Probing Density Dependence of Symmetry Energy in N-N Correlation Functions

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Hot Quarks 2004, July 18-24, 2004, Taos Ski
Valley, NM
Partonic Effects on Collective Flows at RHIC

• Lie-Wen Chen
• (Cyclotron Institute and Physics Department,
• Texas AM University)

Collaborators V. Greco, C. M. Ko P.
F. Kolb (Technische Universität München)
Z. W. Lin (Ohio State University)
B. Zhang (Arkansas State
University)
Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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Contents

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

References Chen, Ko, Lin, PRC69, 031901(R)
(2004) Kolb, Chen, Greco, Ko, PRC69, 051901(R)
(2004).
Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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Anisotropic flows
Anisotropic flows vn
Sine terms vanish because of the symmetry ??? ?
Initial spatial anisotropy
x
Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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Evaluation of Anisotropic Flows vn

• vns generally depend on transverse momentum pT
  and rapidity
• y, and can be evaluated from (Analytically
  useful)

• Where lt gtdenotes average over the azimuthal
  distribution of particles with transverse
  momentum pT and rapidity y.
• vns can be further expressed in terms of
  following single-
• particle average (Numerically useful)

• Similarly, we can obtain spatial anisotropies
  s1,s2,s3,s4,

Lie-Wen Chen, Cyclotron Institute, Texas AM
University
5
Parton degree of freedom in the AMPT model

• Four important components are needed to be
  included for a general model at RHIC Initial
  Condition, Partonic Stage, Hadronization/QCD
  phase transition, and Hadronic Interactions
• 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,LiLin, PRC61 Zhang,Ko,Li,LinSa,PRC62
  Lin,Pal,Ko,LiZhang,PRC64 LinKo,PRC65
  Zhang,Ko,Li,LinPal,PRC65 Pal,KoLin,NPA707
  Lin,KoPal,PRL89 LinKo,PRC68
  Pal,KoLin,NPA730 Chen,KoLin,PRC69

Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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AMPT model with String Melting
AMPT model with String Melting can describe the
measured strong elliptic flow and pion HBT at
RHIC (LinKo, PRC65, Lin,Ko,Pal,PRL89)
Wang Gyulassy PRD43,44,45
HIJING (Heavy Ion Jet Interaction
Generator) Energy in strings and minijet partons
AA
Fragment excited strings into partons
ZPC (Zhang's Parton Cascade)
Zhang, CPC82
Till parton freezeout (last coll.)
Coalescence into hadrons
ART (A Relativistic Transport model for hadrons)
Decay all resonances Final particle spectra
LiKoPRC52
Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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String melting and Quark Coalescence
String melting Excited string (Lund-)Fragment
into hadrons, and then melt into quarks according
to hadron valence structure

• 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

Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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Anisotropic flows at mid-rapidity
Spatial and momentum Anisotropy in partonic stage
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
v4 is a more sensitive probe for the initial
partonic dynamics !!!
Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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pT-dependence of charged hadrons
pT-dependence of v2, v4, and v6 of charged
hadrons at mid-rapidity ??1.2 ?p10 mb seems
to give a better fit to the data v4 is a more
sensitive probe for the initial partonic
dynamics !!!
Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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Scaling relation among hadron vns
AMPT model
Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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Scaling relation among parton vns
Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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Scaling relations from naïve coalescence model
Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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Scaling relations from naïve coalescence model
Lie-Wen Chen, Cyclotron Institute, Texas AM
University
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Pseudorapidity dependence of vn (Preliminary)
Pseudorapidity dependence of v1 and v2

• String melting can only describe the data near
  mid-rapidity(?lt1.5)
• The data can be explained by a hadronic model at
  large rapidity (?gt3)
• Is a pure partonic matter formed only
  near mid-rapidity ???

Lie-Wen Chen, Cyclotron Institute, Texas AM
University
15
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 AM
University
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Summary

• v4 is a more sensitive probe for the initial
  partonic
• dynamics than v2
• Parton v4 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!!!

Lie-Wen Chen, Cyclotron Institute, Texas AM
University