Landau Hydrodynamics

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

• Were 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

• Fermis 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 Tmp

LandauBilenkijMilekhin ShuryakCooper Frye Schon
bergCarruthers 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 1980s
• 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 _at_ 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, y0 not special
• Most of the energy goes forward
• Correctness of initial conditions must be based
  on data
• Apparently led to many disagreements in 70s

11
Bjorken or Landau _at_ ISR?
Carruthers Duong-van 1973
ISR 53 GeV PISA/SUNYSB 1972 (unpub.)

• Boost invariant
• Pseudorapidty
• Near mid-h
• Gaussian
• Rapidity
• Look everywhere

12
Connections vs. Coincidences
13
PHOBOS dN/dh
130 GeV
200 GeV
19.6 GeV
dN/dh
Npart
h
h
h

• These plots are interpreted as the emergence of
  the central plateau with increasing collision
  energy

14
Coincidence 1 BRAHMS dN/dy
BRAHMS showsno plateau
BRAHMS Preliminary 2003
15
Limiting Fragmentation
PHOBOS AuAu
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

Kharzeev, Levin, Nardi (2001)

• Overall scale
• Jacobian
• Quark counting

(LPHD)
Energy, Rapidity, Centrality
18
Coincidence 3
Compare dN/dy
KLN, l.3
Normalized here
Landau Hydro
Default KLN parameters(normalize _at_ 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

• Landaus 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 ee-
PHOBOS
Relative to pp, NA49 featuresRelative to ee-,
different story
22
Baryon Density Entropy
PAS, Work in progress
Fix pp vs. AA by removingenergy of leading
particles Can use thermal modelapproach to
fix AA Predictable decreasein entropy
densityfrom baryon numberconservation
No more features
23
Historical Interlude

• Landau (1953) considered pp, pA, AA
• Cooper Frye (1973) tried ee-
• More compact initial state (R1/?s)
• Initial expectations 31D, jets ? 11D!
• 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_at_?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 ee- thermal?
• Why is pQCD blackbody formula?
• Are leading particles relevant?
• AA 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-pT p0 described by
• Coincidence 5, is the transverse spectrum also
  gaussian in rapidity?
• Carruthers conjecture
• Lets 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 AA
• Mass dependence of yT

PHENIX ds p0 STAR dN hh-
28
Conclusions

• Landaus 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 31D. 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
ProceedingsLandau 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 1980s
• 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
KLN, l.3
Normalized here
Landau Hydro
Default KLN parameters(normalize _at_ 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_at_?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 AA
• Mass dependence of yT

PHENIX ds p0 STAR dN hh-