# Presentation: 177365

##               Lie-Wen Chen

- Partonic Effects on Collective Flows at RHIC

-               Lie-Wen Chen
- (Cyclotron Institute and Physics Department,
- Texas A&M University)

- Collaborators: V. Greco, C. M. Ko
- 	            P. F. Kolb (Technische Universität München)
-                   Z. W. Lin (Ohio State University)
-                         B. Zhang (Arkansas State University)

**Hot Quarks 2004, ****July**** 18-24, 2004, Taos Ski Valley, NM**

## Anisotropic flows
Parton degree of freedom in the AMPT model
Anisotropic flows at mid-rapidity
Pseudorapidity dependence of vn’s (preliminary)
Charm elliptic flow (preliminary)
Summary

- Parton degree of freedom in the AMPT model
- Anisotropic flows at mid-rapidity
- Pseudorapidity dependence of vn’s (preliminary)
- Charm elliptic flow (preliminary)
- Summary

- Contents

**References:***** ***
***Chen, Ko, Lin, PRC69, 031901(R) (2004); ***
***Kolb, Chen, Greco, Ko, PRC69, 051901(R) (2004).***

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## Anisotropic flows

- Anisotropic flows *v**n*

- Sine terms vanish because of the symmetry  

- Initial
- spatial
- anisotropy

- x

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## Evaluation of Anisotropic Flows vn

*       **y, *and can be evaluated from (Analytically useful)

- Where 〈 ・・・ 〉denotes average over the azimuthal distribution of particles with transverse momentum *p**T* and rapidity *y.*
* *
-  vn’s can be further expressed in terms of following single-
-       particle average (Numerically useful) :

- _Evaluation of Anisotropic Flows__ __*v*__*n*_

-  Similarly, we can obtain spatial anisotropies: *s**1**,s**2**,s**3**,s**4**,...*

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## AMPT(A Multi-Phase Transport) model

- _AMPT(A Multi-Phase Transport) model_
- Initial Condition for Particle and Energy Production:
-             Soft Strings and Hard Minijets from HIJING
- Partonic Stage with EOS:
-             Parton cascade
- Hadronization/QCD phase transition:
-             String fragmentation or Quark Coalescence
- Hadronic Interactions
-             Hadron cascade
-              _A useful model for investigating reaction dynamics at RHIC:_
- Zhang,Ko,Li&Lin, PRC61; Zhang,Ko,Li,Lin&Sa,PRC62; Lin,Pal,Ko,Li&Zhang,PRC64; Lin&Ko,PRC65; Zhang,Ko,Li,Lin&Pal,PRC65; Pal,Ko&Lin,NPA707; Lin,Ko&Pal,PRL89; Lin&Ko,PRC68; Pal,Ko&Lin,NPA730; Chen,Ko&Lin,PRC69

- Parton degree of freedom in the AMPT model

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## A+A

*Energy in *strings* and *minijet partons* *

- ZPC (Zhang's Parton Cascade)

*Till parton freezeout (last coll.)*

- ART (A Relativistic Transport model for hadrons)

*Decay all resonances;*
*Final particle spectra*

- AMPT model with **String Melting** can describe the measured strong elliptic flow and pion HBT at RHIC (Lin&Ko, PRC65, Lin,Ko,Pal,PRL89)

*Fragment excited strings *
*into partons*

*Coalescence into hadrons*

- Li&KoPRC52

- _AMPT model with String Melting_

- Zhang, CPC82

- Wang&
- Gyulassy
- PRD43,44,45

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## String melting and Quark Coalescence

- Quark Coalescence:
- When the partonic interactions stop (last collision of parton), all partons must be converted to hadrons (hadronization). A simple quark coalescence model is used for hadronization:
-     Nearest quarks form a hadron
-     Determine Flavor according to quarks’ invariant mass
-     Most hadrons in Pythia are included:

- String melting:
- Excited string (Lund-)Fragment into hadrons, and then melt into quarks according to hadron valence structure:

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## Anisotropic flows at mid-rapidity

- v4 is a more sensitive probe for
- the initial partonic dynamics !!!

- At mid-rapidity in collisions with equal mass nuclei: Odd-order anisotropic flows (v1,v3,v5,...) vanish because of the symmetry +

- p= 3 mb         10 mb
- s2= 9%           4%
- s4= 1.1%         0.56%
- v2= 5.4%        7.5%
- v4= 0.29%      0.67%
- s6, s8, v6,v8 are essentially zero

- _Spatial and momentum Anisotropy in partonic stage_

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## pT-dependence of v2, v4, 

- pT-dependence of v2, v4,
- and v6 of charged hadrons
- at mid-rapidity ||1.2
- p=10 mb seems to give a
- better fit to the data
- v4 is a more sensitive probe
- for the initial partonic dynamics !!!

- _p__T__-dependence of charged hadrons_

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## Scaling relation among hadron vn’s

- _Scaling relation among hadron v__n’__s_

- AMPT model

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## Scaling relation among parton vn’s

- _Scaling relation among parton v__n’__s_

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## Scaling relations from naïve coalescence model

- _Scaling relations from naïve coalescence model_

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## Scaling relations from naïve coalescence model

- _Scaling relations from naïve coalescence model_

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## Pseudorapidity dependence of vn (Preliminary)

- _Pseudorapidity dependence of v__1__ and v__2_

-  String melting can only describe the data near mid-rapidity(||<1.5)
-  The data can be explained by a hadronic model at large rapidity (||>3)
-           Is a pure partonic matter formed only near mid-rapidity ???

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

## Charm elliptic flow (Preliminary)

-  Charm quark displays roughly same v2 as light quarks at higher pT
-  The pT dependence of charm quark is very different from those of
-    light quarks
-  Charm elliptic flow is also sensitive to parton cross sections

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***

##                           Thank you!!!

-    dynamics than *v**2*
-  Parton *v**4* is non-negligible and satisfy scaling relation
*     *
-  The scaling relation                       can be naturally
-    understood from quark coalescence model
-  Is a pure partonic matter formed only near mid-rapidity??? Yes!!!
-  Charm quark has strong elliptic flow at RHIC
-                           Thank you!!!

- Summary

***Lie-Wen Chen, Cyclotron Institute, Texas A&M University***