Recent Developments of A Multi-Phase Transport Model
Zi-Wei Lin
Department of Physics
East Carolina University
AMPT Collaborators:
Che Ming Ko (Texas A&M University)
Bao-An Li (Texas A&M University-Commerce)
Subrata Pal (Tata Institute of Fundamental Research, India)
Bin Zhang (Arkansas State University)
Acknowledgements to
Helmholtz International Center for FAIR,
Workshop organizers
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
1/31
Outline
Structure of A Multi-Phase Transport (AMPT) model
Present status of AMPT
Recent developments
Possible future directions
Summary
All the best, Kryzrof
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
2/31
What do we need for simulations of high energy heavy ion collisions?
We need:
Initial particle/energy production
Options:
Soft+hard model, CGC, pQCD, ...
Partonic interactions,
thermalization & evolution
Parton cascade (ZPC, MPC, BAMPS),
(ideal, viscous) hydrodynamics, dE/dx, ...
Hadronization
/QCD phase transition
String fragmentation,
quark coalescence/parton recombination,
statistical hadronization, Cooper-Frye,
independent fragmentation, rate equations, ...
Hadronic interactions
Hadron cascade (ART, RQMD, UrQMD, ...),
thermal model (w/ freezeout temperatures), …
The AMPT model currently includes the green components.
In particular, it can be used to study
fluctuation, quark coalescence, multi-particle correlation, …
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
3/31
Structure of AMPT v1.xx (default version)
A+B
HIJING (parton dist. functions, nuclear shadowing):
minijet partons,
excited strings, spectators
ZPC (parton cascade)
Partons freeze out
Hadronization (Lund string fragmentation)
Extended ART
Hadrons freeze out (at a global cut-off time);
strong-decay all remaining resonances
Final particle spectra
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
4/31
A central Au+Au event at 200AGeV from the default AMPT model
after the
primary AA
collisions
Only formed
particles
are shown
60fm box
Beam axis
1st frame:
spectator nucleons.
Dynamics is
time-delayed
at large rapidities
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
5/31
A central Au+Au event at 200AGeV from the default AMPT model
View on
the beam axis
E.g.
at middle right:
rho (green)
decayed at 7.0 fm/c
at lower right:
K*bar is produced
at 16.6 fm/c
&
vanishes at 20.8fm/c.
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
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Why string melting version of AMPT?
Estimate the initial energy density in AA collisions:
dET / dy dET / dy
e0 ~
»
6
2
3 ~ 2.5
p R t 0 150 fm SPS RHIC
Nuclear radius
20 GeV/fm3
LHC
>>critical energy density
Proper formation time,
for QCD phase transition:
taken as 1 fm/c
εc ~ O(1) GeV/fm3
At high-enough energies,
hadronic matter such as strings cannot exist early on,
they should be represented by a high density partonic matter:

the string melting version of AMPT
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
Lin&Ko, PRC65
June 15, 2013
7/31
Structure of AMPT v2.xx (String Melting version)
A+B
HIJING (parton dist. functions, nuclear shadowing):
minijet partons,
excited strings, spectators
"Melt" to q & qbar via
intermediate hadrons
ZPC (parton cascade)
Partons freeze out
Hadronization (Quark Coalescence)
Extended ART
Hadrons freeze out (at a global cut-off time);
strong-decay all remaining resonances
Final particle spectra
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
8/31
A central Au+Au event at 200AGeV from the String Melting AMPT
σp=3mb
60fm box
Beam axis
E.g. middle region
(near mid-rapidity):
coalescence of
q (red) and
qbar (cyan)
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
9/31
A central Au+Au event at 200AGeV from the String Melting AMPT
View on
the beam axis
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
10/31
Compare the same event
default AMPT
vs
String Melting AMPT
At t=5 fm/c:
With string melting:
many more partons,
parton stage dominates;
hadron stage starts much later
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
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Present status of AMPT
First public release of AMPT codes: ~ April 2004.
Detailed physics descriptions in the long paper:
Lin, Ko, Li, Zhang & Pal, PRC 72, 064901 (2005).
