1. Peter Steinberg CIPANP 2003 Dynamics of Soft Particle Production in Heavy Ion Collisions Peter Steinberg Brookhaven National Laboratory Visiting Fulbright Professor at University of Cape Town, South Africa CIPANP May 19-24 2003 New York City, NY USA

2. Peter Steinberg CIPANP 2003 1.Can we understand the early dynamics? 2.Is the initial state modified before freezeout? 3.Can simple regularities in the data teach us how to disentangle energy & geometry? Statistical Mechanic s Hydrodynamic s Geometry QCD Parton saturation Bjorken Hydro Glauber Model Statistical/Therma l Models stoppingmultiplicity spectra Radial flow Elliptic flow Strangeness HBT Energy Density A Briefer History of Time

3. Peter Steinberg CIPANP 2003 Question 1 Where does the entropy come from? What are the degrees of freedom of a Au+Au collision at RHIC?

4. Peter Steinberg CIPANP 2003 Energy & Geometry b Participant Binary Collisions “Glauber Model”  s NN /2 Nucleon- Nucleon CMS Energy Short distance, Incoherent Long distance, Coherent

5. Peter Steinberg CIPANP 2003 Nucleon Structure & Nuclear Collisions With increasing energy: quarks  partons Nuclei act as overlapping layers of nucleons  increased density Proton Quark ModelHigh Energy “snapshot” of vacuum fluctuations High Energy Proton High Energy Proton in a Nucleus Figures from H. Satz, QM2002

6. Peter Steinberg CIPANP 2003 Parton Saturation Density (thickness)  momentum scale Q s Below Q s, target is “black”, cross section saturates Theoretical approach: “Color Glass Condensate” Weak coupling  Strong fields! “Packing Factor” Lipatov, Levin, Ryskin, McLerran, Venugopalan, Mueller, Iancu, Jalilian-Marian, Dumitru, etc.

7. Peter Steinberg CIPANP 2003 Saturation Phenomenology Q s controls low-x physics: applies to HERA & RHIC Golec-Biernat-Wusthoff energy scaling of   p cross section Rapidity (geometric scaling) Centrality – N part scaling (sources) modified by thickness McLerran-Venugopalan  Mueller  Kharzeev/Nardi GeometryQCD Initial  Final

8. Peter Steinberg CIPANP 2003 LPHD: How do we “see” saturation? Saturation calculations depend on hypothesis: “Local parton hadron duality” tested in e+e- Dokshitzer, Mueller, Khoze, Ochs, etc. pQCD mysteriously “works” at low p Hadronization is “soft” No modification of parton spectrum and yield

9. Peter Steinberg CIPANP 2003 Initial state  LPHD  Final state! limiting fragmentation (1-x) 4 Shape seems be found in pp (& e+e-) as well… Saturation vs. Multiplicity Data Kharzeev, Levin, Nardi “Quark counting” at high-x (Phenomenology!) PHOBOS 200 GeV 130 GeV 19.6 GeV 

10. Peter Steinberg CIPANP 2003 Saturation vs. Spectra Low-x  * p physics controlled by dimensionless quantity RHIC data shows evidence of simliar “geometric scaling”: Further evidence that one scale may control much of the observed physics Schaffner-Bielich, McLerran, Venugopalan, Kharzeev

11. Peter Steinberg CIPANP 2003 Implications for Initial State Initial state  Final State Coherence  lower entropy than pQCD Q s determines initial physics Momentum, Density, Formation Time Early formation time  large energy densities PHENIX

12. Peter Steinberg CIPANP 2003 Critical remarks Saturation approach is appealing Unifies many features of data with one scale Trying to reconcile pQCD & unitarity Qualitative connection to many aspects of data However, not a complete physical picture Phenomenological factors need justification LPHD is still a hypothesis! – needs testing

13. Peter Steinberg CIPANP 2003 Question 2 What happens between the initial state and final state? Can a hydrodynamic description make sense? Thermalization Dynamics (EOS) Observables

14. Peter Steinberg CIPANP 2003 Thermal Model Calculations “Strangeness Suppression” (Cleymans, Redlich, Braun- Munziger, Stachel, Magestro, Kaneta, Xu…) Grand Canonical Ensemble Chemical Freezeout Temperature Baryon Chemical Potential Fireball Volume Excellent fit to RHIC data Equilibration mechanism? Conservation laws obeyed globally, not locally!

