Topics in Heavy Ion Collisions, 2003 Montreal, June 25-28, 2003

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Topics in Heavy Ion Collisions, 2003Montreal,
June 25-28, 2003
Flow effects and their measurable consequences in
ultra-relativistic heavy-ion collisions
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Collaboration

• U of Bergen Cs. Anderlik, L.P. Csernai,
  Ø. Heggø-Hansen, V. Magas (U
  Lisbon), E. Molnár, A. Nyiri, D.
  Röhrich, and K. Tamousiunas (Trento)
• U of Oulu A. Keranen, J. Manninen
• U of Sao Paulo F. Grassi, Y. Hama
• U of Rio de Janeiro T. Kodama
• U of Frankfurt H. Stöcker, W. Greiner
• Los Alamos Nat. Lab. D.D. Strottman
• 0.5 Tera-flop IBM e-series supercomputer, w/ 96
  Power4 processors a 5.2 Giga-flop each (Bergen
  Computational Physics Lab. EU Research
  Infrastructure)

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COLLECTIVE FLOW - History

• Is fluid dynamics applicable in relativistic
  nuclear physics?
• Collective Nuclear Flow proposed Greiner et
  al., 1973
• Transverse Flow Exp. Proof 1984 Plastic
  Ball, LBL
• By now Mc increases close to macro,
  continuous matter
• Many flow-patterns are observed in nuclear
  collisions
• Not trivial - complex analysis is needed
  theory exper.

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Collective FLOW Patterns
URQMD, U. Frankfurt, 2000
Lorentz contraction changes the GEOMETRY and
Reaction Mechanism !
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Local equilibrium

• Large no. of degrees of freedom
• Strong stopping (AGS, SPS) / equilibration (RHIC)
  
• Local equilibration ?
• Equation of State (EoS) characterizes the
  equilibrium properties of matter 1
• Dynamics is well approximated by fluid dynamics
  (perfect, viscous, ) at Mid Coll.!
• Multi Module Modeling 2

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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
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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 !
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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 But,
does it recover at higher energies ?
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Multi Module Modeling

• A Initial state - Fitted to measured data (?)
• B 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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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, Pys. Rev. C 2001
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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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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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Initial state
3rd flow component
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Modified Initial State
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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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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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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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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
8.7 x 4.4 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
.
.
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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Global Flow Patterns
Directed Transverse flow
3rd flow component (anti - flow)
X
b
Z
Squeeze out
Elliptic flow
Spherical flow
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Note (1) There is no boost invariance !!
. (2) Hydro Hirano yields less
stopping
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Hirano, QM02 hydro results
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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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K0s Anti-Flow AuAu 6 AGeV
proton
Chung et al., Phys. Rev Lett 85, 940 (2000) Pal
et al., Phys. Rev. C 62, 061903 (2000)

• Striking opposite flow for K0s
• Reproduced using repulsive mean-field for K0

Chris Pinkenberg E895 Talk
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Anti-flow from shadowing
L. Bravina, et al., PL B470 (99) 27.
Only for b gt 8 fm !
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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).

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3rd flow component
Hydro Csernai, HIPAGS93
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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 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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Sudden Freeze-Out Hadronization from Sc. QGP
Negative P (Positive T)
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A 0.065
11.4 fm/c
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Wiggle, PbPb, Elab40 and 158GeV NA49-QM02
Talk by A. Wetzler
v1 lt 0
158 GeV/A
Note different scale for 40 and 158 GeV!
The wiggle is there!
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v2(pt), non-flow vs pt
S.A. Voloshin

• Non-flow contribution (on average)
• - about 7-10 at SPS, 160 GeV.
• about 15 _at_ 130 GeV
• about 20 _at_ 200 GeV
• could slightly increase with transverse momentum

Arises from event by event flow fluctuations and
from impact parameter fluctuations at fixed Y !
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v1(y) is not measured yet at RHIC!?
As v2 is measured, the reaction plane x,z is
known, just the target/projectile side should be
selected. This is not done due to the (Bjorken
model) prejudice that the distribution of emitted
particles is mirror-symmetric in CM f CM (
x, y, z, px, py, pz ) f CM ( x, y, -z,
px, py, -pz ) This is wrong (!) as the
presented hydro calculations and SPS data show.
At finite impact parameters, (2-15) there is a
fwd / bwd central symmetry. Calculate event
by event the Q-vector (a la Danielewicz,
Odyniecz, PL (1985) )
Qk Sik yCM px For all particles, i, of
type k. Only the sign is relevant, as the plane
is known already. This Q-vector will select the
same side (e.g. projectile) in each event.
Discussions with Art Poskanzer and Roy Lacey are
gratefully acknowledged.
O.K.
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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 ?

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Conclusions

• Hydro works amazingly well! Stronger and stronger
  hydro effects are observed!
• ? 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 determination of reaction plane is vital for
  flow, HBT, and for ALL observables influenced by
  the collective collision dynamics.