Flow and Collective Phenomena in
Nucleus-Nucleus Collisions
Huan Z Huang
Department of Physics and Astronomy
University of California, Los Angeles
Department of Engineering Physics
Tsinghua University
Ultra Relativistic Heavy Ion Collisions
Quark Gluon Plasma
In Pictures
-4.8, 0.66, 2.86,
9.39, 18.48, 35.96
Evolution
Q2
?
?
?
1) Initial Condition
- baryon transfer
- ET production
- partons dof
v2 saturates
W
K*
?
2) System Evolves
- parton/hadron
expansion
?
?
time
J/y, D
3) Bulk Freeze-out
- hadrons dof
- interactions stop
X
F, L
p, K
D, p
d, HBT
bT saturates
Inspiration from Hydrodynamics
Ne
U
H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980)
Discovery of Collective Flow
Bevalac 400 MeV/A
dN/dcos
Non-zero flow angle distribution
for Nb, but not Ca
Plastic Ball, Gustafsson et al., PRL 52, 1590 (1984)
Squeeze-out
bounce
squeeze
squeeze
Transverse Plane
Anisotropic Flow as a function of rapidity
Tr ans ve r s e Plane
y
x
around the beam axis
Geometry of Nucleus-Nucleus Collisions
Number of Participants
Impact Parameter
Npart – No of participant nucleons
Nbinary – No of binary nucleon-nucleon collisions
cannot be directly measured at RHIC
estimated from Woods-Saxon geometry
Nuclear Collision Evolution Epoches
h=0
0.5
Infinite
Kinetic Freeze-out
--- Interaction ceases
Chemical Freeze-out
--- formation of hadrons
Radial Flow
Partonic: parton-parton scattering, QGP EOS
Hadronic: hadron-hadron scattering, hadron gas
Pressure, Flow, …
y
 

pout  RT  pT

vout  0

Rout

pT

pout
x
Matter flows – all
particles have the
same collective
velocity:
pT  mass  vT
T  Tthermal  mass  vT
2

pout

vout  0
I.Bearden et al, Phys. Rev. Lett. 78, 2080(1997).
Pressure, Flow, …
Thermodynamic identity
 – entropy
p – pressure
U – energy
V – volume
 = kBT, thermal energy per dof
d  dU  pdV
In nuclear collisions, density distribution
and pressure will lead:
 pressure gradient
 flow – integrated effects
 number of degree of freedom
 Equation of State (EOS)
Hydrodynamic Basics
T



pp
  dxdp  f (x,p)
p
f(x,p): phase space distribution function
- information on dynamics
T : energy-momentum tensor
idea hydrodynamics
T


 (ε  p)u u  pg ,

u   (1,v)

JB  nBu


  s  0,
: Lorentz factor
K.J. Eskola, et al., nucl-th/9705015
L. Ch, ISBN-

  JB  0,
u: 4-velocity,

s  su

----------------------------------------------- Initial conditions (?)
- EOS (?)
- Freeze-out conditions (?)

 Hydrodynamics solutions
Bag Model Equation of State
Two Flavor Quarks (up, down)
Degeneracy factors:
quarks Q = (3 color)x(2 flavor)x(2 helicity)=12
gluons G = (8 color)x(2 helicity) = 16
Bag Constant:
(E/V)vac = +B
Free quarks and gluons:
3
Q

