L''P' Csernai

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Multi module modelling of heavy ion collisions
Collective flow and QGP properties RIKEN-BNL
workshop November 17-19, 2003
L..P. Csernai
2
Multi module modelling of heavy ion collisions

• L.P. Csernai, A. Anderlik, Cs. Anderlik, Ø.
  Heggø-Hansen, E. Molnár, A. Nyiri, D.
  Röhrich, and K. Tamousiunas
• U of Valencia V.K. Magas
• U of Oulu A. Keranen, J. Manninen
• Los Alamos National Lab. D.D. Strottman, B.
  Schlei
• U of Sao Paulo F. Grassi, Y. Hama
• U of Rio de Janeiro T. Kodama
• U of Frankfurt H. Stöcker, W. Greiner
• Bergen Computational Physics Lab. EU Research
  Infrastructure,BCCS, Unifob AS, University of
  Bergen, Norway

3
Multi Module Modeling

• Pre Eq. of State (EoS) Phases Local eq.BagM
• A Initial state - Fitted to measured data (?)
• B Initial state - Pre-equilibrium Parton
  Cascade M. Coherent Yang-Mills Magas
• Local Equilibrium ? Hydro, EoS
• Final Freeze-out Kinetic models, measurables.
• If QGP ? Sudden and simultaneous hadronization
  and freeze out (indicated by HBT, Strangeness,
  Entropy puzzle)

4
Phase transition to QGP in small systems !
STATIC
In macroscopic systems two phases of different
densities (e) are in phase equilibrium.
Negligible density fluctuations!
Csernai, Kapusta, Osnes, PRD 67 (03) 045003
5
Small, Mesoscopic Systems
STATIC
If N100, fluctuations are getting strong
(red). Close to the critical point, the two
phases cannot be identified (green). gt Landaus
theory of fluctuations near the critical
point. Nuclear Liquid-Gas phase transition
(first order)
Goodman, Kapusta, Mekjian, PRC 30 (1984) 851
CRAY - 1
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Lattice Field Theory
STATIC
First order (EW) phase transition statistical
ensemble. Fluctuations of density decrease with
increasing Lattice volume !! For macroscopic EoS
extrapolation is needed! For small systems,
100-200 fermi3, fluctuations are REAL !!!
Csernai, Neda PL B337 (94) 25
Farakos, Kajantie, et al. (1995) hep-lat/
Supercomputers are needed !
7
Pressure Soft Point?
LBL, AGS, SPS Collective flow P-x vs. y
Pressure sensitive Directed transverse flow
decreases with increasing energy Holme, et
al., 89 D. Rischke, 95 E. Shuryak,
95 OBSERVED ! But, does it recover at higher
energies ? WHAT HAPPENS?
8
Phase transition dynamics Out of thermal eq.

• Transition to QGP
• 0.1 0.3 fm/c (PCM)
• Structure functions- valence quarks- see quarks
  (stopped)
• Flux-tube models- immediate eq.- Bjorken 83-
  Gyulassy Cs. 86

• Hadronization
• Nucleation 30-100fm/c- local thermal
  equilibrium- Cs. Kapusta 92
• Out of eq. ph.tr. possible- supercooled QGP-
  Csorgo Cs. 94- Cs. Mishustin 95-
  1-2 fm/c
• ? Hadronization and Freeze-out MUST be
  simultaneous ! / No T,p,..- How can the
  Stat.Model work?

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Multi Module Modeling
FO surface
FO transfer
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Multi Module Modeling on GRID
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Fire streak picture - Only in 3 dimensions!
Myers, Gosset, Kapusta, Westfall
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String rope --- Flux tube --- Coherent YM field
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Initial stage Coherent Yang-Mills model
Magas, Csernai, Strottman, Phys. Rev. C64 (01)
014901
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Expanding string ropes Full energy conservation
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Yo Yo Dynamics
wo/ dissipation
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wo/ dissipation
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Initial state
3rd flow component
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Modified Initial State
In the previous model the fwd-bwd surface was too
sharp ? two propagating peaks
Thus, after the formation of uniform streak, the
expansion at its end is included in the model ?
This led to smoother energy density and velocity
profiles ?
e GeV/ fm3
y
Z fm
Z fm
Magas, Csernai, Strottman, in pr.
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Modified Initial State
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Matching Conditions

• Conservation laws
• Nondecreasing entropy

Can be solved easily. Yields, via the Taub
adiabat and Rayleigh line, the final state
behind the hyper-surface. (See at freeze out.)
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3-Dim Hydro for RHIC (PIC)
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Multi Module Modeling

