Norway. 3-dim. QGP Fluid Dynamics and Flow Observables László Csernai (Bergen Computational...
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Transcript of Norway. 3-dim. QGP Fluid Dynamics and Flow Observables László Csernai (Bergen Computational...
Norway
3-dim. QGP Fluid 3-dim. QGP Fluid Dynamics and Flow Dynamics and Flow
ObservablesObservables
3-dim. QGP Fluid 3-dim. QGP Fluid Dynamics and Flow Dynamics and Flow
ObservablesObservables
László Csernai (Bergen Computational Physics Lab., Univ. of Bergen)
IntroductionIntroductionIntroductionIntroduction
Strong flow is observedStrong flow is observed => =>
- Early, local eq., - EoS- Early, local eq., - EoS
- nnqq scaling – QGP flows scaling – QGP flows
- no flow in hadronic matterno flow in hadronic matter > simultaneous hadronization and FO > simultaneous hadronization and FO (HBT, high strangeness abundance) (HBT, high strangeness abundance)
Relativistic Fluid DynamicsRelativistic 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,
P = P (e,n) Solvable for local equilibrium!
EoSEoS
Relativistic Fluid DynamicsRelativistic Fluid DynamicsFor any EoS, P=P(e,n), and any energy-momentum tensor in LE(!):
Not only for high v!
Two theoretical problemsTwo theoretical problemsTwo theoretical problemsTwo theoretical problems
• Initial state – Initial state – - Fitted initial states > moderate insight- Fitted initial states > moderate insight
• Final Freeze OutFinal Freeze Out
- - Realistic Model, Continuos FO, Realistic Model, Continuos FO,
ST layer, Non-eq. distribution ST layer, Non-eq. distribution
Local Equilibration, Fluids
Fluid components, Friction
-------------- One fluid >>> E O E O SS -------------- One fluid >>> E O E O SS
Hadronization, chemical FO, kinetic FO
Freeze Out >>> Detectors
Stages of a CollisionStages of a CollisionStages of a CollisionStages of a Collision
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 !!!
QGP EoS QGP EoS One fluidOne fluid
HadronizatiHadronizationon Chemical Freeze Chemical Freeze
OutOut Kinetic Freeze OutKinetic Freeze Out
Initi
al st
ate
time
Heavy Colliding SystemHeavy Colliding SystemHeavy Colliding SystemHeavy Colliding System
IdealizatioIdealizationsnsFO LayerFO Layer
FO HSFO HS
Fire streak picture - Only in 3 dimensions!Fire streak picture - Only in 3 dimensions!
Myers, Gosset, Kapusta, Westfall
String rope --- Flux tube --- Coherent YM field
Initial state
3rd flow component
3-Dim Hydro for RHIC (PIC)3-Dim Hydro for RHIC (PIC)
3-dim Hydro for RHIC Energies
Au+Au ECM=65 GeV/nucl. b=0.5 bmax Aσ=0.08 => σ~10 GeV/fm
e [ GeV / fm3 ] T [ MeV]
t=0.0 fm/c, Tmax= 420 MeV, emax= 20.0 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm
. .
EoS: p= e/3 - B/3,
B = 397 MeV/fm3
8.7 x 4.4 fm
Au+Au ECM=65 GeV/nucl. b=0.5 bmax Aσ=0.08 => σ~10 GeV/fm
e [ GeV / fm3 ] T [ MeV]
t=9.1 fm/c, Tmax= 417 MeV, emax= 19.6 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm
. .
20.3 x 5.8 fm
Au+Au ECM=65 GeV/nucl. b=0.5 bmax Aσ=0.08 => σ~10 GeV/fm
e [ GeV / fm3 ] T [ MeV]
t=18.2 fm/c, Tmax= 417 MeV, emax= 19.4 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm
. .
34.8 x 8.7 fm
Global Flow patterns:Directed
Transverse flow
Elliptic flow
3rd flow component(anti - flow)
Squeeze out
3rd flow component
Hydro
[Csernai, HIPAGS’93]
[Phys.Lett.B458(99)454]Csernai & Röhrich
“Wiggle”, Pb+Pb, Elab=40 and 158GeV [NA49]
A. Wetzler
Preliminary
158 GeV/A
The “wiggle” is there!
v1 < 0
Flow is a Flow is a diagnosticdiagnostic tool toolFlow is a Flow is a diagnosticdiagnostic tool tool
Impact Impact par.par.
Transparency – Transparency – string tensionstring tension
EquilibrationEquilibrationtimetime
Consequence:Consequence:vv11(y), v(y), v22(y), …(y), …
FOHS - Movies:FOHS - Movies:
B=0, T-fo = 139MeV
B=0, T-fo = 180MeV
B=0.4, T-fo = 139MeV
B=0.4, T-fo = 180MeV
[Bernd Schlei, Los Alamos, [Bernd Schlei, Los Alamos, LA-UR-03-3410]
Freeze OutFreeze OutFreeze OutFreeze Out
• (B) - Freeze out over FOHS- post FO distribution?= 1st.: n, T, u, cons. Laws != 2nd.: non eq. f(x,p) !!! -> (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 -> f(x,p)
The Boltzmann Transport Equation and Freeze OutThe 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
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
The invariant “ Escape” probabilityThe invariant “ Escape” probability
Escape probability factors for different points on FO hypersurface, in the RFG. Momentum values are in units of [mc]
A B C
D E F
t’
x’
[RFG][RFG]
Results – the cooling and retracting of the interacting matterResults – 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]
Results – the contour lines of the FO distribution, f(p)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]
Recent open, flow related issuesRecent open, flow related issuesRecent open, flow related issuesRecent open, flow related issues
• Is QGP a “perfect fluid” ? – Is QGP a “perfect fluid” ? – - Small (?) viscosity, but strong interaction (?)Small (?) viscosity, but strong interaction (?)- Laminar flow, not turbulent -> large viscosity- Laminar flow, not turbulent -> large viscosity- Cascades need high cross section to reproduce flow- Cascades need high cross section to reproduce flow
• Comprehensive flow assessmentComprehensive flow assessment
- - v1, v2, v3 … should be evaluated on equal footing v1, v2, v3 … should be evaluated on equal footing - There is one reaction plane, - There is one reaction plane, , (not , (not 11 22 33 … ) … ) - y, - y, , pT correlations are equally important (y ?), pT correlations are equally important (y ?)
• Solution:Solution: Event by Event flow evaluationEvent by Event flow evaluationEvent by Event flow evaluationEvent by Event flow evaluation