L P Csernai C Anderlik V Magas D

L. P. Csernai, C. Anderlik, V. Magas, D. Strottman LP. Csernai, Sept. 4, 2001, Palaiseau FR 1

Multi Module Modeling • Initial state - pre-equilibrium: Parton Cascade; Coherent Yang-Mills [Magas] • Local Equilibrium Hydro, Eo. S • 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) LP. Csernai, Sept. 4, 2001, Palaiseau FR 2

Matching Conditions § Conservation laws § Nondecreasing entropy LP. Csernai, Sept. 4, 2001, Palaiseau FR 3

INITIAL STATE LP. Csernai, Sept. 4, 2001, Palaiseau FR 4

LP. Csernai, Sept. 4, 2001, Palaiseau FR 5

Firestreak Picture Myers, Gosset, Kapusta, Westfall LP. Csernai, Sept. 4, 2001, Palaiseau FR 6

String rope --- Flux tube --- Coherent YM field LP. Csernai, Sept. 4, 2001, Palaiseau FR 7

Initial stage: Coherent Yang-Mills model [Magas, Csernai, Strottman, NEW’ 2001] LP. Csernai, Sept. 4, 2001, Palaiseau FR 8

Yo – Yo Dynamics LP. Csernai, Sept. 4, 2001, Palaiseau FR 9

LP. Csernai, Sept. 4, 2001, Palaiseau FR 10

Expanding string ropes – Full energy conservation LP. Csernai, Sept. 4, 2001, Palaiseau FR 11

Initial state 3 rd flow component LP. Csernai, Sept. 4, 2001, Palaiseau FR 12

3 -Dim Hydro for RHIC (PIC) LP. Csernai, Sept. 4, 2001, Palaiseau FR 13

3 -dim Hydro for RHIC Energies Au+Au ECM=65 Ge. V/nucl. b=0. 1 bmax Aσ=0. 08 => σ~10 Ge. V/fm. n / n 0 [ 1 ] e [ Ge. V / fm 3 ]. T= 0. 0 fm/c nmax = 8. 67 emax=32. 46 Ge. V / fm 3 Lx, y= 1. 45 fm Lz=0. 145 fm 4. 4 x 1. 3 fm LP. Csernai, Sept. 4, 2001, Palaiseau FR 14

3 -dim Hydro for RHIC Energies Au+Au ECM=65 Ge. V/nucl. b=0. 1 bmax Aσ=0. 08 => σ~10 Ge. V/fm. n / n 0 [ 1 ] e [ Ge. V / fm 3 ]. T=1. 9 fm/c nmax = 8. 66 emax= 31. 82 Ge. V / fm 3 Lx, y= 1. 45 fm Lz=0. 145 fm LP. Csernai, Sept. 4, 2001, Palaiseau FR 15

3 -dim Hydro for RHIC Energies Au+Au ECM=65 Ge. V/nucl. b=0. 1 bmax Aσ=0. 08 => σ~10 Ge. V/fm. n / n 0 [ 1 ] e [ Ge. V / fm 3 ]. . T= 3. 8 fm/c nmax = 7. 77 emax= 27. 22 Ge. V / fm 3 Lx, y= 1. 45 fm Lz=0. 145 fm 4. 4 x 1. 3 fm LP. Csernai, Sept. 4, 2001, Palaiseau FR 16

3 -dim Hydro for RHIC Energies Au+Au ECM=65 Ge. V/nucl. b=0. 1 bmax Aσ=0. 08 => σ~10 Ge. V/fm. n / n 0 [ 1 ] e [ Ge. V / fm 3 ]. T= 5. 7 fm/c nmax = 6. 36 emax= 26. 31 Ge. V / fm 3 Lx, y= 1. 45 fm Lz=0. 145 fm LP. Csernai, Sept. 4, 2001, Palaiseau FR 17

3 -dim Hydro for RHIC Energies Au+Au ECM=65 Ge. V/nucl. b=0. 1 bmax Aσ=0. 08 => σ~10 Ge. V/fm. n / n 0 [ 1 ] e [ Ge. V / fm 3 ]. T= 7. 6 fm/c nmax = 5. 22 emax= 37. 16 Ge. V / fm 3 Lx, y= 1. 45 fm Lz=0. 145 fm LP. Csernai, Sept. 4, 2001, Palaiseau FR 18

3 -dim Hydro for RHIC Energies Au+Au ECM=65 Ge. V/nucl. b=0. 1 bmax Aσ=0. 08 => σ~10 Ge. V/fm. n / n 0 [ 1 ] e [ Ge. V / fm 3 ]. T= 9. 5 fm/c nmax = 4. 45 emax= 32. 86 Ge. V / fm 3 Lx, y= 1. 45 fm Lz=0. 145 fm LP. Csernai, Sept. 4, 2001, Palaiseau FR 19

Directed 3 rd flow component (anti - flow) Global Flow Transverse flow Squeeze out Elliptic flow LP. Csernai, Sept. 4, 2001, Palaiseau FR 20

Third flow component [SPS NA 49] LP. Csernai, Sept. 4, 2001, Palaiseau FR 21

Third flow component / SPS / NA 49 LP. Csernai, Sept. 4, 2001, Palaiseau FR 22

3 rd flow component and QGP • Csernai & Röhrich [Phys. Lett. B 458(99)454] observed a 3 rd flow component at SPS energies, not discussed before. • Also observed that in ALL earlier fluid dynamical calculations with QGP in the Eo. S there is 3 rd 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. LP. Csernai, Sept. 4, 2001, Palaiseau FR 23

3 rd flow component Hydro [Csernai, HIPAGS’ 93] LP. Csernai, Sept. 4, 2001, Palaiseau FR 24

A= 0. 08 11. 4 fm / c LP. Csernai, Sept. 4, 2001, Palaiseau FR 25

A= 0. 065 11. 4 fm/c LP. Csernai, Sept. 4, 2001, Palaiseau FR 26

Freeze out LP. Csernai, Sept. 4, 2001, Palaiseau FR 27

Hypersurface LP. Csernai, Sept. 4, 2001, Palaiseau FR 28

“Cooper-Frye” formula LP. Csernai, Sept. 4, 2001, Palaiseau FR 29

Consequences of conservation laws: (Space-like [Taub 1948], Time-like [Csernai 1987]) Ø Non-decreasing entropy current across front! LP. Csernai, Sept. 4, 2001, Palaiseau FR 30

Space-like hypersurface LP. Csernai, Sept. 4, 2001, Palaiseau FR 31

Cut – Juttner distribution: [Anderlik et al. , Phys. Rev. C 59(99)3309] [Bugaev, Nucl. Phys. A 606(96)559] Θ(p. dσ) f(x, p) Pre FO velocity LP. Csernai, Sept. 4, 2001, Palaiseau FR 32

Kinetic freeze-out models § Kinetic approach § f (x, p) out of equilibrium § Asymmetry LP. Csernai, Sept. 4, 2001, Palaiseau FR 33

Freeze out model with rescattering [Anderlik et al. , Phys. Rev. C 59: 388 -394, 1999 ] LP. Csernai, Sept. 4, 2001, Palaiseau FR 34

Freeze out distribution with rescattering V=0 [V. Magas, et al. , ] Heavy Ion Phys. 9: 193 -216, 1999 LP. Csernai, Sept. 4, 2001, Palaiseau FR 35

P-t distribution (T=130 Me. V) [V. Magas et al. , Phys. Lett. B 459(99)33] LP. Csernai, Sept. 4, 2001, Palaiseau FR 36

LP. Csernai, Sept. 4, 2001, Palaiseau FR 37