• Initial state - pre-equilibrium Parton
  Cascade Coherent Yang-Mills Magas
• Local Equilibrium ? Hydro, EoS
• Final Freeze-out Kinetic models, measurables
  -
  If QGP ? Sudden and simultaneous hadronization
  and freeze out (indicated by HBT, Strangeness,
  Entropy puzzle)

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Relativistic Fluid Dynamics
Eg. from kinetic theory. BTE for the evolution
of phase-space distribution
Then using microscopic conservation laws in the
collision integral C
These conservation laws are valid for any, eq. or
non-eq. distribution, f(x,p). These cannot be
solved, more info is needed!
Boltzmann H-theorem (i) for arbitrary f, the
entropy increases,
(ii) for stationary, eq. solution the
entropy is maximal, ?? EoS
P P (e,n)
Solvable for local equilibrium!
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Relativistic Fluid Dynamics
For any EoS, PP(e,n), and any energy-momentum
tensor in LE(!)
Not only for high v!
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t0.0 fm/c, Tmax 420 MeV, emax 20.0 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
EoS p e/3 - 4B/3
B 397 MeV/fm3
4 times elongated !!
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t2.3 fm/c, Tmax 420 MeV, emax 20.0 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
11.6 x 4.6 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t4.6 fm/c, Tmax 419 MeV, emax 19.9 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
14.5 x 4.9 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t6.9 fm/c, Tmax 418 MeV, emax 19.7 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
17.4 x 5.5 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t9.1 fm/c, Tmax 417 MeV, emax 19.6 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
20.3 x 5.8 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t11.4 fm/c, Tmax 416 MeV, emax 19.5 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
23.2 x 6.7 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t13.7 fm/c, Tmax 417 MeV, emax 19.4 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
26.1 x 7.3 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t16.0 fm/c, Tmax 417 MeV, emax 19.4 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
31.9 x 8.1 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t18.2 fm/c, Tmax 417 MeV, emax 19.4 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
34.8 x 8.7 fm
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z
DYNAMIC
Heavy Ion Coll. at RHIC - Transverse velocities
- b0.5
Strottman, Magas, Csernai, BCPL User Mtg.
Trento, 2003
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Multi Module Modeling

• Initial state - pre-equilibrium Parton
  Cascade Coherent Yang-Mills Magas
• Local Equilibrium ? Hydro, EoS
• Final Freeze-out F.O. Surface
• Final Freeze-out Kinetic models -
  If QGP ? Sudden and simultaneous hadronization
  and freeze out (indicated by HBT, Strangeness,
  Entropy puzzle)

Landau (1953), Milekhin (1958), Cooper Frye
(1974)
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Freeze-Out Hyper-Surface Extraction with Digital
Image Processing Techniques VESTA and Projections
of FOHS (e.g., Firestreaks for Au Au _at_ RHIC)
Bernd R. Schlei (T-1) - LA-UR-03-3410
In 31 D Hydrodynamical Calculations, VESTA is
useful for the Graphical Rendering of Projections
of FOHS. A Construction of a 4D FOHS requires a
Generalization of VESTA into 4D.
xyz - Projection
t fixed
xtz - Projection
y fixed
y
z
x
Impact Parameter b 0.5
t
31 D Hydrodynamic Density Data are based on
Firestreak Initial Conditions V. K. Magas, L.
P. Csernai, D. Strottman, Nucl. Phys. A712 (2002)
167.
z
x
Impact Parameter b 0.5
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Freeze-Out Hyper-Surface Extraction with Digital
Image Processing Techniques Time-Sequence of FOHS
Projections
10 times elongated !!
Bernd R. Schlei (T-1) - LA-UR-03-3410
VESTA Rendering of FOHS in 31 D Hydrodynamics at
fixed Times (t1 lt lt t14).
z
y
Impact Parameter b 0.0
x
t1
t2
t3
t4
t5
t6
t7
t8
t14
t13
t12
t11
t10
t9
31 D Hydrodynamic Density Data, courtesy D.
Strottman, Theoretical Division, Los Alamos
National Laboratory.
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Freeze-Out Hyper-Surface Extraction with Digital
Image Processing Techniques Movie Time-Sequence
of F.O. H-S Projections
b0.
Bernd R. Schlei (T-1)
Y
Z
10 times elongated in z-direction, to compensate
for L. contraction !
Bernd R. Schlei (T-1) LA-UR-03-3410
31 D Hydrodynamic Density Data, D. Strottman,
Theoretical Division, Los Alamos National
Laboratory.
X
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Modified Initial State
Z
b0.5 bmax
Y
X
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Quick Time Movie - External
Due to MSs competitive business
practices Axonometric view Heavy Ion reaction -
Surface visualization T 139 MeV Hy-mov-004.mov
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Reaction Plane - X , Z
Z
X
45
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Quick Time - Movie - External
Due to MSs competitive business
practices Reaction Plane Surface at T 139
MeV Hy-mov-00.mov
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Multi Module Modeling

