Thermal Fest: BNL July 20-21, 2001

1. Workshop on Thermalization and ChemicalEquilibration in Heavy Ions Collisions at RHIC Thermal Fest: BNL July 20-21, 2001 • PHOBOS results • BRAHMS results • Spectra: PHENIX results • Ratios: PHENIX results • Spectra: STAR results • Ratios: STAR results • Thermal models at RHIC • Recent NA49 results on hadron production and statistical model • Energy dependence of hadron production and maximum strangeness content in heavy ion collisions • Hadronization and strangeness production in heavy ion collisions from AGS to SPS collider energies • Chemical equilibrium of strangeness • Some thoughts, conventional and unconventional, about equilibration • Balance Functions • Dynamical freezeout vs. chemical equilibrium at SPS and RHIC • How can large entropy be generated so early at RHIC? • Charm production • Early thermalization I • Early thermalization II • Equilibration in parton transport • Thermalization from QCD • Color glass condensate and initial conditions in heavy ion collisions • QGP at Tc vs. ideal QGP

2. Thermalization:what do we know about it, what have we learnt from it? Introduction Chemical Freeze-out: Ratios, Yields, and Thermal Models Elementary Collisions Heavy Ion Collisions Transverse Flow Elliptic Flow Conclusions Thomas S. Ullrich Gordon Conference July 26, 2001

3. Introduction • Goal of Relativistic Heavy-Ion Physics: • study of the phase diagram of strongly interacting matter at high T and . • Discussion of phase diagram  thermodynamic language • Phase transition from initial QGP to hadronic state can only be reasonably well defined if the system under study is in a state of approximate local equilibrium • Thermalization = Thermodynamic Equilibrium • (not “thermal” looking spectra) • Landaus Definition: if in any subsystem the macroscopic physical quantities are (to a high degree) equal to their mean values • Heavy-Ion collisions: dynamic, no confining box • local equilibrium vs. global equilibrium

4. Introduction (cont’d) • Two kinds of equilibration: • Thermal equilibration • Chemical equilibration (implies thermal equilibrium) Early times: Direct Probes: strongly interacting signals e.g. heavy quarks, jets (see Jamie and Axel) and possibly by accumulative effects such as elliptic flow which builds up in the first few fm. Thermalization requires interaction (rescattering) among the participants  Flow is an unavoidable consequence • At Freeze-out: • Radial Flow: • reflected by shape of spectra • Chemical equilibrium: • reflected in yields and ratios , Tch • driven by inelastic cross-sections

5. Thermalization in Elementary Collisions ? • Thermal Model: • e+e-  qq hadronic jets ~ hadron gas = fireball (2 jets = 2 fireballs) • Correlated jets: small systems + quantum numbers conservation  canonical form • Recipe: • Assume thermal and chemical equilibrium • canonical ensemble to describe partition function • input: measured particle yields • output: T, V, s determined by fit (s to account forincomplete saturation of strangeness) • Studies performed at several s and various systems: pp , pp, e+e-

6. Thermalization in Elementary Collisions ? Seems to work rather well ?! Beccatini, Heinz, Z.Phys. C76 (1997) 269

7. Thermalization in Elementary Collisions ? Beccatini, Heinz, Z.Phys. C76 (1997) 269 • T of fireball from fitting hadron yields does not (or only weakly) depend on s • T  170 MeV • Universal hadronization mechanism at critical values ?

8. Thermalization in Elementary Collisions ? • Does the agreement with data mean we that the assumption of thermal and chemical equilibrium are correct ? NO ! • Is a process which leads to multiparticle production thermal? • Microcanonical Ensemble vs Canonical Ensemble: • Difference between MCE and CE vanishes as the size of the system N increases • Any mechanism for producing hadrons which evenly populates the free particle phase space will mimic a microcanonical ensemble • thermal behavior even if there is no interaction between particles This type of “thermal” behaviour requires no rescattering and no interactions. The collisions simply serve as as a mechanism to populating phase space without ever reaching thermal or chemical equilibrium In RHI we are looking for large collective effects.