E
kd
k
3
G
   B 
kd k (nk  n k ) 
3 
3  bk
V
(2p )
2p  e  1
3

1 Q
kd
k 
3
G
p  B  
kd k (nk  n k ) 

3 
3  bk
3  (2p )
2p  e  1
1 Q
3
B 
kd
k (nk  n k )
3 
3 (2p )
Bag Model EOS
Free quark and gluons in a bag:
3 (p+B) =  – B (B bag constant)
1) At finite baryon density B=2kF2/3p2 and zero T
3(p+B) = -B = 3kF4/2p2
Fermi pressure keeps the bubble from collapsing
2) At finite T and vanishing baryon density B=0
3(p+B) = -B = 37p2(kBT)4/30
Thermal pressure keeps the bubble from collapsing
EOS of Nucleon DOF @T=0
Mix Hadrons and the QGP
QCD on Lattice
1) Large increase in  !
2) Not reach idea non-interaction
S. Boltzmann limit !
 many body interactions
 Collective modes
 Quasi-particles are necessary
3) TC ~ 170 MeV robust!
Lattice calculations predict
TC ~ 170 MeV
Z. Fordor et al, JHEP 0203:014(02)
Z. Fodor et al, hep-lat/0204001
C.R. Allton et al, hep-lat/0204010
F. Karsch, Nucl. Phys. A698, 199c(02).
Sample QGP EOS
Latent Heat 0.4 GeV
Latent Heat 0.8 GeV
Resonant Gas
Collision Dynamics
Final Spectra Reflect the Kinetic Freeze-out
Final State Hadronic Rescattering
important
Elliptic Flow
Reaction
plane
z
y
x
Initial Geometry Important
y x
Eccentricity =
2
2
y x
2
2
Time Evolution of the Asymmetry
Elliptic Flow v2 and Early Dynamics
Coordinate space:
initial asymmetry
Momentum space:
final asymmetry
py
y
Pressure induced flow +
Surface emission pattern +
Final state rescattering –
x
y  x 
 2 2
y  x 
2
2
v 2  cos2 ,   tan (
1
dN/d 1 + 2v2 cos2
py
px
)
V2 and the Early Stage EOS
Elliptic Flow: ultra-cold Fermi-Gas
• Li-atoms released from an optical trap exhibit
elliptic flow analogous to what is observed in ultrarelativistic heavy-ion collisions
 Elliptic flow is a general feature of strongly
interacting systems!
Dynamical Origin of Elliptic Flow
y
STAR Preliminary
Au+Au 200 GeV
x
Small expansion velocity
Collective Pressure
High pressure gradient
Large expansion velocity
pT dependent !
Low particle density
Surface Geometrical Phase Space
Surface Emission Pattern
High particle density
pT independent ! or
pT dependence may come
from surface thickness (pT)
V2 in the high pT region:
should large parton energy loss lead to
surface emission pattern ?!
Particle Dependence of v2 ?
Three pT Regions
LOW
INTERMEDIATE
STAR
PHENIX
HIGH
Elliptic Flow v2
PRL 92 (2004) 052302; PRL 91 (2003) 182301
Hydro calculations
break-down at higher
pT (as expected).
How is v2 established
at pT above 2 GeV/c?
Why is baryon v2 so
large?
Large radial flow reduces v2 for
Blast wave peak
protons
depends on 
High pT
protons
Low pT
protons
x
y
pT
•Radial flow pushes protons to high
pT regions
•Low pT protons are likely to come
from fluid elements with small
radial flow
Even for positive elliptic flow of matter, v2 for
heavy particles can be negative in low pT regions!
Multi-strange Baryon v2
STAR Preliminary; PRL 91 (2003) 182301
Multi-strange hadrons,
, X and W, are
expected to have
smaller hadronic xsections.
X and W v2 values are
large: apparently
independent hadronic
x-section.
Consistant with the
creation of v2 before
hadron formation.
F meson flow
 meson (s-sbar) state!
Jinhui Chen
Guoliang Ma
SINAP
Constituent Quark Degree of Freedom
Hadronization Scheme for
Bulk Partonic Matter:
KS – two quark coalescence
L– three quark coalescence
from the partonic matter surface?!
Particle v2 may be related to
quark matter anisotropy !!
pT < 1 GeV/c may be affected
by hydrodynamic flow !
Quark Coalescence – (ALCOR-J.Zimanyi et al, AMPT-Lin et al,
Rafelski+Danos, Molnar+Voloshin …..)
Quark Recombination – (R.J. Fries et al, R. Hwa et al)
Multi-Parton Dynamics for Bulk Matter
Hadronization
Essential difference:
Traditional fragmentation  particle properties mostly
determined by the leading quark !
Emerging picture from RHIC data (RAA/RCP and v2)  all
constituent quarks are almost equally important in
determining particle properties !
v2 of hadron comes from v2 of all constituent quarks !
The fact that in order to explain the v2 of hadrons
individual constituent quarks (n=2-meson,3-baryon) must
have a collective elliptic flow v2 and the hadron v2 is the
sum of quark v2  Strong Evidence for Deconfiement !
Implication of the Experimental Observation
1) At the moment of hadronization in nucleus-nucleus
collisions at RHIC the dominant degrees of freedom
is related to number of constituent (valence) quarks.
2) These ‘constituent quarks’ exhibit an angular
anisotropy resulting from collective interactions.
3) Hadrons seem to be formed from coalescence or
recombination of the ‘constituent quarks’, and the
hadron properties are determined by the sum of
‘constituent quarks’.
Is this picture consistent with recent LQCD on spectral
function calculations near Tc ?
Recombination Model Including Hadron Structure
Muller et al nucl-th/0503003
Constituent Quark Number Scaling
Systematic particle dependence from internal structure
Heavy Quark Flow
Heavy Quark Energy Loss, Elliptic Flow, B and D Contributions
-- outstanding issues in heavy ion physics !!
Quark-Gluon Fluid
Experimental Indications:
Hydrodynamic Description of Bulk Particle
Properties – v2 and Spectra Shape – Successful.
Hydrodynamic Calculation – Ideal Fluid.
v2 saturation and coalescence picture.
Uncertainties – uniqueness for hydro calculation?
-- Initial conditions ?
Theoretical Understanding:
How come a strongly coupled quark-gluon
matter has small viscosity?
Hadronization in hydrodynamic calculation?
Equilibration condition?
Hadronic stage radial flow?
Quark Cluster Formation from Strongly
Interacting Partonic Matter
L
X
W
Volcanic mediate pT – Spatter (clumps)
Strangeness
enhancement from QGP
is most prominent
in the region where
particle formation from
quark coalescence is
dominant !
pT Scales and Physical Processes
RCP
Three PT Regions:
-- Fragmentation
-- multi-parton dynamics
(recombination or
coalescence or …)
-- Hydrodynamics
(constituent quarks ?
parton dynamics
from gluons to
constituent quarks? )
The END