15. Peter Steinberg CIPANP 2003 Thermal Model Systematics A+A looks like thermalized hadron gas So do elementary systems  not a hadronic effect Consensus: “born into” equilibrium well before freezeout Kaneta & Xu LEP Cleymans & Redlich

16. Peter Steinberg CIPANP 2003 Hydrodynamic Approach Landau (1953) Strongly interacting degrees of freedom Short mean-free path Specify initial conditions, and then conserve: Energy-momentum & “charges” (e.g. baryon #) Two basic approaches developed: Landau (1953): Complete Stopping 1D  3D expansion dN/dy ~ Gaussian Bjorken (1983): Boost Invariance dN/dy ~ const ISR data (now RHIC data) seemed to prefer Bjorken…

17. Peter Steinberg CIPANP 2003 The Hydro “Machine” Energy-Momentum Conservation Baryon Number Conservation Equation of State (EOS) Freezeout Hypersurface  (x,t) Velocity field u  (x,t) Cooper-Frye Formula Boost Invariant Initial Conditions Ideal gas Lauret, Shuryak, Teaney

18. Peter Steinberg CIPANP 2003 Hydro Initial Conditions Glauber  Matching to final state multiplicity (Kolb/Heinz) Heinz/Kolb (Lauret, Shuryak, Teaney) Typical values: Allows study of centrality dependence of initial state (Wounded Nucleons) (Binary Collisions)

19. Peter Steinberg CIPANP 2003 Particle Spectra Centrality dependence  radial velocity NB:  ~ T 4 ->  (T=120 MeV) <<  (T~165 MeV) Pion ‘excess’ reduced by attention to chemical freezeout conditions P. Kolb & R. Rapp Heinz/Kolb

20. Peter Steinberg CIPANP 2003 Equation of State EOS encodes all of the bulk dynamics 1 st order phase transition (a la lattice) leads to softening of EOS: c s  0 (Landau 1953: ideal, massless) B (resonance gas, much softer) (QGP) (Speed of sound) Heinz/Kolb

21. Peter Steinberg CIPANP 2003 Elliptic Flow PHOBOS data Momentum Space Glauber relates b to  Solutions to Hydro Equations: Coordinate Space

22. Peter Steinberg CIPANP 2003 v 2 results have differing sensitivity to EOS Heavy particles sensitive to EOS Less affected by thermal smearing Current results prefer 1 st order PT! Elliptic Flow Results R. Snellings, STAR preliminary

23. Peter Steinberg CIPANP 2003 Trouble Down the Hill? Trouble for hydro in the longitudinal direction HBT: R long has problems (M. Lisa) Elliptic flow away from 90 o (T. Hirano) Where is the problem: initial state or freezeout? 3D modeling? Viscosity (Teaney)? Is boost invariance justified, even at y=0? T. Hirano Heinz/Kolb

24. Peter Steinberg CIPANP 2003 Hydro vs. Saturation If hydro is truly applicable then cf. Saturation + LPHD (parton-hadron duality) Interesting that numbers from saturation are not incompatible w/ hydro! “Bottom up” (BMSS), Eskola, et al (U.Heinz) Initial State  Final State Initial State  Final State

25. Peter Steinberg CIPANP 2003 Critical Remarks Ambiguities: Initial state Need additional input beyond 2D Glauber Which EOS is required Consistency with broad range of data Freezeout conditions Many variations, incl. “Blast wave” (M. Lisa) Assumption of boost-invariance Hiding important dynamics? Systematic studies are crucial!