"Official" versions v1.11/v2.11 (2004) and v1.21/v2.21 (2008)
are available at
https://karman.physics.purdue.edu/OSCAR
More versions, including recent & test versions, are available at
http://personal.ecu.edu/linz/ampt/
v1.25t3/v2.25t3
(8/2009)
v1.25t7/v2.25t7
(9/2011)
v1.25t7d/v2.25t7d
(4/2012)
v1.26t1/v2.26t1
(9/2012)
The webpage looks like
this
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
Juneor
15,this
2013 (offline)
12/31
The heavy ion community is also using AMPT as a valuable tool
Simplified Picture
What really happens in an event
Example:
Triangular Flow
discovered
using AMPT:
Alver & Roland,
PRC81
From Alver’s talk:
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
13/31
A b=10fm Au+Au event at 200AGeV from String Melting AMPT
View on
the beam axis
Initial overlap
region
has
an irregular
geometry
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June 15, 2013
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Summary of modifications in AMPT (1)
9/2012 test version v1.26t1/v2.26t1:
To avoid crash (segmentation fault due to s<0) at high energy
such as LHC at large NT:
use double precision in art1f.f when calculating sqrt(s),
use double precision in linana.f to calculate β avoid NaN.
use a more general formula in amptsub.f to calculate rapidity (valid for
hadrons at large rapidities that have |PZ|≥E due to finite precision)
4/2012 test version v1.25t7d/v2.25t7d:
Added an option to enable π0 electromagnetic decay after hadron cascade
2/2012 test version v1.25t7b/v2.25t7b:
Added an option to enable random orientation of reaction plane
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
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Summary of modifications in AMPT (2)
5/2011 test version v1.25t4/v2.25t5:
Include finite widths of resonances (K* η ρ ω Φ Δ)
when produced from quark coalescence in the string melting version,
added for the purpose of resonance reconstruction using invariant mass.
7/2009 test version v1.25t2/v2.25t2:
Added an option to enable users to modify nuclear shadowing
smoothly between no-shadowing and the default HIJING shadowing
6/2009 test version v1.25t1/v2.25t1:
Added an option of event selection so that each event will have at least
1 mini-jet parton above a set Pt value in the initial condition;
added an option to embed a back-to-back high-Pt q/qbar pair in each event;
write out Npart information (spatial coordinates and status of
each incoming nucleon);
added option to write complete parton information before & after parton cascade
and the full parton collision history for the string melting version
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
16/31
Summary of modifications in AMPT (3)
3/2009 test version v1.23/v2.23:
Included a subroutine to enable users to insert user-defined hadrons
before the start of the hadron cascade
10/2008 test version v1.22/v2.22:
Included deuteron(d) interactions in hadron cascade via d+M ↔ B+B
(M or B represents a meson or a baryon),
also included elastic collisions of d+M and d+B;
similar anti-deuteron interactions are also included
10/2008 v1.21/v2.21:
Added option to turn off φ meson decays at the end of hadron cascade
i.e., at NT=NTMAX
……
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
17/31
Example: extension of AMPT to deformed Uranium (1)
0.8
This test version (v1.25t8/v2.25t8) is not online.
0.6
< e2>
2011: Added deformed Uranium U238
as projectile/target.
U+U body
U+U tip
U+U side
U+U
Au+Au
AMPT-Default
(a)
0.4
0.2
0
0
100
200
300
400
500
Npart
0.8
< e3>
0.6
U+U body
U+U tip
U+U side
U+U
Au+Au
AMPT-Default
(b)
0.4
0.2
Considered a few special geometries and MB UU
Rihan Haque, Lin & Mohanty, PRC 85
0
0
100
200
300
400
500
Npart
Spatial anisotropy
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
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Example: extension of AMPT to deformed Uranium (2)
v2 closely resembles ε2
AMPT-SM
|h|<0.5
0.8
(a)
0.1
0.6
< e2>
<v2>
0.15
U+U body
U+U tip
U+U side
U+U
Au+Au
U+U body
U+U tip
U+U side
U+U
Au+Au
AMPT-Default
(a)
0.4
0.05
0.2
0
0
100
200
300
400
500
0
0
Npart
<v3>
0.03
0.8
U+U body
U+U tip
U+U side
U+U
Au+Au
200
300
400
500
Npart
AMPT-SM
|h|<0.5
0.6
< e3>
0.04
100
(b)
0.02
U+U body
U+U tip
U+U side
U+U
Au+Au
AMPT-Default
(b)
0.4
0.2
0.01
0
0
0
0
100
200
300
400
100
200
300
400
500
Npart
500
Npart
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
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Ongoing work: fix charge conservation in AMPT (1)
After fixing this problem,
AMPT will be better suited
for studies of charge fluctuation and balance functions.
Why is charge conservation violated in AMPT?
