Norway

1
Norway
2
3-dim. QGP Fluid Dynamics and Flow Observables
László Csernai (Bergen Computational Physics
Lab., Univ. of Bergen)
3
Introduction

• Strong flow is observed gt
• - Early, local eq., - EoS
• nq scaling QGP flows
• no flow in hadronic matter gt simultaneous
  hadronization and FO (HBT, high strangeness
  abundance)

4
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!
5
Relativistic Fluid Dynamics
For any EoS, PP(e,n), and any energy-momentum
tensor in LE(!)
Not only for high v!
6
Two theoretical problems

• Initial state
• - Fitted initial states gt moderate insight
• Final Freeze Out
• - Realistic Model, Continuos FO,
  ST layer, Non-eq. distribution

7
Stages of a Collision
Freeze Out gtgtgt Detectors
Hadronization, chemical FO, kinetic FO
-------------- One fluid gtgtgt E O S
Fluid components, Friction

Local Equilibration, Fluids
Collective flow reveals the EoS ifwe have
dominantly one fluid with local equilibrium in a
substantial part of the space-time domain of the
collision !!!
8
Heavy Colliding System
Initial state
Idealizations
FO Layer
FO HS
time
QGP EoS One fluid
Hadronization
Chemical Freeze Out
Kinetic Freeze Out
9
Fire streak picture - Only in 3 dimensions!
Myers, Gosset, Kapusta, Westfall
10
String rope --- Flux tube --- Coherent YM field
11
Initial state
3rd flow component
12
3-Dim Hydro for RHIC (PIC)
13
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
8.7 x 4.4 fm
EoS p e/3 - B/3, B 397 MeV/fm3
14
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
15
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
16
Global Flow patterns
Directed Transverse flow
3rd flow component (anti - flow)
X
Z
b
Squeeze out
Spherical flow
Elliptic flow
17
3rd flow component
Csernai Röhrich
Phys.Lett.B458(99)454
Hydro Csernai, HIPAGS93
18
Wiggle, PbPb, Elab40 and 158GeV NA49
A. Wetzler
v1 lt 0
158 GeV/A
The wiggle is there!
19
Flow is a diagnostic tool
Impact par.
Equilibrationtime
Transparency string tension
Consequencev1(y), v2(y),
20
FOHS - Movies
Freeze Out
B0, T-fo 139MeV
B0.4, T-fo 139MeV
B0, T-fo 180MeV
B0.4, T-fo 180MeV
Bernd Schlei, Los Alamos, LA-UR-03-3410
21

• (B) - Freeze out over FOHS- post FO
  distribution? 1st. n, T, u, cons. Laws !
  2nd. non eq. f(x,p) !!! -gt (C)
• (Ci) Simple kinetic model
• (Cii) Covariant, kinetic F.O. description
• (Ciii) Freeze out form transport equation
• Note ABC together is too involved!B C can be
  done separately -gt f(x,p)

22
The Boltzmann Transport Equation and Freeze Out

• Freeze out is
• Strongly directed process
• Delocalized
• The m.f.p. - reaches infinity
• Finite characteristic length
• Modified Boltzmann Transport Equation for Freeze
  Out description

The change is not negligible in the FO direction
23
The invariant Escape probability in finite
layer

• The escape form the int to free component
• Not to collide, depends on remaining distance
• If the particle momentum is not normal to the
  surface, the spatial distance increases

Early models
1
24
The invariant Escape probability
A
B
C
t
x
D
E
F
RFG
Escape probability factors for different points
on FO hypersurface, in the RFG. Momentum values
are in units of mc
25
Results the cooling and retracting of the
interacting matter

• Space-Like FO
  Time-Like FO
• 
  cooling
• 
  retracting
• ? Cut-off factor flow
  velocity No Cut-off

RFF
RFF
26
Results the contour lines of the FO
distribution, f(p)

• Space-Like FO
  Time-Like FO
• 
  jump in
• 
  RFF
• With different initial flow velocities

RFF
RFF
27
Recent open, flow related issues

• Is QGP a perfect fluid ?
• Small (?) viscosity, but strong interaction
  (?)- Laminar flow, not turbulent -gt large
  viscosity- Cascades need high cross section
  to reproduce flow
• Comprehensive flow assessment
• - v1, v2, v3 should be evaluated on
  equal footing - There is one reaction
  plane, ?, (not ?1 ?2 ?3 ) - y, ?, pT
  correlations are equally important (y ?)
• Solution

Event by Event flow evaluation
28
(No Transcript)