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Peter SteinbergBNL/RIKEN Flow Workshop Landau Hydrodynamics & RHIC Phenomenology Peter Steinberg Brookhaven National Laboratory Workshop on Collective Flow & QGP Properties November 17-19, 2003

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Peter SteinbergBNL/RIKEN Flow Workshop Radial Flow RHIC Data & Calculations by U. Heinz / P. Kolb =.6 c

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Peter SteinbergBNL/RIKEN Flow Workshop A different perspective We’re used to this in the transverse direction What about the longitudinal direction? Clearly not isotropic!

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Peter SteinbergBNL/RIKEN Flow Workshop Landau Physical Picture Incoming hadrons or nuclei Full stopping Longitudinal explosion Rapid Thermalization Entropy production Pressure gradient R Rapidity Distributions

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Peter SteinbergBNL/RIKEN Flow Workshop Entropy Production Fermi’s argument: If we assume the system is a perfect blackbody but system is Lorentz-contracted

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Peter SteinbergBNL/RIKEN Flow Workshop “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~m Energy-Momentum Conservation Equation of State (EOS) Landau Bilenkij Milekhin Shuryak Cooper Frye Schonberg Carruthers Andersson …

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Peter SteinbergBNL/RIKEN Flow Workshop Entropy from EOS Cooper, Frye, Schonberg 1975 N(s) depends on EOS

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Peter SteinbergBNL/RIKEN Flow Workshop 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 p T spectra

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Peter SteinbergBNL/RIKEN Flow Workshop Universality in 1981 Carruthers 1981

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Peter SteinbergBNL/RIKEN Flow Workshop Landau vs. Bjorken Landau is not what we expected for RHIC Expected Bjorken to simplify things @ 90 0 “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

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Peter SteinbergBNL/RIKEN Flow Workshop Bjorken or Landau @ ISR? Boost invariant Pseudorapidty Near mid- Gaussian Rapidity Look everywhere Carruthers & Duong-van 1973 ISR 53 GeV PISA/SUNYSB 1972 (unpub.) “duck or rabbit”

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Peter SteinbergBNL/RIKEN Flow Workshop Connections vs. Coincidences

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Peter SteinbergBNL/RIKEN Flow Workshop dN/d 19.6 GeV 130 GeV200 GeV N part PHOBOS dN/dh These plots are interpreted as the emergence of the central plateau with increasing collision energy

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Peter SteinbergBNL/RIKEN Flow Workshop Coincidence #1: BRAHMS dN/dy BRAHMS Preliminary 2003 BRAHMS shows no plateau

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Peter SteinbergBNL/RIKEN Flow Workshop = - y beam PHOBOS Au+Au 19.6 GeV 130 GeV 200 GeV Limiting Fragmentation Seen generically in many systems (AA, pp…)

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Peter SteinbergBNL/RIKEN Flow Workshop Coincidence #2 Limiting fragmentation (x scaling) somehow “built-in” Cooper & Schonberg 1973

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Peter SteinbergBNL/RIKEN Flow Workshop CGC Calculations KLN: Final state from 2 1 gluon scattering Overall scale Jacobian Quark counting (LPHD) Energy, Rapidity, Centrality Kharzeev, Levin, Nardi (2001)

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Peter SteinbergBNL/RIKEN Flow Workshop Coincidence #3 KLN, =.3 Landau Hydro Normalized here “Default” KLN parameters (normalize @ 200 GeV peak) Scale in similar fashion both height & width Compare dN/dy This was a surprise. Of course different KLN parameters can make the agreement worse

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Peter SteinbergBNL/RIKEN Flow Workshop Landau & The QGP Landau’s physics is still used in relevant physics arguments Gazdzicki et al (NA49) Massless EOS Chemical potential = 0 “Entropy” pions ~ s 1/4 Lots of features vs. pp Pion suppression Crossover Enhancement! Is this evidence of a phase transition?

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Peter SteinbergBNL/RIKEN Flow Workshop Some Issues Landau left out B ( = 0 is OK) OK for pp, not AA All particles contribute to the entropy Thermal models determine all species given T, B Landau & Bilenkij

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Peter SteinbergBNL/RIKEN Flow Workshop Comparison with e + e - (Mueller 1983) Relative to p+p, NA49 features Relative to e+e-, different story PHOBOS

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Peter SteinbergBNL/RIKEN Flow Workshop Baryon Density & Entropy PAS, Cleymans, et al AGSSPSRHIC Fix pp vs. AA by removing energy of leading particles Can use thermal model approach to “fix” A+A: Predictable decrease in entropy density from baryon number conservation PAS, Work in progress No more features

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Peter SteinbergBNL/RIKEN Flow Workshop 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.

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Peter SteinbergBNL/RIKEN Flow Workshop Coincidence #4: Landau vs. Mueller Landau “better” at low energies MLLA QCD better at higher energies (esp. including pp@ s/2) Difference increases dramatically at higher energies (LHC day-1 important) Oddity: slower increase from pQCD is like Landau

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Peter SteinbergBNL/RIKEN Flow Workshop 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” (N part 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…

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Peter SteinbergBNL/RIKEN Flow Workshop Transverse Expansion? Carruthers & Minh Noticed that spectrum of high-p T 0 described by Coincidence #5, is the transverse spectrum also gaussian in rapidity? Carruthers conjecture Let’s look at higher energy, higher p T Carruthers & Duong-van (PRL 1973)

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Peter SteinbergBNL/RIKEN Flow Workshop 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 y T PHENIX d 0 STAR dN h + h -

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Peter SteinbergBNL/RIKEN Flow Workshop 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/dy T 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

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Peter SteinbergBNL/RIKEN Flow Workshop 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”

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Peter SteinbergBNL/RIKEN Flow Workshop “Proceedings”: Landau Hydrodynamics & RHIC Phenomenology Peter Steinberg Brookhaven National Laboratory Workshop on Collective Flow & QGP Properties November 17-19, 2003

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Peter SteinbergBNL/RIKEN Flow Workshop The “Landau Solution” Many authors refined original ideas This is how things ended up by early 1980’s Universal Entropy Gaussian Rapidity Distributions Thermal p T spectra R Incoming hadrons or nuclei Full stopping Longitudinal explosion

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Peter SteinbergBNL/RIKEN Flow Workshop Coincidence #1: BRAHMS dN/dy BRAHMS Preliminary 2003

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Peter SteinbergBNL/RIKEN Flow Workshop Coincidence #2: Scaling Limiting fragmentation (x scaling) somehow “built-in” Cooper & Schonberg 1973

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Peter SteinbergBNL/RIKEN Flow Workshop Coincidence #3: KLN KLN, =.3 Landau Hydro Normalized here “Default” KLN parameters (normalize @ 200 GeV peak) Scale in similar fashion both height & width Compare dN/dy This was a surprise. Of course different KLN parameters can make the agreement worse

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Peter SteinbergBNL/RIKEN Flow Workshop Coincidence #4: Landau vs. Mueller Landau “better” at low energies MLLA QCD better at higher energies (esp. including pp@ s/2) Difference increases dramatically at higher energies (LHC day-1 important) Oddity: slower increase from pQCD is like Landau

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Peter SteinbergBNL/RIKEN Flow Workshop 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 y T PHENIX d 0 STAR dN h + h -

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