Problems come from
hadron cascade of AMPT
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
20/31
Ongoing work: fix charge conservation in AMPT (2)
History of hadron cascade in AMPT
Based on the ART model
Li&Ko, PRC52
Kbar interactions added
Song,Li&Ko, NPA646
NNbar <> mesons
Zhang et al, PRC61
BBbar <> mesons, explicit K*
Lin et al, PRC64, NPA698
 interactions
Lin&Ko,PRC65
 interactions
Pal,Ko&Lin, NPA707
Multi-strange interactions (  )
Pal,Ko&Lin, NPA730
Deuteron interactions
Oh,Lin&Ko, PRC80, NPA834
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June 15, 2013
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Ongoing work: fix charge conservation in AMPT (3)
Hadronization
Why is charge conservation violated in AMPT?
First reason:
The hadron cascade
has K+ and K- as explicit particles,
but not K0 and K0-bar.
K0
To let all kaons interact:
•
before hadron cascade,
we change K0 to K+ (also: K0-bar to K-)
•
after hadron cascade,
we change half of final K+ into K0.
K-
K+
K-
K0-bar
Hadron cascade
K0
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
K+
K+
K-
K+
K-
June 15, 2013
K0-bar
22/31
Ongoing work: fix charge conservation in AMPT (4)
Why is charge conservation violated in AMPT?
Second reason:
Many reactions in the hadron cascade
are not implemented for each possible isospin configuration:
•
isospin-averaged cross section is used,
•
final state particles have randomly-generated isospin.
For example:
p h ®p p
each final-state pion could have +, 0, – charge in AMPT:
so we can have p + h ® p + p 0
or
p+ h ®p+
allowed
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
p-
should be forbidden
June 15, 2013
23/31
Ongoing work: fix charge conservation in AMPT (5)
We need to:
add K0 & K0-bar as explicit particles,
allow similar interaction types as for K+ & K-.
Hadronization
Several steps:
K0 K+ K0-bar K-
1) Forbid final states that violate charge conservation:
this is enough to conserve charge.
2) Update/determine cross sections of allowed final states
including the branching ratios
Hadron cascade
(w/ full isospin)
3) Check detailed balance among related cross sections
K0 K+ K0-bar KRequires checking essentially all hadron reactions in AMPT
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
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Ongoing work: fix charge conservation in AMPT (6)
Meson-Meson channels
SU(2):
With strangeness:
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
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Ongoing work: fix charge conservation in AMPT (7)
Meson-Baryon & Baryon-Baryon channels
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Possible future directions
1
2
• Improve parton recombination
by using local density as criteria
• Coalescence in phase-space
• Couple AMPT with
viscous
hydrodynamics
• Gluons in parton recombination
(energy-momentum conservation)
• Fragmentation of high-Pt partons
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Possible future direction 1: Coalescence
Improve the quark coalescence model for hadronization
Currently, a parton can coalesce after kinetic freeze-out
(i.e. after it will not have further interactions)
Average parton density at coalescence
depends on parton scattering cross section σp;
& typical value is too low (<< εc ~ 1 GeV/fm3)
We need to start coalescence
around energy density ~εc
independent of σp
Quark coalescence will work better
due to the much higher density
at the time of coalescence
Zhang,Chen&Ko, JPG35
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June 15, 2013
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Possible future direction 2: hybrid model
A+B
HIJING (parton dist. functions, nuclear shadowing):
minijet partons,
excited strings, spectators
"Melt" to q & qbar via
intermediate hadrons
AMPT v2.xx
(String Melting)
ZPC (parton cascade)
Partons freeze out
Hadronization (Quark Coalescence)
Extended ART
Final particle spectra
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
29/31
Possible future direction 2: hybrid model
HIJING (parton dist. functions, nuclear shadowing):
minijet partons,
excited strings, spectators
A+B
Direct link to QCD:
(EoS, viscosity)
Partons  Distribution
Self-contained
initial condition,
including fluctuations
Other initial condition
allowed, e.g. CGC
Can compare with
current AMPT:
hydro vs parton cascade
"Melt" to q & qbar via
intermediate hadrons
Hydrodynamics
(viscous, 3+1d, event-by-event )
Distribution  hadrons
Extended ART
Final particle spectra
XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław
June 15, 2013
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Summary
AMPT has been a self-contained phenomenological model
(from initial condition to final observables event-by-event):
includes fluctuations and non-equilibrium dynamics;
can be a test-bed of different conceptual ideas;
should incorporate essential stages of heavy ion collisions.
The approach needs further developments
(more direct link to QCD variables & properties):
improving the parton recombination model for hadronization
or
couple with 3+1d viscous hydrodynamics.
Comments, suggestions, collaborations
are greatly welcome.
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