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Landau Hydrodynamics & RHIC Phenomenology

Landau Hydrodynamics & RHIC Phenomenology. Peter Steinberg Brookhaven National Laboratory Workshop on Collective Flow & QGP Properties November 17-19, 2003. Radial Flow. RHIC Data & Calculations by U. Heinz / P. Kolb. b T =.6c. A different perspective.

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Landau Hydrodynamics & RHIC Phenomenology

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  1. Landau Hydrodynamics &RHIC Phenomenology Peter SteinbergBrookhaven National Laboratory Workshop on Collective Flow & QGP Properties November 17-19, 2003

  2. Radial Flow RHIC Data & Calculations by U. Heinz / P. Kolb bT=.6c

  3. A different perspective • We’re used to this in the transverse direction • What about the longitudinal direction? Clearly not isotropic!

  4. Landau Physical Picture Incominghadrons ornuclei Rapid Thermalization Entropy productionPressure gradient Full stopping R d Longitudinalexplosion RapidityDistributions

  5. Entropy Production • Fermi’s argument: If we assume the system is a perfect blackbody but system is Lorentz-contracted

  6. “Landau Hydro” • Source-free 3D hydro equations • Massless EOS • No scale in the problem (scale invariance) • Only from boundary conditions (Carruthers) • Initial geometry, freezeout temperature T~mp LandauBilenkijMilekhin ShuryakCooper Frye SchonbergCarruthers Andersson … Energy-MomentumConservation Equation ofState (EOS)

  7. Entropy from EOS Cooper, Frye, Schonberg 1975 N(s) depends on EOS

  8. The “Landau Solution” • Many authors refined original ideas • This is how things ended up by early 1980’s • Universal multiplicity formula • Gaussian Rapidity Distributions • Thermal pT spectra

  9. Universality in 1981 Carruthers 1981

  10. Landau vs. Bjorken • Landau is not what we expected for RHIC • Expected Bjorken to simplify things @ 900 • “very reasonable that for nucleus-nucleus collisions the initial conditions for fluid of quanta produced between the receding pancakes are the same as existed in any other frame” • For Landau, y=0 not special • Most of the energy goes forward • Correctness of initial conditions must be based on data • Apparently led to many disagreements in 70’s

  11. Bjorken or Landau @ ISR? Boost invariant Pseudorapidty Near mid-h Gaussian Rapidity Look everywhere “duck orrabbit” Carruthers & Duong-van 1973 ISR 53 GeV PISA/SUNYSB 1972 (unpub.)

  12. Connections vs. Coincidences

  13. PHOBOS dN/dh • These plots are interpreted as the emergence of the central plateau with increasing collision energy 130 GeV 200 GeV 19.6 GeV dN/dh Npart h h h

  14. Coincidence #1: BRAHMS dN/dy BRAHMS showsno plateau BRAHMS Preliminary 2003

  15. Limiting Fragmentation PHOBOS Au+Au 200 GeV 130 GeV 19.6 GeV h = h - ybeam Seen generically in manysystems (AA, pp…)

  16. Coincidence #2 Limiting fragmentation (x scaling) somehow “built-in” Cooper & Schonberg 1973

  17. CGC Calculations KLN: Final state from 21 gluon scattering Overall scale Jacobian Quark counting Kharzeev, Levin, Nardi (2001) (LPHD) Energy, Rapidity, Centrality

  18. Coincidence #3 Compare dN/dy Normalized here KLN, l=.3 Landau Hydro “Default” KLN parameters(normalize @ 200 GeV peak) Scale in similar fashionboth height & width This was a surprise. Of course different KLNparameters can make theagreement worse

  19. Landau & The QGP Landau’s physics is still used in relevant physics arguments Gazdzicki et al (NA49) Massless EOS Chemical potential = 0 “Entropy”  pions ~ s1/4 Lots of features vs. pp Pion suppression Crossover Enhancement! Is this evidence of a phase transition?