26. Peter Steinberg CIPANP 2003 Question 3 How much does simple “scaling” behavior in the data teach us? What drives the physics? Energy Geometry

27. Peter Steinberg CIPANP 2003 Simple Behavior of N ch PHOBOS observes that e+e- sets multiplicity scale The rest is linear participant scaling (soft) Simple argument: reduced leading particle effect PHOBOS, QM2002  N ch  / e + e - fit Is this “scaling”? Au+Au e + +e - p+p

28. Peter Steinberg CIPANP 2003 Scaling of Thermal Parameters Thermal parameters: rapid change  “saturation” JC, PBM, KR, etc.

29. Peter Steinberg CIPANP 2003 Entropy & Chemistry Thermodynamics   B supresses s Increasing energy lowers  B PAS, Cleymans, et al AGSSPSRHIC  “Scaling” Additional energy just makes a “bigger” system: LHC ~ RHIC (entropy density)

30. Peter Steinberg CIPANP 2003 Strangeness Enhancement ss 1 0.6 0.4 0.2 0.8 0 100 200300 400 N part J. Cleymans, B. Kaempfer, PAS, S. Wheaton, nucl-th/0212335 PHENIX J. Cleymans Energy:  B  0, AA is “different” Geometry: fraction of multiply-struck participants drives system towards full chemical equilibrium? NA49, E910

31. Peter Steinberg CIPANP 2003 What have we learned? RHIC provides extensive systematics in energy, geometry (& rapidity)! Which variables control the physics! Energy  Larger multiplicity, “Saturation” as  B  0 Nuclear geometry  multiple collisions Leading particles attenuated (e+e-) Chemical equilibrium (strangeness) Caveat: Beware of coincidences! Strive for uniqueness, or broad applicability

32. Peter Steinberg CIPANP 2003 What is “stopping”? None of this was predicted  we don’t understand some basic features of the initial state! Transfer of energy: longitudinal  transverse 20 years after Busza&Goldhaber: what is stopping? dE/dx? Or “destroying” nucleons completely!? GRV-HO Net Baryon Bass & Muller, nucl-th/0212103

33. Peter Steinberg CIPANP 2003 Status of Soft Dynamics Saturation is a reasonable picture of initial state One scale to rule them all! Phenomenology  many assumptions need justification Hydro addresses dynamics after initial state Final state  Information moving beyond R>R p Results sensitive to arbitrary initial conditions, EOS, and final state! Systematics are crucial. Empirical scaling is a reality check Chemistry matters! Nuclear geometry matters! Beware of accidents: distinguish cause from correlation Global dynamics matter! Strongly interacting, conservative system Longitudinal dynamics may be very important Be careful about what we factorize away!

34. Peter Steinberg CIPANP 2003

35. Peter Steinberg CIPANP 2003 Scope of this talk Dynamics With increasing time, energy scales decrease Must consider range of dynamical scenarios since the soft processes are omnipresent! Soft particle production Bulk (99%) of produced particles These will be the “freezeout” of the QGP Momentum scales are < 2 GeV Heavy Ion Collisions d+A data is just becoming available Will be an important contribution

36. Peter Steinberg CIPANP 2003 Multiplicity Scaling WA98 WA97/NA57 Phobos NA49 E917/866 STAR (PRELIMINARY) RESULTS E877 PHENIX BRAHMS Phobos Does the particle density act as a scale? Elliptic flow “scales” in the same way… Z. Xu NA49 compilation Charged Particle Density at  =0

37. Peter Steinberg CIPANP 2003 Multiplicity & v 2 Empirically is also a function of multiplicity & mass: Hydro or CGC? Both predict this sort of behavior Schaffner-Bielich et al Particles Area v 2 data from AGS  RHIC scales with local particle density Challenge to hydro? NA49