1 transport and hydrodynamic model for ultra-relativistic heavy ion collisions yu-liang yan china...
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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
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Stages of heavy ion collisions
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– 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
PACIAE model
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Particle list
particle order position and four momentum
particle 1particle 2particle 3……
x, y, z, px, py, pz, E of particle 1x, y, z, px, py, pz, E of particle 2x, y, z, px, py, pz, E of particle 3……
Collision list
collision order collision pair
123
……
collision time
Part. i and j Part. l and mPart. l and n
……
col. time for ij col. time for lmcol. time for ln
……
nn collision happens if their least approaching distance min
totd
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Remnant
Remnant Initial state radiation
Final state radiation
Hadronization
kf
lf
Rescattering ?
Decay
)(xf ai
)(xf aj
h
a
b
…
ˆd
dt
• Sketch for pp simulation in PYTHIA
Parton Distribution Function
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1) Parton Initializationa) Nucleus-nucleus collision is decomposed into
nucleon-nucleon (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).
PACIAE model
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3) Hadronization
4) Hadron Evolution (Hadron Rescattering)
String Fragmentation (SF) model in PYTHIA, and Coalescence model. The coalescence model is used in the hybrid model.
Only and their antiparticles arecondsidered, and the usual two-body collision model is used.
/),(,,,,,,, Jknp
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.)
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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1) The baryon charge related marker particles are introduced to represent the motion of the fluid.
Particle in Cell (PIC) method
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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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.
Particle in Cell (PIC) method
Reference :Phys. Rev. C 17 (1978) 2080Phys. 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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Quantities of cells in Hydro
Quantities of particles in
PACIAE model1), Particle number: N
2), Particle type: KF code
3), Momentum and energy of each particle: E, px, py, pz
4), Coordinates and time of each particle: vx, vy, vz, T
1), Energy density: Ecf
2), Baryon density: n
3), Pressure: p
4), Velocity: vx, vy, vz
5), Temperature and Entropy: T and sq
Physical Quantities in Hydro and PACIAE 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.
}2
)]([)()(exp{
),,(
2
222
pzpp
cf
zzyyxxN
zyxE
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Case 1: Isochronous transition, t = Constant. Case 2: Transition takes place on the hyperboloid, τ=Constant.Case 3: Realistic and complex condition.
From Hydro to PACIAE model
)0,0,0,1(d
),0,0,1( vd
celleachindifferentd
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dppxfpd
dNE i ),(
3Cooper-Frye formula
Solutions of Boundary Conditions
Fermi distribution for Quark and anti-quark:
1)2(
1)( /)(3 T
iii ie
gf
Bose distribution for Gluon:
1)2(
1)( /)(3 T
iii ie
gf
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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).
Structure of the hybrid model
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Charged Hadron Pseudorapiditydistribution:
Results of the Hybid model
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
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
10-1
100
101
102
103
(1/2p
T)d
N2
/dp
Td
[(G
eV/c
)-2]
pT(GeV/c)
Pb+Pb 2.76TeV
PACIAE Hybrid ALICE
Total charged particles
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0.0 0.5 1.0 1.5 2.0 2.5 3.010-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
40-50%
-0.5<<0.5
Pb+Pb 2.76TeV
20-30%
10-20%
5-10%
30-40%
0-5%
(1
/2p
T)d
N2
/dp T
d[(
GeV
/c)-2
]
pT(GeV/c)
Transverse momentum distribution of pion
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0.5 1.0 1.5 2.0 2.5 3.0
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
40-50%
30-40%
-0.5<<0.5
(1/2p
T)d
N2
/dp
Td[
(Ge
V/c
)-2]
pT(GeV/c)
Pb+Pb 2.76TeV
K
20-30%
10-20%
5-10%
0-5%
Transverse momentum distribution of kaon
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0.5 1.0 1.5 2.0 2.5 3.0
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
40-50%
Pb+Pb 2.76TeV
30-40%
20-30%
10-20%
5-10%
pT(GeV/c)
(1/2p
T)d
N2
/dp
Td[
(Ge
V/c
)-2]
p0-5%
-0.5<<0.5
Transverse momentum distribution of proton
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Elliptic flow from Hybrid and PACIAE model
Deformation parameter in PACIAE:
22
222
,4
,xy
xyrp
rprrp C
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Elliptic flow for pion, kaon, and proton
0.5 1.0 1.5 2.0 2.50.00
0.05
0.10
0.15
0.20
0.25
0.30
pT(GeV/c)
Pb+Pb 2.76TeV
pion kion proton
v 2
40-50%
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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 yourattention!