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