Transcript Document

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)
May. 7 - 13, 2014, CCNU, Wuhan, China
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Outline
• Introduction
• PACIAE model
• Hydrodynamic model
• Transport and Hydrodynamic hybrid Model
(PACIAE+HYDRO+ PACIAE)
• Results and Summary
2
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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Particle list
particle order
position and four momentum
particle 1
particle 2
particle 3
……
x, y, z, px, py, pz, E of particle 1
x, y, z, px, py, pz, E of particle 2
x, y, z, px, py, pz, E of particle 3
……
Collision list
nn collision happens if their least
approaching distance
d min
 tot


collision order
collision pair
collision time
1
2
3
……
Part. i and j
Part. l and m
Part. l and n
……
col. time for ij
col. time for lm
col. time for ln
……
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• Sketch for pp simulation in PYTHIA
Remnant
Initial state
a radiation
Rescattering ?
f i a (x)
Parton Distribution
Function
a
j
f (x)
b
Remnant
fk
d
dtˆ
…
h
fl
Decay
Final state
radiation
Hadronization
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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
1) 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
2) Update the baryon charge, momentum, and
energy values. Use the updated values to solve
hydrodynamic equations.
3) Proceed the next time step of the calculations.
Reference：
Phys. Rev. C 17 (1978) 2080
Phys. Lett. B 261 (1991) 352
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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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Physical Quantities in Hydro
and PACIAE model
Quantities of
cells in Hydro
Quantities of
particles in
PACIAE model
1), Energy density: Ecf
2), Baryon density: n
1), Particle number: N
3), Pressure: p
3), Momentum and energy of
each particle: E, px, py, pz
4), Coordinates and time of
each particle: vx, vy, vz, T
4), Velocity: vx, vy, vz
5), Temperature and
Entropy: T and sq
2), Particle type: KF code
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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
(effective string rope model (ESRM)
and/or 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 Hybid 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
2
-2
(1/2pT)dN /dpTd[(GeV/c) ]
3
10
Pb+Pb 2.76TeV
2
10
Total charged particles
1
10
PACIAE
Hybrid
ALICE
0
10
-1
10
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
pT(GeV/c)
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Transverse momentum distribution of pion
3
10
Pb+Pb 2.76TeV

2
2
-2
(1/2pT)dN /dpTd[(GeV/c) ]
10
1
0-5%
10
0
10
5-10%
-1
10
10-20%
-2
10
20-30%
-3
10
30-40%
-4
10
-5
10
-6
10
40-50%
-0.5<<0.5
-7
10
0.0
0.5
1.0
1.5
2.0
pT(GeV/c)
2.5
3.0
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Transverse momentum distribution of kaon
2
10
Pb+Pb 2.76TeV
1
2
-2
(1/2pT)dN /dpTd[(GeV/c) ]
10
0
10
0-5%
K
5-10%
-1
10
10-20%
-2
10
20-30%
-3
10
30-40%
-4
10
-5
10
-6
10
40-50%
-0.5<<0.5
-7
10
0.5
1.0
1.5
2.0
pT(GeV/c)
2.5
3.0
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Transverse momentum distribution of proton
1
10
Pb+Pb 2.76TeV
2
-2
(1/2pT)dN /dpTd[(GeV/c) ]
0
10
p
0-5%
-1
10
5-10%
-2
10
10-20%
-3
10
20-30%
-4
10
-5
30-40%
-6
40-50%
10
10
-0.5<<0.5
-7
10
0.5
1.0
1.5
2.0
pT(GeV/c)
2.5
3.0
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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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Elliptic flow for pion, kaon, and proton
0.30
0.25
v2
0.20
Pb+Pb 2.76TeV
40-50%
0.15
0.10
pion
kion
proton
0.05
0.00
0.5
1.0
1.5
pT(GeV/c)
2.0
2.5
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Summary
•
Based on the PACIAE and Hydrodynamic model, a hybrid
model, ESRM +HYDRO+PACIAE and
PACIAE+HYDRO+PACIAE, is established.
•
The ESRM (or 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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