Peter SteinbergBNL/RIKEN Flow Workshop Landau Hydrodynamics & RHIC Phenomenology Peter Steinberg Brookhaven National Laboratory Workshop on Collective

Peter Steinberg BNL/RIKEN Flow Workshop

Landau Hydrodynamics &RHIC Phenomenology

Peter SteinbergBrookhaven National Laboratory

Workshop on Collective Flow & QGP PropertiesNovember 17-19, 2003


Radial Flow

RHIC Data & Calculations by U. Heinz / P. Kolb

=.6c


A different perspective• We’re used to this in the transverse direction

• What about the longitudinal direction? Clearly not isotropic!


Landau Physical Picture

Incominghadrons or

nuclei

Full stopping

Longitudinalexplosion

Rapid ThermalizationEntropy productionPressure gradient0VV

R

RapidityDistributions


Entropy Production• Fermi’s argument: If we assume the

system is a perfect blackbody but system is Lorentz-contracted

3 3/ 4n T s

4

0

s sT s

V V

1/ 4T s

3/ 4 3/ 43 1/ 4

1/ 2

s sN nV VT s s

s


“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

0T

0p

Energy-MomentumConservation

Equation ofState (EOS)

3p

LandauBilenkijMilekhinShuryakCooperFryeSchonbergCarruthersAndersson…


Entropy from EOS

3/ 4

1/ 4

1/ 4

0

4

3

~

~

~

n Ts p

Ts p

d Tds

s

T

N

20p c

2020

1

1

aN s

ca

c

Cooper, Frye, Schonberg 1975

N(s) depends on EOS


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

2 / 2

1/ 4 2ln ln22

y L

yp

dN e sKs L

dy mL

1/ 4~chN Ks

exp /TT T

dNp T

p dp


Universality in 1981Carruthers 1981


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


Bjorken or Landau @ ISR?

• Boost invariant• Pseudorapidty• Near mid-

• Gaussian• Rapidity• Look everywhere

Carruthers & Duong-van 1973

ISR 53 GeVPISA/SUNYSB

1972 (unpub.)

“duck orrabbit”


Connections vs. Coincidences


dN

/d

19.6 GeV 130 GeV 200 GeV

Npart

PHOBOS dN/dh

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


Coincidence #1: BRAHMS dN/dy

BRAHMS Preliminary 2003

~ 2.3

ln 100 2.15

BRAHMSy

Landauy

BRAHMS showsno plateau


= - ybeam

PHOBOS Au+Au

19.6 GeV

130 GeV

200 GeV

Limiting Fragmentation

' ~ ln ln /beam T py x p M

2part

dNdN

Seen generically in manysystems (AA, pp…)


Coincidence #2Limiting fragmentation (x scaling) somehow “built-in”

20s GeV

60s GeV

130s GeV

200s GeV

Cooper & Schonberg 1973


CGC Calculations• KLN: Final state from 21 gluon scattering

• Overall scale

• Jacobian

• Quark counting

gN cN

~dN dN

d dy

41 x

(LPHD)

Energy, Rapidity, Centrality

Kharzeev, Levin, Nardi (2001)


Coincidence #3

KLN, =.3Landau Hydro

30s GeV

60GeV

200GeV

Normalized here

“Default” KLN parameters(normalize @ 200 GeV peak)

Scale in similar fashionboth height & width

Compare dN/dy

This was a surprise.

Of course different KLNparameters can make the

agreement worse


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?


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

~ 4

S N

Ts p Bn


Comparison with e+e-

(Mueller 1983)

)/exp( sAsch BN

Relative to p+p, NA49 featuresRelative to e+e-, different story

PHOBOS


Baryon Density & Entropy

PAS, Cleymans, et al

AGS SPS RHIC

Fix pp vs. AA by removingenergy of leading particles

Can use thermal modelapproach to “fix” A+A:Predictable decrease

in entropy densityfrom baryon number

conservation

PAS, Work in progress

No more features


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.


Coincidence #4: Landau vs. Mueller

Landau “better” atlow energies

MLLA QCD better athigher energies

(esp. including pp@s/2)

Difference increasesdramatically athigher energies

(LHC day-1 important)

Oddity: slower increasefrom pQCD is like

2 1/ 3sc

Landau


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…


Transverse Expansion?• Carruthers & Minh

• Noticed that spectrum of high-pT 0 described by

• Coincidence #5, is the transverse spectrum also gaussian in rapidity?• Carruthers conjecture

• Let’s look at higher energy, higher pT

2exp / 2TT T

dNC y L

p dp

1ln2

T TT

T T

m py

m p

~ .51L

Carruthers & Duong-van (PRL 1973)


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 d 0

STAR dN h+h-

0

1n

Tp

p


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

~ ln / 2y s


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”


“Proceedings”:Landau Hydrodynamics &

RHIC Phenomenology

Peter SteinbergBrookhaven National Laboratory

Workshop on Collective Flow & QGP PropertiesNovember 17-19, 2003


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

2 / 2

1/ 4 2ln ln22

y L

yp

dN e sKs L

dy mL

1/ 4~chN Ks

exp /TT T

dNp T

p dp

R

Incominghadrons or

nuclei

Full stopping

Longitudinalexplosion

0VV


Coincidence #1: BRAHMS dN/dy

BRAHMS Preliminary 2003

~ 2.3

ln 100 2.15

BRAHMSy

Landauy


Coincidence #2: ScalingLimiting fragmentation (x scaling) somehow “built-in”

20s GeV

60s GeV

130s GeV

200s GeV

Cooper & Schonberg 1973


Coincidence #3: KLN

KLN, =.3Landau Hydro

30s GeV

60GeV

200GeV

Normalized here

“Default” KLN parameters(normalize @ 200 GeV peak)

Scale in similar fashionboth height & width

Compare dN/dy

This was a surprise.

Of course different KLNparameters can make the

agreement worse


Coincidence #4: Landau vs. Mueller

Landau “better” atlow energies

MLLA QCD better athigher energies

(esp. including pp@s/2)

Difference increasesdramatically athigher energies

(LHC day-1 important)

Oddity: slower increasefrom pQCD is like

2 1/ 3sc

Landau


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 d 0

STAR dN h+h-

0

1n

Tp

p

2exp / 2TT T

dNC y L

p dp

1ln2

T TT

T T

m py

m p

Documents

Peter SteinbergBNL/RIKEN Flow Workshop Landau Hydrodynamics & RHIC Phenomenology Peter Steinberg Brookhaven National Laboratory Workshop on Collective