xu

## distribution of collision angles

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

- at RHIC energies

- Zhe Xu

## BUT, this is not the full story !

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

- Zhe Xu

## 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.

- assume

- Zhe Xu

## Transport Rates

**Large Effect of gg->ggg !**

- Zhe Xu

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

- toward isotropy than a gg->gg process.

- Zhe Xu

## Shear Viscosity 

- From Boltzmann-Eq.

- relation between  and Rtr

- Shear Viscosity 

- Zhe Xu

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

- AdS/CFT

**RHIC**

- ZX and C.Greiner, arXiv: 0710.5719 [nucl-th], to be published in PRL.

- Zhe Xu

## /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

- Zhe Xu

## Conclusion

**Fast ****Thermalization**
**Large ****Collective Flow**
**Small**** shear Viscosity of QCD matter at RHIC**
**Part**** of energy loss (for very high energy parton collisional energy loss due to 2-2 dominates.) **
**Initial conditions, hadronization and afterburning determine **
**how ****imperfect**** the QGP at RHIC & LHC can be.**

- Zhe Xu

## Outlook

**Jet Quenching (Oliver Fochler)**
**Mach Cone (Ioannis Bouras)**
**Dependence on initial conditions (Luan Cheng)**
**Transport coefficients (Felix Reining)**
**Parton Cascade vs. Viscous Hydrodynamics (Andrej El)**
**Hadronization and afterburning (Petersen, Burau, Xu)**
**HBT**
**Ridge**
**Quarks, Heavy Quarks, Direct Photon**
**Entropy production**
**LHC predictions**
**Many body interactions: 3 ******** 3, 2 ******** 4, ...**
**Including fields, coherent effects (Björn Schenke, Xu)**

- Zhe Xu

## Slide 32

- Zhe Xu

## Initial conditions in heavy ion collisions

- 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

- Zhe Xu

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

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

- Zhe Xu