Transport and Hydrodynamic Model for
Ultra-relativistic Heavy Ion Collisions
Yu-Liang Yan
China Institute of Atomic Energy
Collaborators: Yun Cheng (CCNU, China)
Dai-Mei Zhou (CCNU, China)
Bao-Guo Dong (CIAE, China)
Xu Cai (CCNU, China)
Ben-Hao Sa (CIAE, China)
L. P. Csernai (UiB, Norway)
10th Workshop on QCD Phase Transition and Relativistic Heavy-ion
Physics, Aug. 8 - 10, 2013, Chengdu.
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Outline
• Introduction
• PACIAE model
• Hydrodynamic model
• Connecting the PACIAE and Hydrodynamic
model
• Transport and Hydrodynamic hybrid Model
(PACIAE+HYDRO+ PACIAE)
• Results and Summary
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Stages of heavy ion collisions
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PACIAE model
– The PACIAE model is a parton and hadron
cascade model , which is based on PYTHIA.
– PYTHIA is a famous model for relativistic
hadron-hadron collisions.
– The PACIAE model is composed of
(1) Parton initialization
(2) Parton evolution
(3) Hadronization
(4) Hadron evolution
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PACIAE model
1) Parton Initialization
a) Nucleus-nucleus collision is decomposed into nucleonnucleon (NN) collisions.
b) NN collision is described by the PYTHIA model, and
the string fragmentation is switched-off.
c) The diquarks (anti-diquarks) are broken into quarks
(anti-quarks), so the consequence of this NN collision
is a partonic final state (quarks, anti-quarks, and
gluons, beside a few remnants).
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PACIAE model
2) Parton Evolution (Parton Recattering)
Only 2→2 process are considered, 2 → 2 Leading-Order (LO-)
pQCD differential cross sections. (Replaced by the Hydro
evolution in the hybrid model.)
3) Hadronization
String Fragmentation (SF) model in PYTHIA, and Coalescence
model. The coalescence model is used in the hybrid model.
4) Hadron Evolution (Hadron Rescattering)
Only p, n,  , k , , , ,  ( ), J /  and their antiparticles are
condsidered, and the usual two-body collision model is used.
Reference：Ben-Hao Sa, et al, Comp. Phys. Comm. 183 (2012)
333-346.
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Hydrodynamical model
Relativistic fluid dynamics (FD) is based on the
assumption of local equilibrium and the conservation
laws.
The MIT bag model is used for the equation of state
(EoS).
Algorithms for solving the hydrodynamic equations:
PIC, SHASTA, and RHHLE etc. Particle in Cell (PIC)
method is used in hydro code.
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Particle in Cell (PIC) method
The baryon charge related marker particles are
introduced to represent the motion of the fluid.
a) The momentum and energy are distributed evenly
among the marker particles.
b) Each marker particle is given an effective velocity.
c) In a time step t, if the marker particle crosses to
a new cell, then it transfers the corresponding
amount of baryon charge, momentum, and energy
from the donor cell to the acceptor cell.
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Particle in Cell
(PIC) method
Initial marker particle position
Time step is 100 cycles.
Time step is 200 cycles.
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Initial state for Hydrodynamic model
There are many initial state models, such as:
• perturbative QCD (hard scatterings) plus saturation
model,
• Glauber-based parametrization method,
• color glass condensate inspired model,
• effective string rope model,
• transport model, etc.
In the HYDRO-PACIAE model, the effective string rope
model is used to generate initial state.
We choose the transport model PACIAE to generate
initial state in the new hybrid model.
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From PACIAE model to Hydro
• PACIAE model is Monte Carlo transport model.
• Event-by-event fluctuations of the initial state
can naturally included.
• The energy, momentum, and baryon number
density are described by three-dimensional
Gaussian distribution.
Ecf ( x, y, z ) 
( x  x p )  ( y  y p )  [ z ( z  z p )]
2
N exp{
2
2
2
2
}
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From Hydro to PACIAE model

Case 1: Isochronous transition, t = Constant. d  (1,0,0,0)
Case 2: Transition takes place on the hyperboloid,
τ=Constant.
d     (1,0,0, v )
Case 3: Realistic and complex condition.
d   differentin each cell
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Solutions of Boundary Conditions
Cooper-Frye formula
E
dN


f
(
x
,
p
)
p
d 
i
3


d p
Fermi distribution for Quark and anti-quark:
gi
1
f i ( i ) 
(2)3 e ( i   ) / T  1
Bose distribution for Gluon:
gi
1
f i ( i ) 
(2)3 e ( i   ) / T  1
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Structure of the hybrid model
1. Initial stage for hydrodynamic (PACIAE
model).
2. Hydrodynamic evolution (Hydro code).
3. Translate hydro into parton
(Cooper-Frye formula).
4. Hadronization (PACIAE model).
5. Hadron rescattering (PACIAE model).
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Results of the Hydro-PACIAE model
Charged Hadron Pseudorapidity distribution:
Reference：Yu-Liang Yan, et al, J. Phys. G: Nucl. Part. Phys. 40
(2013) 025102
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Transverse momentum distribution from Hybrid
and PACIAE model
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Elliptic flow from Hybrid and PACIAE model
Deformation parameter in PACIAE:
 rp2
 y2   x2
 p  C r ,  r 
,  rp  2
4
 y   x2
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Summary
•
Based on the PACIAE and Hydrodynamic model, a hybrid
model, PACIAE+HYDRO+PACIAE, is established.
•
The PACIAE+HYDRO+PACIAE model is a partonic
based integrated hybrid model, which can reproduce the
experimental data well.
•
The PACIAE+HYDRO+PACIAE hybrid model can be used
to study the partonic degrees of freedom, quark number
scaling, and the initial state fluctuations, etc.
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Thanks for your
attention!
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