1. Peter Steinberg Bulk Dynamics in Heavy Ion Collisions Peter Steinberg Brookhaven National Laboratory INPC2004 June 27-July 2, 2004 Göteborg, Sweden

2. Peter Steinberg Strongly-Interacting Matter On the lattice, only reach 75-80% of Stefan-Boltzmann limit In context of N=4 SUSY QCD this is the signature of a strongly-interacting plasma (Klebanov et al) Shift of paradigm: QCD does not predict weakly interacting QGP for accessible T Have we discovered strongly-interacting matter in A+A collisions? (RBRC Workshop May 14-15, 2004 & RHIC Whitepapers)

3. Peter Steinberg The Bulk of Particles: dN/d  Ñ“Bulk Dynamics” is the comprehensive study of particle production in A+A Energy Centrality Rapidity dN/d    19.6 GeV 130 GeV200 GeV Most Central  PHOBOS Participant Spectator

4. Peter Steinberg The Bulk of Particles: dN/dp T STAR PHOBOS

5. Peter Steinberg The Dynamical Model Approach Parton distributions Nuclear Geometry Nuclear shadowing Parton production & reinteraction Chemical Freezeout & Quark Recombination Jet Fragmentation Functions Hadron Rescattering Thermal Freezeout & Hadron decays Independent stages: Bulk physics integrates time history 0 fm/c 2 fm/c 7 fm/c >7 fm/c

6. Peter Steinberg Dynamical Models vs. Data HIJING Hard + Soft Hadron Transport RHIC Data pp Data Particle Density near y=0 Large variation in predictions Compilation by V. Topor-Pop

7. Peter Steinberg The Big Surprise Bulk observables are “simple” (but not “trivial”) …just not necessarily at  =0!

8. Peter Steinberg Participant Scaling N ch ~ N part /2  Long-range rapidity correlations R. Nouicer, QM2004 PHOBOS PRL91 (2003)

9. Peter Steinberg “Limiting Fragmentation” in A+A Yield depends on  ’  -y beam ~ln(x F ) Logarithmic increase at  =0  centrality-dependent “universal curve” peripheral central PHOBOS PRL91 (2003)

10. Peter Steinberg Difference between p+p vs. A+A In a head-on p+p collision… …half of energy emerges as “leading particles” flat in x F In a typical A+A collision… …“leading particles” can be struck again! May make sense to consider A+A as having most of available energy for particle production Batista & Covolan (1998) NA49

11. Peter Steinberg Universality of Total Multiplicity A+A per participant pair ~ p+p @  s/2 ~ e+e- @  s A real surprise at RHIC – not predicted by SPS extrapolations LEP 200 GeV

12. Peter Steinberg Essential Features of A+A 1.N part scaling Factorization of Energy & Geometry 2.Universal multiplicity / N part /2 Connections to e+e- & p+p 3.“Limiting fragmentation” How can we understand this in a simple way? Dynamical models have many independent stages CGC captures several essential physics features (L. McLerran, Monday)

13. Peter Steinberg Hydrodynamic Evolution Strongly-interacting 6 Li released from an asymmetric trap O’Hara, et al, Science 298 2179 (2002) A new canonical image for heavy-ion physics Hydro useful for strongly interacting matter: buildup of pressure gradients Does it work for A+A?…

14. Peter Steinberg Longitudinal  Transverse z y x y pzpz pTpT Longitudinal dynamics provide initial conditions for transverse dynamics

15. Peter Steinberg Longitudinal Dynamics 1.Early thermalization 2.Blackbody EOS 3.Multiplicity formula: 4.N part scaling 5.Gaussian dN/dy z y Landau Extreme physics scenario: Assume matter stops briefly and explodes longitudinally Landau, Milekhin, Khalatnikov, Cooper/Frye, Carruthers, Andersson, Shuryak, Prakash, Venugopalan…

16. Peter Steinberg Universal Multiplicity Formula N ch =2.2s 1/4 PHOBOS nucl-ex/0301017

17. Peter Steinberg dN/dy: Longitudinal Dynamics M. Murray, BRAHMS No extended “boost invariant” plateau. dN/dy is consequence of hydrodynamic expansion of Lorentz contracted early stage = DYNAMICS

18. Peter Steinberg Limiting Fragmentation y-y T Naïve use of Landau expressions give approximate scaling in y’ P. Steinberg, WWND2004

19. Peter Steinberg Transverse Dynamics 1.Assume boost-invariance 2.dN/dy is initial condition 3.Non-trivial EOS Ñ1 st order, 2 nd order… 4.Pressure gradients ÑRadial & elliptic flow 5.Cooper-Frye Freezeout Heinz, Kolb, Shuryak, Teaney, Lauret, Huovinen,Ollitrault, et al… Heinz, Kolb

20. Peter Steinberg Radial Flow A clear mass effect on top of “thermal” spectrum Kolb & Rapp 20% normalization at 2 GeV Subm. to PRL nucl-ex/0401006 Au+Au 200 GeV Kolb/Rapp

