A. Ster A. Ster 1, T. Csörgő 1,2, M. Csanád 3, B. Lörstad 4, B. Tomasik 5 Oscillating HBT radii and the time evolution of the source 200 GeV Au+Au data.

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Presentation transcript:

A. Ster A. Ster 1, T. Csörgő 1,2, M. Csanád 3, B. Lörstad 4, B. Tomasik 5 Oscillating HBT radii and the time evolution of the source 200 GeV Au+Au data analyzed with asBuda-Lund 1 MTA KFKI RMKI, Budapest, Hungary 2 Department of Physics, Harvard University, Cambridge, USA 3 ELTE University, Budapest, Hungary 4 Lund University, Lund, Sweden 5 NPI ASCR, Prague, Czech Republic

A. Ster Exact solutions of 1+3d NR hydro with ellipsoidal symmetry Spherical  Ellipsoidal symmetry From fluid of nucleons  exact simple models for RHIC Refs: J. Bondorf, S. Garpman and J. Zimányi, Nucl. Phys. A296: ,1978 T. Cs, S. V. Akkelin, Y. Hama, Yu. Sinyukov, Phys.Rev.C67:034904,2003 T. Cs, Acta Phys.Polon.B37: ,2006 Viscous solution: in preparation Hydrodynamically evolving core + halo of resonances Ref: T. Cs, B. Lörstad and J. Zimányi, Z.Phys.C71: ,1996 Generalization to relativistic solutions Ref: T. Cs, L.P. Csernai, Y. Hama, T. Kodama, Heavy Ion Phys.A21:73-84,2004, but for Hubble flows only Observation: elliptic flow scaling laws first from non-rel 3d perfect fluid solution v 2 (w): dimensionless(dimensionless)‏ recent result: holds for exact Navier-Stokes solutions, too Ref: M. Csanád et al, Eur.Phys.J.A38: ,2008, + T. Cs. in prep. Motivation Core: π ±, K ±, Λ, Σ, … Halo: η’, η, ω, K S

A. Ster Buda-Lund: universal scaling of v 2

A. Ster Motivation

A. Ster Motivation

A. Ster Motivation

A. Ster Old idea: Quark Gluon Plasma More recent: Liquid of quarks Input from lattice: EoS of QCD Matter T c =176±3 MeV (~2 terakelvin) ‏ (hep-ph/ ) ‏ at  = 0, a cross-over Aoki, Endrődi, Fodor, Katz, Szabó hep-lat/ LQCD input for hydro: p(,T) ‏ LQCD for RHIC region: p~p(T), c s 2 = p/e = c s 2 (T) = 1/(T) ‏ It’s in the family exact hydro solutions! TcTc

A. Ster Illustrated initial T-> density profiles Determines density profile! Examples of density profiles - Fireball - Ring of fire - Embedded shells of fire Exact integrals of hydro Scales expand in time Time evolution of the scales (X,Y,Z) ‏ follows a classic potential motion. Scales at freeze out -> observables. info on history LOST! No go theorem - constraints on initial conditions (penetrating probels) indispensable.

A. Ster Solution of the “HBT puzzle” HBT volume Full volume Geometrical sizes keep on increasing. Expansion velocities tend to constants. HBT radii R x, R y, R z approach a direction independent constant. Slope parameters tend to direction dependent constants. General property, independent of initial conditions - a beautiful exact result.

A. Ster Scaling from exact hydro M. Csanád, M. Vargyas Eur.Phys.J.A44: ,2010 Scales at freeze out -> observables. info on history LOST! No go theorem - illustrated, BUT PHENIX QGP claim, T init ≥ 330 MeV Confirmed for any reasonable p/e ≥ 0.1 See talk of M. Csanád On analysis of photon spectra For more details + constraints on evolution + constraints on EoS

A. Ster Intro/Reminder, Buda-Lund hydro model Axially symmetric: T. Cs, B. Lörstad, hep-ph/ Ellipsoidal generalization: M. Csanád, T.Cs., B. Lörsrad, nucl-th/

A. Ster Results, asBuda-Lund fits to spectra Fits % centrality Fits are done simulatenously To spectra, v 2 and asHBT Analytic formulas, precision < 2-4 % Buda-Lund parameters Optimized by CERN Minuit Spectra are corrected for long-lived Resonance effects using core-halo model. Both positive and negative spectra described in stat. acceptable way

A. Ster Results, asBuda-Lund fits to asHBT Fits % centrality Fits are done simulatenously To spectra, v 2 and asHBT Analytic formulas, precision < 2-4 % Buda-Lund parameters Optimized by CERN Minuit Oscillations of HBT radii are described reasonably well, as a function of transverse mass. Simultaneously with charged particle elliptic flow and spectra.

A. Ster Results, asBuda-Lund fits to asHBT Fits % centrality Fits are done simulatenously To spectra, v 2 and asHBT Analytic formulas, precision < 2-4 % Buda-Lund parameters Optimized by CERN Minuit Oscillations of HBT radii are described reasonably well, as a function of angle small but systematics in out and side. But chi2/NDF = /152 CL = 0.78 % acceptable Beyond Gaussian H() distribution?

A. Ster Results: from spectra, v 2, asHBT + Buda-Lund CL > 0.1 % Acceptable. Temperatures: Similar. Strong expansion in impact parameter direction. Homogeneity region: out-of-plane elongated Actual source: in-plane elongated a little (5  stat)

A. Ster Illustration A. Ster, talk at WPCF 2009: First indication of in-plane extended source confirmed by the final analysis too

A. Ster Summary Au+Au elliptic flow data at RHIC satisfy UNIVERSAL scaling laws predicted in 2001, 2003 by Buda-Lund hydro model, based on exact solutions of hydrodynamics. Quantitative evidence for a perfect fluid in Au+Au at RHIC - but quark number scaling suggests flow on quark level. Buda-Lund model predicted the HBT radii successfully at RHIC, describes azimuthal oscillations of HBT radii. Model specific predictions: HBT oscillation amplitudes of side, out and os are the same V 2 is given by flow asymmetry alone

A. Ster Buda-Lund hydro fits to NA22 h+p data N. M. Agababyan et al, EHS/NA22, PLB 422 (1998) 395 T. Csörgő, hep-ph/001233, Heavy Ion Phys. 15 (2002) 1-80

A. Ster Buda-Lund hydro fits to NA22 h+p data N. M. Agababyan et al, EHS/NA22, PLB 422 (1998) 395 T. Csörgő, hep-ph/001233, Heavy Ion Phys. 15 (2002) 1-80

A. Ster Buda-Lund hydro fits to NA22 h+p data W. Kittel, E. A. De Wolf: Soft Multihadron Dynamics, World Sci. (2005) T. Cs, S. Hegyi, G. Jancsó, R. C. Hwa, Correlations and Fluctuations'98, World Sci. (1999)