LP. Csernai, Montreal 26.6.03 1 Topics in Heavy Ion Collisions, 2003 Montreal, June 25-28, 2003 Flow effects and their measurable consequences in ultra-relativistic.

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

LP. Csernai, Montreal 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)

LP. Csernai, Montreal

4 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.

LP. Csernai, Montreal Collective FLOW Patterns: Lorentz contraction changes the GEOMETRY and Reaction Mechanism ! [ URQMD, U. Frankfurt, 2000]

LP. Csernai, Montreal 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]

LP. Csernai, Montreal Phase transition to QGP in small systems ! In macroscopic systems two phases of different densities (e) are in phase equilibrium. Negligible density fluctuations! [Csernai, Kapusta, Osnes, PRD 67 (03) ] STATIC

LP. Csernai, Montreal Small, Mesoscopic Systems If N=100, fluctuations are getting strong (red). Close to the critical point, the two phases cannot be identified (green). ~~> Landau’s theory of fluctuations near the critical point. Nuclear Liquid-Gas phase transition (first order) [ Goodman, Kapusta, Mekjian, PRC 30 (1984) 851 ] CRAY - 1 STATIC

LP. Csernai, Montreal Lattice Field Theory [Farakos, Kajantie, et al. (1995) hep-lat/ ] First order (EW) phase transition: statistical ensemble. Fluctuations of density decrease with increasing Lattice volume !! For macroscopic EoS extrapolation is needed! For small systems, ~ fermi 3, fluctuations are REAL !!! Supercomputers are needed ! [Csernai, Neda PL B337 (94) 25] STATIC

LP. Csernai, Montreal 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 ?

LP. Csernai, Montreal 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)

LP. Csernai, Montreal

LP. Csernai, Montreal Fire streak picture - Only in 3 dimensions! Myers, Gosset, Kapusta, Westfall

LP. Csernai, Montreal String rope --- Flux tube --- Coherent YM field

LP. Csernai, Montreal Initial stage: Coherent Yang-Mills model [Magas, Csernai, Strottman, Pys. Rev. C ‘2001]

LP. Csernai, Montreal Expanding string ropes – Full energy conservation

LP. Csernai, Montreal Yo – Yo Dynamics wo/ dissipation

LP. Csernai, Montreal wo/ dissipation

LP. Csernai, Montreal 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  Z [fm] y e [GeV/ fm 3 ] [Magas, Csernai, Strottman, in pr.]

LP. Csernai, Montreal Initial state 3 rd flow component

LP. Csernai, Montreal Modified Initial State

LP. Csernai, Montreal 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)

LP. Csernai, Montreal 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!

LP. Csernai, Montreal Relativistic Fluid Dynamics For any EoS, P=P(e,n), and any energy-momentum tensor in LE(!): Not only for high v!

LP. Csernai, Montreal 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.)

LP. Csernai, Montreal Dim Hydro for RHIC (PIC)

LP. Csernai, Montreal dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=0.0 fm/c, T max = 420 MeV, e max = 20.0 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm.. EoS: p= e/3 - 4B/3 B = 397 MeV/fm x 4.4 fm

LP. Csernai, Montreal dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=2.3 fm/c, T max = 420 MeV, e max = 20.0 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm x 4.6 fm

LP. Csernai, Montreal dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=4.6 fm/c, T max = 419 MeV, e max = 19.9 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm x 4.9 fm

LP. Csernai, Montreal dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=6.9 fm/c, T max = 418 MeV, e max = 19.7 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm x 5.5 fm

LP. Csernai, Montreal dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=9.1 fm/c, T max = 417 MeV, e max = 19.6 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm x 5.8 fm

LP. Csernai, Montreal dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=11.4 fm/c, T max = 416 MeV, e max = 19.5 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm x 6.7 fm

LP. Csernai, Montreal dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=13.7 fm/c, T max = 417 MeV, e max = 19.4 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm x 7.3 fm

LP. Csernai, Montreal dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=16.0 fm/c, T max = 417 MeV, e max = 19.4 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm x 8.1 fm

LP. Csernai, Montreal dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=18.2 fm/c, T max = 417 MeV, e max = 19.4 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm x 8.7 fm

LP. Csernai, Montreal Global Flow Patterns: Directed Transverse flow Elliptic flow 3 rd flow component (anti - flow) Squeeze out

LP. Csernai, Montreal

LP. Csernai, Montreal Talk by S. Manly Note: (1) There is no boost invariance !!. (2) Hydro [Hirano] yields less stopping

LP. Csernai, Montreal [ Hirano, QM’02 hydro results ]

LP. Csernai, Montreal Global Flow Directed Transverse flow Elliptic flow 3 rd flow component (anti - flow) 3 rd flow component (anti - flow) Squeeze out

LP. Csernai, Montreal K 0 s Anti-Flow Au+Au 6 AGeV Striking opposite flow for K 0 s Reproduced using repulsive mean-field for K 0 Chris Pinkenberg E895 Talk proton Chung et al., Phys. Rev Lett 85, 940 (2000) Pal et al., Phys. Rev. C 62, (2000) K0sK0s

LP. Csernai, Montreal Anti-flow from shadowing : [ L. Bravina, et al., PL B470 (99) 27.] Only for b > 8 fm !

LP. Csernai, Montreal Third flow component [SPS NA49]

LP. Csernai, Montreal rd flow component and QGP Csernai & Röhrich [Phys.Lett.B458(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 EoS there is 3 rd flow comp. The effect was absent without QGP. In string and RQMD models only peripheral collision showed the effect (shadowing).

LP. Csernai, Montreal rd flow component Hydro [Csernai, HIPAGS’93]

LP. Csernai, Montreal Heavy Ion Coll. at RHIC - Transverse velocities - b=0.5 [ Strottman, Magas, Csernai, BCPL User Mtg. Trento, 2003 ] DYNAMIC z

LP. Csernai, Montreal 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)

LP. Csernai, Montreal Sudden Freeze-Out & Hadronization from Sc. QGP Negative P (Positive T)

LP. Csernai, Montreal A= fm/c

LP. Csernai, Montreal “Wiggle”, Pb+Pb, E lab =40 and 158GeV [NA49-QM’02] Talk by A. Wetzler Preliminary 158 GeV/A Note different scale for 40 and 158 GeV! The “wiggle” is there! v 1 < 0

LP. Csernai, Montreal v 2 (p t ), non-flow vs p t Non-flow contribution (on average) : - about 7-10% at SPS, 160 GeV. - about 130 GeV - about 200 GeV - could slightly increase with transverse momentum STAR Preliminary [S.A. Voloshin] Arises from event by event flow fluctuations and from impact parameter fluctuations at fixed Y !

LP. Csernai, Montreal v 1 (y) is not measured yet at RHIC!? As v 2 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, p x, p y, p z ) = f CM ( x, y, -z, p x, p y, -p z ) 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)] ): Q k = S i k y CM p x 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.

LP. Csernai, Montreal Flow & Azimuthal effects in HBT HBT is biased by theor. Assumptions, eq. C(q,K)  R=2fm /Gauss | R=8fm/u.Sphr. Flow changes C(q,K) essentially ! Use of analysis based on static sphr. Gauss. S is ?

LP. Csernai, Montreal 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.