• Initial state - pre-equilibrium Parton
  Cascade Coherent Yang-Mills Magas
• Local Equilibrium ? Hydro, EoS
• Final Freeze-out F.O. Surface
• Final Freeze-out Kinetic models
  QGP ? Sudden and simultaneous hadronization and
  freeze out CF formula
• Problem 1 Conservation laws to non-eq!
• Problem 2 Post FO, non-eq. distribution!

53
Matching Conditions Again

• Conservation laws
• Nondecreasing entropy

Can be solved easily. Yields, via the Taub
adiabat and Rayleigh line, the final state
behind the hyper-surface. (See at freeze out.)
54
Freeze out
L Bravina et al.
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Hypersurface
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Space-like hypersurface - Problem II
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Space-like hypersurface II
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Post F.O. - Cut-Jüttner distribution
Bugaev, Nucl.Phys.A606(96)559
No Eq., T, p, , EoS !!!
Proposed by
p
x
Anderlik et al., Phys.Rev.C59(99)3309
Solved
Post F.O. distribution ??pmLm??f(p)
p
y
V-flow
Matching conditions determine 5 parameters only .
Ansatz in needed for final f(x,p) !
V-parameter
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Phase-Space FO probability
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Phase-Space FO probability
A. Anderlik, E. Molnar, et al.
A
B
d3?? u?
C
Time-like F.O.
Uniform 1
D
E
F
Space-like F.O.
61
Freeze out distribution with rescattering from
kinetic model across a layer
V0
V. Magas, et al., Heavy Ion Phys.9193-216,1999
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Analytic fit to Kinetic Model Solution
.
.
Karolis Tamosiunas et al.
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Cancelling Juttner Distribution Karolis
Tamosiunas et al.
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Sudden Freeze-Out Hadronization from Sc. QGP
Negative P (Positive T)
O. Heggo-Hansen, MSc. Thesis, 03
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Global Flow
Directed Transverse flow
3rd flow component (anti - flow)
X
b
Z
Squeeze out
Elliptic flow
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Note (1) There is no boost invariance !!
. (2) Hydro Hirano yields less
stopping
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3rd flow component and QGP

• Csernai Röhrich Phys.Lett.B458(99)454
  observed a 3rd flow component at SPS energies,
  not discussed before.
• Also observed that in ALL earlier fluid dynamical
  calculations with QGP in the EoS there is 3rd
  flow comp.

• The effect was absent without QGP.
• In string and RQMD models only peripheral
  collision showed the effect (shadowing).

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3rd flow component
Hydro Csernai, HIPAGS93
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Third flow component
SPS NA49
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Anti-flow from shadowing
L. Bravina, et al., PL B470 (99) 27.
N
Only for b gt 8 fm !
?
71
A 0.065
11.4 fm/c
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Wiggle, PbPb, Elab40 and 158GeV NA49
Talk by A. Wetzler
v1 ? 0
158 GeV/A
Different scale for 40 and 158 GeV!
The wiggle is there!
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V-1 flow at RHIC/STAR
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Consequences

• If v1 ? 0 , earlier v2 results have
  to be modified (re-analyzed)
• 3-dim models and 3-dim initial conditions are
  needed to fit data
• Impact parameter / multiplicity dependence is
  essential (more data)
• Detailed models including equilibrium and
  non-equilibrium features will be required to
  describe the data

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Flow Azimuthal effects in HBT

• HBT is biased by theor. Assumptions, eq. C(q,K)
  ? R2fm /Gauss R8fm/u.Sphr.
• Flow changes C(q,K) essentially ! Use of
  analysis based on static sphr. Gauss. S is ?

STAR 01, Phenix 02, Hydro P Kolb et al 03
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Conclusions

• Hydro works well! 3-dim. hydro, initial final
  state models are important!
• ? Local Equilibrium and EoS exists ( in part of
  the reaction )
• We have a good possibility to learn more and more
  about the EoS, with improved experimental and
  theoretical accuracy!
• The detailed determination of flow patterns is
  vital for HBT, and for ALL observables influenced
  by the collective collision dynamics.