Dynamics of Soft Particle Production in Heavy Ion Collisions

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

2. A Briefer History of Time Statistical Mechanics Geometry Partonsaturation BjorkenHydro QCD GlauberModel Hydrodynamics Statistical/ThermalModels spectra EnergyDensity Radial flow Strangeness Elliptic flow stopping multiplicity HBT • Can we understand the early dynamics? • Is the initial state modified before freezeout? • Can simple regularities in the data teach us how to disentangle energy & geometry?

3. Question 1 Where does the entropy come from? What are the degrees of freedom ofa Au+Au collision at RHIC?

4. Energy & Geometry “Glauber Model” Nucleon-NucleonCMS Energy BinaryCollisions b sNN/2 sNN/2 Participant Short distance,Incoherent Long distance,Coherent

5. Nucleon Structure & Nuclear Collisions • With increasing energy: quarks  partons • Nuclei act as overlapping layers of nucleons  increased density “snapshot”of vacuumfluctuations Quark Model High Energy Proton High EnergyProton in aNucleus High EnergyProton Figures from H. Satz, QM2002

6. Parton Saturation • Density (thickness)  momentum scale Qs • Below Qs, 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. Saturation Phenomenology • Qs controls low-x physics: applies to HERA & RHIC • Golec-Biernat-Wusthoff energy scaling of g*p cross section • Rapidity (geometric scaling) • Centrality – Npart scaling (sources) modified by thickness • McLerran-VenugopalanMuellerKharzeev/Nardi Geometry QCD InitialFinal

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

10. Saturation vs. Spectra • Low-x g*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. Implications for Initial State • Initial state  Final State • Coherence  lower entropy than pQCD • Qs determines initial physics • Momentum, Density, Formation Time • Early formation time large energy densities PHENIX

12. 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. Question 2 • What happens between the initial state and final state? • Can a hydrodynamic description make sense? • Thermalization • Dynamics (EOS) • Observables

14. Thermal Model Calculations (Cleymans,Redlich, Braun-Munziger, Stachel,Magestro, Kaneta, Xu…) GrandCanonicalEnsemble Chemical FreezeoutTemperature Fireball Volume “StrangenessSuppression” Baryon ChemicalPotential • Excellent fit to RHIC data • Equilibration mechanism? • Conservation laws obeyed globally,not locally!

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

16. 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 expansiondN/dy ~ Gaussian Bjorken (1983): Boost Invariance dN/dy ~ const ISR data (now RHIC data) seemed to prefer Bjorken…

17. The Hydro “Machine” Lauret, Shuryak, Teaney Boost Invariant Initial Conditions Energy-MomentumConservation Baryon NumberConservation Equation ofState (EOS) Freezeout Hypersurface s(x,t) Velocity field um(x,t) Cooper-Frye Formula Ideal gas

18. Hydro Initial Conditions Glauber  Matching to final state multiplicity Heinz/Kolb (WoundedNucleons) (BinaryCollisions) Typical values: (Kolb/Heinz) (Lauret, Shuryak, Teaney) Allows study of centralitydependence of initial state

19. Particle Spectra • Centrality dependence  radial velocity • NB: e ~ T4 -> e(T=120 MeV) << e(T~165 MeV) Heinz/Kolb P. Kolb & R. Rapp Pion ‘excess’ reduced by attentionto chemical freezeout conditions

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

21. Elliptic Flow Solutions to Hydro Equations: PHOBOS data CoordinateSpace MomentumSpace Glauber relates b to e

22. Elliptic Flow Results • v2 results have differing sensitivity to EOS • Heavy particles sensitive to EOS • Less affected by thermal smearing • Current results prefer 1st order PT! R. Snellings, STAR preliminary

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

24. 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 Initial State  Final State (U.Heinz) Initial State  Final State

25. 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. Question 3 • How much does simple “scaling” behavior in the data teach us? • What drives the physics? • Energy • Geometry

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

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

29. Entropy & Chemistry • Thermodynamics mB supresses s • Increasing energy lowers mB (entropy density) PAS, Cleymans, et al AGS SPS RHIC  “Scaling” Additional energy justmakes a “bigger” system:LHC ~ RHIC

30. Strangeness Enhancement gs J. Cleymans PHENIX 1 0.8 0.6 0.4 J. Cleymans, B. Kaempfer, PAS, S. Wheaton, nucl-th/0212335 0.2 Energy: mB 0, AA is “different” 400 200 300 100 0 Npart Geometry: fraction of multiply-struck participantsdrives system towards full chemical equilibrium? NA49, E910

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

32. 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!? Bass & Muller, nucl-th/0212103 GRV-HO Net Baryon

33. 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>Rp • 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. The End

35. 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. Multiplicity Scaling STAR (PRELIMINARY) RESULTS Phobos PHENIX BRAHMS WA98 Phobos WA97/NA57 NA49 E917/866 E877 • Does the particle density act as a scale? • Elliptic flow “scales” in the same way… Z. Xu NA49 compilation Charged Particle Densityat h=0

37. Multiplicity & v2 Schaffner-Bielich et al Empirically <pT> is also a function of multiplicity & mass: Hydro or CGC?Both predict this sort of behavior NA49 v2 data from AGSRHICscales with local particle density Particles Area Challenge to hydro?