1. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Landau on the Beach: Hydrodynamics & RHIC Phenomenology Peter Steinberg Brookhaven National Laboratory 20 th Winter Workshop on Nuclear Dynamics Starfish Resort, Trelawny Beach, Jamaica March 15-20, 2004

2. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Taking the Long View Hydro is used in the transverse direction at y=0 What about the longitudinal direction (|y|>0) x y x z Longitudinal expansion?

3. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Landau-Fermi Approach In early 1950’s… Landau & Fermi considered collisions of Lorentz-contracted nucleons & nuclei

4. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Entropy Generation Two main physics assumptions: 1.Rapid and complete thermalization in Lorentz-contracted volume 2.Massless blackbody EOS Entropy from complete thermalization

5. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Landau’s Hydrodynamics Evolution of system according to ideal (isentropic, non-viscous) hydrodynamics 1+1D Evolution: Landau, Khalatnikov,Milekhin, etc. Longitudinal explosion, Limited p T

6. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Freezeout to Hadrons Freezeout when interactions stop: Thermal-Statistical Phenomenology Good guess! more like 160-170 MeV O. Barannikova’s Talk

7. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Landau’s Predictions Universal entropy formula Gaussian rapidity distributions Thermal-statistical model @ freezeout All in one paper: Landau & Bilenkij (1956)! All in one paper: Landau & Bilenkij (1956)! 1970’s: Carruthers, Cooper/Frye/Schonberg, Shuryak, Andersson, etc.

8. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 N part Scaling: A+A An under-appreciated prediction: “Since the mass density in the nucleus is about the same as the mass density of the proton, relative to its range of action, the energy density immediately after the collision remains the same as in a collision between nucleons. Since the Lorentz contraction also evidently remains unchanged, the change in entropy will be simply proportional to the volume of the nuclei, i.e. to A.” V AA (  s) PHOBOS, nucl-ex/0301017 V AA (  s) Not exactly: leading particles different Not bad. Should we expect similar dN/dy? Landau & Bilenkij:

9. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Universal Entropy (1981) Carruthers 1981

10. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Coincidence?: Hydro vs. pQCD MuellerLandau A puzzle since 1980’s: Predictions similar over a wide range in beam energy Remember, these are opposite limits ( MFP =0,  ) Carruthers 1972

11. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Coincidence?: Universal Entropy (2004) What’s up with A+A below 20 GeV?

12. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Thermal-Statistical Model Figure from P. Braun-Munziger, D. Magestro, J. Stachel e+e- & pp? (Beccatini ‘95) Low energy High energy Kaneta & Xu RHIC approaches limiting T and  B =0, same for e+e- & p+p Manninen’s Talk

13. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Total Multiplicity in A+A and e + e - ExperimentalTheoreticalAssumption! Can calculate entropy density in thermal models V ee (  s) V AA V AA (  s)

14. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 A+A vs. e + e - below 20 GeV Qualititative agreement J. Cleymans & M. Stankiewicz Honours Thesis, University of Cape Town

15. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Is Entropy Really Kinky? Gazdzicki et al do not account for Landau’s omission of baryochemical potential Also, mesons are only part of entropy (<1/2 at low energy)! Blume’s Talk

16. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Feynman/Bjorken vs. Landau Assume strong interaction is short- range (Feynman) Plateau assumed to be characteristic of strong interactions (Bjorken) Assume whole system starts out strongly coupled (long-range) Gaussians “emerge” from hydro equations Energy Energy y-y T y

17. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Bjorken or Landau @ ISR? Carruthers & Duong-van 1973 ISR 53 GeV PISA/SUNYSB 1972 (unpub.) “duck or rabbit” A ever-changing, observer-dependent conclusion…

18. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Compilation of h+p data Carruthers & Duong-Van (1973) Gaussian fits to rapidity distributions

19. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 dN/d  for Au+Au @ RHIC dN/d     19.6 GeV 130 GeV200 GeV PHOBOS PRL91 (2003) Emergence of a rapidity plateau? Revenge of Feynman/Bjorken? NB:  has a “dip” from kinematics! Busza’s talk

20. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 dN/dy for A+A @ AGS  RHIC D. Ouerdane, QM04 G. Roland, QM04 Landau gets shape of dN/dy along with total multiplicity

21. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Coincidence?: Limiting Fragmentation Limiting fragmentation (x scaling) somehow “built-in” for large x So is “scaling violation” at low x! Cooper & Schonberg 1973 y-y T

22. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Coincidence?: G(x) at low-x Is the relevance of Landau just the manifestation of the measured low-x gluon structure of nucleon? Similar exponent ~ ¼ KLN “tracks” Landau Insight or coincidence? KLN, =.3 Landau Hydro Normalized here

23. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Pure phenomenology: Carruthers & Duong-Van noticed that transverse spectra of  0 @ ISR follow Gaussian in rapidity No explanation, but perhaps symmetry with longitudinal Gaussian Transverse Gaussians Carruthers & Duong-van (PRL 1973)

24. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Coincidence?: y T @ RHIC One parameter fit to STAR & PHENIX pp data L = 0.570±.001 (STAR) L = 0.541±.001 (PHENIX) Power-law has two: Notes Star is inclusive charged PHENIX RAA relatively flat with p T At the very least, an efficient description of existing data PHENIX d   0 STAR dN h + h - Data/“ Theory”

25. Peter Steinberg 20 th Winter Workshop, Jamaica 2004Conclusions Landau hydro may be relevant to RHIC phenomena Boost invariance may not be Coincidences or Connections? #1 Gaussian dN/dy observed #2 Universal multiplicity formula vs. pQCD #2a Hydro exponent vs. Low-x Gluon Structure #3 “Limiting fragmentation” vs. scaling violations #4 Gaussian dN/dy T works for p+p (#5 Shifted Gaussians in p+A) Big Question: How can system thermalize so fast? Any conflict with known physics (e.g. QM) Relevance to QGP? Is Landau’s picture some kind of limit relevant to QCD?

26. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Landau & the QGP Even if Landau is somehow talking about the QGP, where are the quarks & gluon DOFs?

27. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Thoughts for the Beach Flow puzzle HBT puzzle Could Landau picture help? (3+1D, no boost-invariant I.C….)

28. Peter Steinberg 20 th Winter Workshop, Jamaica 2004

29. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Coincidence?: Brahms dN/dy This is compared to a prediction from 1953 Data can also be fit to a gaussian D. Ouerdane, BRAHMS QM04

30. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Radial Flow RHIC Data & Calculations by U. Heinz / P. Kolb   =.6 c We already accept hydro as a part of life at midrapidity Largest particle density  Thermalization

31. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Landau on p+A A somewhat complicated argument, based on propagation of shock wave through nucleus Predicted approximate N part scaling for not-so-thick nuclei ( <4) l d

32. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Participant Scaling in d+Au Au+Au nucl-ex/0301017 d+Au & p+p preliminary PHOBOS 200 GeV Difference explained by leading particle effect

33. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Mysteries in p(d)+A? nucl-ex/0311009 N part scaling seen in d+Au at RHIC Why does the dN/d  look asymmetric? Stopping? Cascading?

34. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Local Rapidity Shift The CMS of the whole ( +1) nucleon system would be the natural one if everything thermalizes early (a common assumption in hydro calcs) This would “shift” the gaussian relative to y=0. (Carruthers 1972 discussed “shifts” for  +p,  +p) However, not easy to reconcile with N part scaling. Difficult to conserve energy AND momentum

35. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Coincidence?: Shifted Gaussians in p+A? Raw dN/dy dN/dy N part / 2 dN/dy’ NA5 DeMarzo et al. (1984) Prediction Fit Normalized

36. Peter Steinberg 20 th Winter Workshop, Jamaica 2004 Shifted Gaussians @ RHIC? Shift PYTHIA dN/dy by  y = -1 Scale up by N part /2 Recalculate dN/d    PHOBOS d+Au & PYTHIA p+p have similar dN/dy shapes   Must run afoul of energy conservation at large y Let’s be naïve and see what shifted dN/dy does to dN/d 