21. Peter Steinberg Elliptic Flow vs. Geometry Hydrodynamic limit STAR PHOBOS Hydrodynamic limit STAR PHOBOS Compilation and Figure from M. Kaneta Observation of “elliptic flow” Reasonable agreement with hydro in more central events

22. Peter Steinberg p T Dependence “fine structure” (mass dependence) sensitive to EOS  Qualitatively described by hydro (and hydro-inspired) fits STAR

23. Peter Steinberg Pseudorapidity Dependence “Limiting fragmentation” works for v 2 (  ) (almost too well!) Further indication of no boost-invariant plateau Challenge even for 3D hydro calculations, even if “rule” looks simple! T. Hirano - CGC+Hydro T. Hirano, Nov ‘03 PHOBOS nucl-ex/0406019 19.6, 62,130,200 GeV PHOBOS 130 GeV

24. Peter Steinberg Hydro approach appears to be warranted by a wide range of data (but no single model gets everything right!) Joining longitudinal & tranverse stages is not well-defined at present (fit parameter in boost-invariant codes) Serious conceptual issues regarding relevance of hydro to small systems…

25. Peter Steinberg More similarities: AA & e+e- Similar “longitudinal dynamics”? Similar “energy density”?

26. Peter Steinberg Limiting Fragmentation DELPHI PLB 459 (1999) p+p e+e-e+e- Generic feature of energy dependence of multiparticle production

27. Peter Steinberg Similar Freezeout Properties e+e-e+e- A+A From Braun-Munzinger, Stachel, Redlich (2003) Becattini (1995) Relative particle yields described using thermal-statistical models in both e+e- and A+A

28. Peter Steinberg Radial Expansion in p+p? R. Witt, STAR Collaboration Is p+p qualitatively or just quantitatively different than A+A?

29. Peter Steinberg Radial Expansion in p+p? HBT radii have similar relative momentum dependence: Similar “expansion dynamics”? R out / R out (pp) R side / R side (pp) R long / R long (pp) STAR T. Gutierrez, QM04

30. Peter Steinberg Soft Physics = Difficult Physics? Dynamical models have many independent stages. Data seems to suggest global constraints.

31. Peter Steinberg Incoming nuclei: N part, Lorentz contraction Rapid thermalization: Entropy production 1D expansion stage: Rapidity distributions 3D expansion stage: Elliptic & radial flow Freezeout into hadrons: Statistical phenomenology t = 0.0 fm/c t = 0.1 fm/c t < 0.6 fm/c t = 0.6 fm/c t = 6-10 fm/c Soft Physics = Hydrodynamics? System may be strongly interacting throughout (conserving entropy for the full evolution!)

32. Peter Steinberg Paths to Progress ÑHow do we understand differences and similarities between A+A and p+p, e+e-? How does hydro connect with Color Glass Condensate? ÑHow could the system thermalize so rapidly? Which degrees of freedom thermalize and when? Partons, hadrons, or something else (G. Brown)? ÑHow can we integrate the longitudinal and transverse physics? For now, study systematics of initial state, EOS, final state Ultimately, need 3D hydrodynamic calculations starting at the earliest times  minimize # of parameters! ÑData over a broad rapidity range with PID is essential Soft physics is global physics: y = 0 may not be special Baryon dynamics is a crucial issue to resolve

33. Peter Steinberg Extra Slides

34. Peter Steinberg Available Energy BRAHMS data suggests only 75% “available energy” Contradiction? Possibly. SLD: Leading K ± in ss jets ~1.5 units from end of rapidity range Do we consider this to NOT be part of the jet?

35. Peter Steinberg Energy Density Energy density related to energy created near  =0

36. Peter Steinberg Total Multiplicity vs. Models

37. Peter Steinberg Centrality Dependence 200/19.6 200/130 Changes in one rapidity region are correlated with particles in distant regions Evolution of particle density with centrality is energy-independent

38. Peter Steinberg Importance of Viscosity Viscous effects do not substantially modify ideal hydro Teaney

39. Peter Steinberg Marek’s Kink Are pions the only carriers of entropy? PHOBOS “approach”: Trade in p+p for e+e- Baryon density affects global particle production P. Steinberg, WW04

40. Peter Steinberg RHIC Experiments (to scale) Two BIG Spectrometers: 100’s-1000’s particles event Particle ID, photons & leptons Two small detectors: Forward particles, Particle multiplicity PHENIX STAR BRAHMS PHOBOS

41. Peter Steinberg dN/dy Gaussians & Widths E895 3.0 GeV Au+Au BRAHMS prel. NA49 3.6 GeV Au+Au 4.1 GeV Au+Au 8.8 GeV Pb+Pb 17.3 GeV Pb+Pb 200 GeV Au+Au In central events, pion rapidity distributions are Gaussian! No boost invariance in any region of phase space

42. Peter Steinberg Energy & Geometry “Factorize” 62 GeV 200 GeV

43. Peter Steinberg What Controls v 2 ? Particle density appears to be a control variable Is there really a “hydro limit”? NA49 Phys.Rev. C68 (2003) 034903