9. Statistical Thermal Models in Heavy-Ion Collisions: SPS • Assume: • thermally and chemically equilibrated fireball at hadro-chemical freeze-out • Recipe: • grand canonical ensemble to describe partition function  density of particles of species I • fixed by constraints: Volume V, , strangeness chemical potentialS,isospin • input: measured particle ratios • output: temperature T and baryo-chemical potential B • SPS: Tch = 160-170 MeV, B = 270 MeV

10. Particle Ratios at RHIC RHIC: Lots of data on ratios from ALL expriments: So far most ratios measured around midrapidity and mostly antiparticle/particle ratios

11. STAR Preliminary Particle Ratios at RHIC /, +/ -, K+/K-, p/p ratios so far show little pt, y dependence and very weak centrality dependence STAR STAR Preliminary

12. Particle Ratios at RHIC • Ratios at midrapidity: • p/p = 0.61  0.02 (stat.)  0.06 (sys.) • = 0.60 0.04 (stat.)  0.06 (sys.) • = 0.64±0.01(stat.)±0.07 (sys.) • = 0.64±0.04(stat.)±0.06 (sys.) • = 0.66±0.03(stat.)±0.06 (sys.) y ~ 0.7 • = 0.41±0.04(stat.)±0.06 (sys.) y ~ 2 • / = 0.73 ± 0.03 (stat.) • X+/X- = 0.82 ± 0.08 (stat.) • / = 1.00 ± 0.01(stat.) ± 0.02 (sys.) • = 0.95 ± 0.03(stat.) ± 0.05 (sys.) • K-/K+ = 0.89±0.008 (stat.) ± 0.05 (sys.) • = 0.91±0.07 (stat.) ± 0.06 (sys.) • = 0.89±0.008 (stat.) ± 0.05 (sys.) • = 0.89±0.07 (stat.) ± 0.05 (sys.) • K*/h-= 0.060 ± 0.06 (stat.)± 0.01 (sys.) • K*/h-= 0.058 ± 0.06 (stat.) ± 0.01 (sys.) • PHOBOS, STAR, PHENIX, BRAHMS Important “thermometers”: K-/p- = p/ = Excellent agreement between the RHIC Experiments !!!

13. Statistical Thermal Models in Heavy-Ion Collisions: RHIC Phobos (submitted to PRL) B = 45±5 MeV P. Braun-Munzinger et al: hep-ph/105229 P. Braun-Munzinger,D.Magestro, K. Redlich, and J. Stachel, hep-ph/0105229 W. Florkwski, W. Broniowski, and M. Michalec, nucl-th/0106009 F. Becattini, workshop in Trento, June, 2001. N. Xu and M. Kaneta, nucl-exp/0104021 • Further hints for thermalization: • global strangeness fraction s (SPS & RHIC) ~ 1 • factor > 2 larger than in e+e- and pp collisions • this increase must reflect a difference in properties of pre-hadronic state Extreme: Hadrons in box (cascade transport model) for K: ch ~ 40 fm/c, for  ~ few fm/c

14. 250 200 early universe 150 RHIC quark-gluon plasma 100 Lattice QCD Chemical Temperature Tch [MeV] SPS AGS deconfinement chiral restauration thermal freeze-out 50 SIS hadron gas 0 neutron stars atomic nuclei 0 200 400 600 800 1000 1200 Baryonic Potential B [MeV] How Valid are Thermal Models in Heavy-Ion Collisions? • Issues: • Ratios at y=0 or 4 ? F. Becattini: s = 1 at SPS at y=0 but not for 4, different T and  • Influence of weak down corrections (experimental corrections vs. correction in model) • In medium mass-corrections: influence on result? • Change of chemical composition after hadronization? All models so far (despite small differences in the details) Give similar results: RHIC  Tch ~ 170 MeV , B = 45 MeV Compare to QCD on Lattice (ref. Karsch QM01) : Tc = 154±8 MeV (Nf=3) Tc = 173±8 MeV (Nf=2) Data + Models: strong hint but is this sufficient ?

15. Dependence from Contributions of Weak Decays J. Stachel @ Thermal Fest: Weak decay corrections: 0%, 50%, 100% 0% = data already perfectly corrected 50% = lousy job 100% = no correction Similar dependencies seen by other authors F. Beccatini: T = 168 – 205 MeV

16. ( ) ~ Ref.: I.G.Bearden et al (NA44), PRL78 2080 (1997) ( ) Ref.: H.v. Gersdorff, QM1990 proceedings p.697c Transverse Flow • Transverse momentum spectra reflect system at freeze-out. • The freeze-out temperatures do NOT tell anything about the earlier phase when equilibrium might be achieved • BUT: one necessary requirement for equilibrium is interactions between constituents  flow • Transverse flow can tell us if the preconditions for equilibration exist • A simple model: • Fit mT distributions with exp(-mT/T) • Inverse slope parameter T

17. Transverse Flow at SPS • most 1/mT dN/dmT spectra well fitted with: exp(-mT/T ) • NA44 reported (PRL78 2080 (1997) ): Tfo=0.14 GeV,<t>= 0.4 c • Why is the W an exception ? Early decoupling from the expanding hadronic medium ? Smaller cross-section?

