Transcript Partonic Effects on Collective Flows at RHIC Lie-Wen Chen P. F. Kolb

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 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)
Lie-Wen Chen, Cyclotron Institute, Texas A&M University
Contents
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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
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 vn

d 3N
dN
1
dN 

E 3 

1   2vn ( pT , y ) cos(n ) 

d p pT dpT dyd 2 pT dpT dy  n 1

Sine terms vanish because of the symmetry  

Initial
x spatial
anisotropy
Pressure
gradient
anisotropy
Anisotropic
flows
Lie-Wen Chen, Cyclotron Institute, Texas A&M University
Anisotropic
Flows pvn and
 vn’s generallyEvaluation
depend on of
transverse
momentum
T
rapidity
y, and can be evaluated from (Analytically useful)
vn ( pT , y )  cos(n )
Where 〈 ・・・ 〉denotes average over the azimuthal distribution
of particles with transverse momentum pT and rapidity y.
 vn’s can be further expressed in terms of following singleparticle average (Numerically useful) :
v1 ( pT , y ) 
v4 ( pT , y ) 
v6 ( pT , y ) 
px
, v2 ( pT , y ) 
pT
px4  6 p x2 p 2y  p 4y
pT4
,
px2  p 2y
v5 ( pT , y ) 
px6  15 p x4 p 2y  15 px2 p 4y  p 6y
pT6
At transverse momentum pT 
,
pT2
v3 ( pT , y ) 
px3  3 px p 2y
pT3
p x5  10 p x3 p 2y  5 p x p 4y
pT5
,
px2  p 2y and rapidity y
 Similarly, we can obtain spatial anisotropies: s1,s2,s3,s4,…
Lie-Wen Chen, Cyclotron Institute, Texas A&M University
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,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
Lie-Wen Chen, Cyclotron Institute, Texas A&M University
AMPT model with String Melting
AMPT model with String Melting can describe the measured strong
elliptic flow and pion HBT at RHIC (Lin&Ko, PRC65, Lin,Ko,Pal,PRL89)
A+A
HIJING (Heavy Ion Jet Interaction Generator)
Energy in strings and minijet partons
Wang&
Gyulassy
PRD43,44,4
5
Fragment excited strings
into partons
ZPC (Zhang's Parton Cascade)
Till parton freezeout (last coll.)
Zhang, CPC82
Coalescence into hadrons
ART (A Relativistic Transport model for hadrons)
Decay all resonances;
Final particle spectra
Li&KoPRC52
Lie-Wen Chen, Cyclotron Institute, Texas A&M University
String melting and Quark Coalescence
String melting:
Excited string (Lund-)Fragment into hadrons, and then melt
into quarks according to hadron valence structure:
m  qm1 qm2 , B  qB1 qB2 qB3 , B  q B1 q B2 q B3
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:
o Nearest quarks form a hadron
qm1 : find a closest q  m
qB1 : find closest q2 and q2  B
o
o
q B1 : find closest q 2 and q3  B
Determine Flavor according to quarks’ invariant mass
Most hadrons in Pythia are included:
 KK * DD* BB*; npN * (1440) N * (1535)
Lie-Wen Chen, Cyclotron Institute, Texas A&M University
Anisotropic flows at mid-rapidity
Spatial in
and
momentum
partonic
stage
At mid-rapidity
collisions
with Anisotropy
equal mass in
nuclei:
Odd-order
anisotropic flows (v1,v3,v5,…) vanish because of the symmetry
+
p= 3 mb
s2= 9%
s4= 1.1%

10 mb
  4%
 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 A&M University
pT-dependence of charged hadrons
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 !!!
Lie-Wen Chen, Cyclotron Institute, Texas A&M University
Scaling relation among hadron vn’s
Scaling: v2 n ( pT ) 1.2v2n ( pT )
STAR Collaboration, PRL 92 (2003) 062301
AMPT model
results for all charged particles,
minimum bars values from
Au+Au@200 AGeV
Lie-Wen Chen, Cyclotron Institute, Texas A&M University
Scaling relation among parton vn’s
Parton v 4 is non-negligible
Scaling v2 n ( pT )
v2n ( pT ) is
still satisfied on parton level
s2  v 2  v 4
s4  v 4 ???
Lie-Wen Chen, Cyclotron Institute, Texas A&M University
Scaling relations from naïve coalescence model
At mid-rapidity in Au+Au collisions, odd-order vn vanish. Assuming quarks have
no v6,q and higher-order vn ,q , from the naive coalescence model:
v2,M 
v2,B 
2v2,q  2v2,q v4,q
1  2( v
2
2,q
v )
2
4, q
, v4,M 
3v2,q  6v2,q v4,q  3v2,3 q  6v2,q v4,2 q
1  6(v
2
2, q
v
2
4, q
v v )
2
2, q 4, q
v4,M 1 1 v4,q
 
,
2
2
v2,M 4 2 v2,q
v4,B 1  v4,q 
 1  2  ,
2
v2,B 3  v2,q 
Scaling: v2 n ( pT )
2v4,q  v2,2 q
1  2( v2,2 q  v4,2 q )
, v4,B 
3v4,q  3v2,2 q  6v2,2 q v4,q  3v4,2 q
1  6( v2,2 q  v4,2 q  v2,2 q v4,q )
v6,M 1  v4,q v6,q 
  2  3 
3
v2,M 4  v2,q v2,q 
v4,q
v6,q 
v6,B
1 

 1  6 2  3 3 
3
v2,B 27 
v2,q
v2,q 
v2n ( pT ) is a natural result if same scaling relation
is satisfied on parton level!
Lie-Wen Chen, Cyclotron Institute, Texas A&M University
Scaling relations from naïve coalescence model
From the AMPT model:
v4,q ( pT ) v6,q ( pT )
1
2
3
v2,q ( pT ) v2,q ( pT )
v4,M ( pT ) 3
 ,
2
v2,M ( pT ) 4
v6,M ( pT ) 1

3
v2,M ( pT ) 2
v4,B ( pT ) 2
 ,
2
v2,B ( pT ) 3
v6,B ( pT ) 10

3
v2,B ( pT ) 27
Experimentally
v2 n ( pT )
v2n ( pT )
1.2 (For Charged Hadrons)
Is naive quark coalescence model perfect???
Momentum spreading?
Resonce decay?
Lie-Wen Chen, Cyclotron Institute, Texas A&M University
Pseudorapidity dependence of vn (Preliminary)
Pseudorapidity dependence of v1 and v2
• String melting can only describe the data near mid-rapidity(||<1
• The data can be explained by a hadronic model at large rapidity (|
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 p
• 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
Summary
• v4 is a more sensitive
probe for the initial partonic
dynamics than v2
• Parton v4 is non-negligible and satisfy scaling
relation
•
n
v
(
p
)
v
2n
T
2 ( pT )relation
The
scaling
can be naturally
n
v
(
p
)
v
2n
T coalescence
2 ( pT )
understood from quark
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 A&M University