Landau Hydrodynamics RHIC Phenomenology Peter Steinberg Brookhaven National

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

Radial Flow RHIC Data & Calculations by U. Heinz / P. Kolb b. T=. 6 c Peter Steinberg BNL/RIKEN Flow Workshop

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

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

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

“Landau Hydro” • Source-free 3 D hydro equations Energy-Momentum Conservation Equation of State (EOS) Landau Bilenkij Milekhin Shuryak Cooper Frye Schonberg Carruthers Andersson … • Massless EOS • No scale in the problem (scale invariance) • Only from boundary conditions (Carruthers) • Initial geometry, freezeout temperature T~mp Peter Steinberg BNL/RIKEN Flow Workshop

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

Universality in 1981 Carruthers 1981 Peter Steinberg BNL/RIKEN Flow Workshop

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 Peter Steinberg BNL/RIKEN Flow Workshop

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

Connections vs. Coincidences Peter Steinberg BNL/RIKEN Flow Workshop

d. N/dh PHOBOS d. N/dh 130 Ge. V 19. 6 Ge. V h h 200 Ge. V h Npart • These plots are interpreted as the emergence of the central plateau with increasing collision energy Peter Steinberg BNL/RIKEN Flow Workshop

Coincidence #1: BRAHMS d. N/dy BRAHMS shows no plateau BRAHMS Preliminary 2003 Peter Steinberg BNL/RIKEN Flow Workshop

Limiting Fragmentation PHOBOS Au+Au 200 Ge. V 130 Ge. V 19. 6 Ge. V h = h - ybeam Peter Steinberg Seen generically in many systems (AA, pp…) BNL/RIKEN Flow Workshop

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

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

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

Landau & The QGP • Landau’s physics is still used in relevant physics arguments • Gazdzicki et al (NA 49) • 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? Peter Steinberg BNL/RIKEN Flow Workshop

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

Comparison with e+e. PHOBOS (Mueller 1983) Relative to p+p, NA 49 features Relative to e+e-, different story Peter Steinberg BNL/RIKEN Flow Workshop

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

Historical Interlude • Landau (1953) considered pp, p. A, AA • Cooper & Frye (1973) tried e+e • More compact initial state (R~1/ s) • Initial expectations 3+1 D, jets 1+1 D! • 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. Peter Steinberg BNL/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 p. QCD is like Peter Steinberg BNL/RIKEN Flow Workshop

Does this make sense? • These comparisons ask more questions than they answer • • • Is e+e- “thermal”? Why is p. QCD ~ 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 p. QCD and hydro? • Hard processes should be immune… Peter Steinberg BNL/RIKEN Flow Workshop

Transverse Expansion? • Carruthers & Minh Carruthers & Duong-van (PRL 1973) • Noticed that spectrum of high-p. T p 0 described by • Coincidence #5, is the transverse spectrum also gaussian in rapidity? • Carruthers conjecture • Let’s look at higher energy, higher p. T Peter Steinberg BNL/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) PHENIX ds p 0 STAR d. N h+h- • Power-law has two: • Not sure if or how this formula works with A+A • Mass dependence of y. T Peter Steinberg BNL/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 #2 #3 #4 #5 Gaussian d. N/dy, widths Limiting fragmentation built-in Similar evolution in Landau & KLN Universal multiplicity formula & QCD Gaussian d. N/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 Peter Steinberg BNL/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+1 D. 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 d. N/dy to central limit theorem or the random walk problem” Peter Steinberg BNL/RIKEN Flow Workshop

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

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

Coincidence #1: BRAHMS d. N/dy BRAHMS Preliminary 2003 Peter Steinberg BNL/RIKEN Flow Workshop

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

Coincidence #3: KLN Normalized here KLN, l=. 3 Landau Hydro Compare d. N/dy “Default” KLN parameters (normalize @ 200 Ge. V peak) Scale in similar fashion both height & width This was a surprise. Of course different KLN parameters can make the agreement worse Peter Steinberg BNL/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 p. QCD is like Peter Steinberg BNL/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) PHENIX ds p 0 STAR d. N h+h- • Power-law has two: • Not sure if or how this formula works with A+A • Mass dependence of y. T Peter Steinberg BNL/RIKEN Flow Workshop