18. STAR Preliminary 1/(2mT) d2N/dmTdy mT – m0 (GeV/c2) Transverse Flow at RHIC: Failure of Naïve Model • Slope T dependence on fit range stronger • than at SPS. • Indication of strong transverse flow but things appear to be more complex at RHIC than SPS • Using p, K,  in fit range mT-m0 < 0.4 GeV ßr (RHIC) = 0.6c Tfo (RHIC) = 0.10-0.12 GeV p & Boltzman L

19. b s 1/mt dN/dmt A Tfo R mt flow profile selected (t =s (r/Rmax)0.5) mT Distribution from Hydrodynamics Type Model Courtesy of M.Kaneta and J. Burward-Hoy s Ref. : E.Schnedermann et al, PRC48 (1993) 2462 t

20. M.Kaneta solid : used for fit - K- - K- 1/mT dN/dmT (a.u.) p p   Tth[GeV] mT - m[GeV/c2] 0 0.4 0 0.4 <r > [c] “Hydro”-Model: STAR contour plot for 95.5%CL At chi square minimum: Tth = 0.13[GeV] <r > = 0.52 [c] STAR The bend is changing with particle mass

21. “Hydro”-Model: PHENIX 5% central data Tfo ~ 104  21 MeV t ~ 0.7  0.1 < t > ~ 0.5  0.1 Systematic errors estimated ~8% in Tfo ~5% in t J. Burward-Hoy, Thermal Fest

22. Full Hydro: The H2H Model Comparison (Hydro 2 Hadrons) • Flowing hadronic fluid AND particle cascade • uses Hydrodynamics + Relativistic Quantum Molecular Dynamics (RQMD) cascade • more constrained  predictive power • no scaling of nucleons to match data • <0> ~ 10.95 GeV/fm3 • , K Tfo ~ 135 MeV <t > ~ 0.55 • nucleons ~ 120 MeV <t > ~ 0.6 D. Teaney, E. Shuryak, et. al. 5% central NOTE: includes weak decays

23. mT distributions: data and model predictions • Issues: • Real fluid dynamic: Tfo = 135 MeV • “Hydro”-like parameterization: • Tf0 = 104 – 130 MeV • flow = 0.55 c – 0.6 c • Influence of weak decays • Strong collective radial expansion at RHIC • high pressure • high rescattering rate • Thermalization likely • Other than elliptic flow, transverse flow is measurable in central collisions Note, vs 0.6 c !!!

24. Elliptic Flow: A schematic view of v2 spatial anisotropy  momentum anisotropy v2: 2nd harmonic Fourier coefficient in dN/d with respect to the reaction plane Elliptic flow observable sensitive to early evolution of system Large v2 is an indication of early thermalization Equal energy density lines P. Kolb, J. Sollfrank, and U. Heinz

25. Elliptic flow and thermalization • Large v2 is an indication of early thermalization Zhang, Gyulassy, Ko, PL B455 (1999) 45

26. Charged particle v2 versus centrality • Boxes show “initial • spatial anisotropy”e • scaled by 0.19-0.25 • (from Hydro Model) STAR, PRL 86, (2001) 402 || < 1.3 0.1 < pt < 2.0 SPS AGS RQMD • Hydro-picture in reasonable agreement with data • compatible with early equilibration

27. Charged particle and charged pion v2(pt) (minimum bias) • Hydro calculations: P. Huovinen et al. v2 proportional to pT pions almost identical to h- but … STAR

28. v2(pt) for a thermal source Simple thermal source Pasi Huovinen

29. Flow for different species (min. bias) a,b=f(r,T) r=r0+racos(2f) T135(20) 100(24) r0 .58(.03) .61(.05) ra.09(.02) .04(.01) S20.0.04(.01) STAR preliminary

30. Conclusions • Thermalization: what do we know about it ? • To answer the question of “equilibration” we need detailed models • Statistical Thermal Models work well at SPS + RHIC • Predict ratios  1 • Tch 170 MeV, B  45 MeV • Large transverse flow  rescattering in early phase • Large radial flow  rescattering • Spectra & flow well described by Hydro (QGP) • There’s more to be studied: • Balance functions (in progress) • Higher resonances to constrain thermal models further (next run) • Elliptic flow of ,  (next run) • HBT vs. reaction plane (in progress) • What did we learn ? • More than subtle hints! Lots of evidence that we observe an equilibrated system. • In my view: no evidence that the hadronic phase is equilibrated.