  20. Some Issues Landau left out mB (mp = 0 is OK)OK for pp, not AA All particles contribute to the entropy Thermal models determine all species given T, mB Landau & Bilenkij

  21. Comparison with e+e- (Mueller 1983) PHOBOS Relative to p+p, NA49 featuresRelative to e+e-, different story

  22. Baryon Density & Entropy PAS, Cleymans, et al AGS SPS RHIC PAS, Work in progress Fix pp vs. AA by removingenergy of leading particles Can use thermal modelapproach to “fix” A+A: Predictable decreasein entropy densityfrom baryon numberconservation No more features

  23. Historical Interlude • Landau (1953) considered pp, pA, AA • Cooper & Frye (1973) tried e+e- • More compact initial state (R~1/s) • Initial expectations 3+1D, jets  1+1D! • In this context, similar multiplicities given similar energies not crazy • However, many competing models on the market. • Parton model / QCD eventually achieved descriptive power in many details.

  24. Coincidence #4: Landau vs. Mueller Landau “better” atlow energies Landau MLLA QCD better athigher energies(esp. including pp@s/2) Difference increasesdramatically athigher energies (LHC day-1 important) Oddity: slower increasefrom pQCD is like

  25. Does this make sense? • These comparisons ask more questions than they answer • Is e+e- “thermal”? • Why is pQCD ~ blackbody formula? • Are leading particles relevant? • A+A looks “local” (Npart scaling) • Little work on this for 30 years • Coincidence #4: Is there a deep theoretical connection between pQCD and hydro? • Hard processes should be immune…

  26. Transverse Expansion? Carruthers & Minh Noticed that spectrum of high-pTp0 described by Coincidence #5, is the transverse spectrum also gaussian in rapidity? Carruthers conjecture Let’s look at higher energy, higher pT Carruthers & Duong-van (PRL 1973)

  27. Coincidence #5: RHIC pp Data One parameter fit to STAR & PHENIX pp data L = 0.570±.001 (STAR) L = 0.541±.001 (PHENIX) Power-law has two: Not sure if or how this formula works with A+A Mass dependence of yT PHENIX dsp0 STAR dN h+h-

  28. Conclusions • Landau’s concepts & results appear to be relevant to RHIC phenomena • Why do we hold on to boost invariance? • Coincidences or Connections? • #1 Gaussian dN/dy, widths • #2 Limiting fragmentation built-in • #3 Similar evolution in Landau & KLN • #4 Universal multiplicity formula & QCD • #5 Gaussian dN/dyT spectra in pp • Serious issue: connection to QCD? • What are the relevant degrees of freedom that thermalize? • Still: with few input ingredients, unified description of many facts

  29. Comments • “A true heresy should arise in the context of an established faith.” (Carruthers 1973) • Does collective-variable approach contrast with QCD? • Does Landau hydro conflict with Bjorken hydro? • Interesting issues in 1973 still sound interesting! • Real solution to 3+1D. What are the “right” initial conditions? • Angular momentum for non-zero impact parameter? Spectators and leading particles? • Incorporating conserved quantities (baryon, charge) • How do we understand hydro microscopically? • “Criteria for the replacement of a field theory by its classical hydrodynamical analogue” • Turbulence, viscosity, heat conduction, surface tension… • “Relation of Gaussian dN/dy to central limit theorem or the random walk problem”

  30. “Proceedings”:Landau Hydrodynamics &RHIC Phenomenology Peter SteinbergBrookhaven National Laboratory Workshop on Collective Flow & QGP Properties November 17-19, 2003

  31. The “Landau Solution” • Many authors refined original ideas • This is how things ended up by early 1980’s • Universal Entropy • Gaussian Rapidity Distributions • Thermal pT spectra Incominghadrons ornuclei R d Full stopping Longitudinalexplosion

  32. Coincidence #1: BRAHMS dN/dy BRAHMS Preliminary 2003

  33. Coincidence #2: Scaling Limiting fragmentation (x scaling) somehow “built-in” Cooper & Schonberg 1973

  34. Coincidence #3: KLN Compare dN/dy Normalized here KLN, l=.3 Landau Hydro “Default” KLN parameters(normalize @ 200 GeV peak) Scale in similar fashionboth height & width This was a surprise. Of course different KLNparameters can make theagreement worse

  35. Coincidence #4: Landau vs. Mueller Landau “better” atlow energies Landau MLLA QCD better athigher energies(esp. including pp@s/2) Difference increasesdramatically athigher energies (LHC day-1 important) Oddity: slower increasefrom pQCD is like

  36. Coincidence #5: RHIC pp Data One parameter fit to STAR & PHENIX pp data L = 0.570±.001 (STAR) L = 0.541±.001 (PHENIX) Power-law has two: Not sure if or how this formula works with A+A Mass dependence of yT PHENIX dsp0 STAR dN h+h-

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