L.P. Csernai, C. Anderlik, V. Magas, D. Strottman

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• L.P. Csernai, C. Anderlik, V. Magas, D. Strottman

Modelling Relativistic Nuclear Collisions
Multi Module Models
Bergen
Computational Physics Lab.
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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)

Landau (1953), Milekhin (1958), Cooper Frye
(1974)
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Matching Conditions

• Conservation laws
• Nondecreasing entropy

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INITIAL STATE
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Firestreak Picture
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, NEW2001
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Yo Yo Dynamics
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Expanding string ropes Full energy conservation
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Initial state
3rd flow component
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3-Dim Hydro for RHIC (PIC)
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.1 bmax As0.08
gt s10 GeV/fm
n / n0 1
e GeV / fm3
.
.
T 0.0 fm/c nmax 8.67 emax32.46 GeV / fm3
Lx,y 1.45 fm Lz0.145 fm
4.4 x 1.3 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.1 bmax As0.08
gt s10 GeV/fm
n / n0 1
e GeV / fm3
.
.
T1.9 fm/c nmax 8.66 emax 31.82 GeV / fm3
Lx,y 1.45 fm Lz0.145 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.1 bmax As0.08
gt s10 GeV/fm
n / n0 1
e GeV / fm3
.
.
.
T 3.8 fm/c nmax 7.77 emax 27.22 GeV / fm3
Lx,y 1.45 fm Lz0.145 fm
4.4 x 1.3 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.1 bmax As0.08
gt s10 GeV/fm
n / n0 1
e GeV / fm3
.
.
T 5.7 fm/c nmax 6.36 emax 26.31 GeV / fm3
Lx,y 1.45 fm Lz0.145 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.1 bmax As0.08
gt s10 GeV/fm
n / n0 1
e GeV / fm3
.
.
T 7.6 fm/c nmax 5.22 emax 37.16 GeV / fm3
Lx,y 1.45 fm Lz0.145 fm
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3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.1 bmax As0.08
gt s10 GeV/fm
n / n0 1
e GeV / fm3
.
.
T 9.5 fm/c nmax 4.45 emax 32.86 GeV / fm3
Lx,y 1.45 fm Lz0.145 fm
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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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Third flow component
SPS NA49
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Third flow component / SPS / NA49
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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).
• The effect is attributed to a flat (Landau type)
  initial condition.
• Similarity to elliptic flow.

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3rd flow component
Hydro Csernai, HIPAGS93
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A 0.08
11.4 fm / c
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A 0.065
11.4 fm/c
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Freeze out
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Hypersurface
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Cooper-Frye formula
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Consequences of conservation laws
(Space-like Taub 1948, Time-like Csernai
1987)

• Non-decreasing entropy current across front!

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Space-like hypersurface
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Cut Juttner distribution
T(p.ds) f(x,p)
Pre FO velocity
Anderlik et al., Phys.Rev.C59(99)3309
Bugaev, Nucl.Phys.A606(96)559
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Kinetic freeze-out models

• Kinetic approach
• f (x,p) out of equilibrium
• Asymmetry

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Freeze out model with rescattering
Anderlik et al., Phys.Rev.C59388-394,1999
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Freeze out distribution with rescattering
V0
V. Magas, et al., Heavy Ion Phys.9193-216,1999
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P-t distribution (T130 MeV)
V. Magas et al., Phys.Lett.B459(99)33
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CERN