Flow and Collective Phenomena in Nucleus-Nucleus Collisions

Huan Z HuangDepartment of Physics and AstronomyUniversity of California, Los Angeles

Department of Engineering PhysicsTsinghua University

Ultra Relativistic Heavy Ion Ultra Relativistic Heavy Ion CollisionsCollisions

QuarkQuark GluonGluon PlasmaPlasma

-4.8, 0.66, 2.86, 9.39, 18.48, 35.96

In Pictures

EvolutionEvolution

1) Initial Condition - baryon transfer - ET production - partons dof

2) System Evolves - parton/hadron expansion

3) Bulk Freeze-out - hadrons dof - interactions stop

??

?

?

?

?

J/D

K*

,

K

p

d, HBT

vv22 saturates saturates

TT saturates saturates

Q2

time

Inspiration from Hydrodynamics

H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980)

U

Ne

Discovery of Collective Flow

Plastic Ball, Gustafsson et al., PRL 52, 1590 (1984)

Non-zero flow angle distributionfor Nb, but not Ca

dN

/dco

s

Bevalac 400 MeV/A

bounce

squeeze squeeze

Squeeze-out

Transverse Plane

Transverse Plane y

x

Anisotropic Flow as a function of rapidity

around the beam axis

Geometry of Nucleus-Nucleus Collisions

Number of Participants

Impact Parameter

Npart – No of participant nucleonsNbinary – No of binary nucleon-nucleon collisions cannot be directly measured at RHIC estimated from Woods-Saxon geometry

= 0 0.5 Infinite

Nuclear Collision Evolution Epoches

Chemical Freeze-out --- formation of hadrons

Kinetic Freeze-out --- Interaction ceases

Radial Flow

Partonic: parton-parton scattering, QGP EOS

Hadronic: hadron-hadron scattering, hadron gas

Pressure, Flow, …Pressure, Flow, …

outp

TTout pRp

outp

Tp

outR

0outv

0outv

x

y Matter flows – all particles have the same collective velocity:

2

Tthermal

TT

vmassTT

vmassp

I.Bearden et al, Phys. Rev. Lett. 78, 2080(1997).

Pressure, Flow, …Pressure, Flow, …

pdVdUd Thermodynamic identity

– entropy p – pressureU – energy V – volume= kBT, thermal energy per dof

In nuclear collisions, density distribution and pressure will lead:

pressure gradient flow – integrated effects number of degree of freedom Equation of State (EOS)

Hydrodynamic BasicsHydrodynamic Basics

sus0,s

unJ0,J

)v(1,u

,pgup)u(εT

p)f(x,p

ppdxdpT

BBB

f(x,p): phase space distribution function - information on dynamicsTenergy-momentum tensor

idea hydrodynamics

u: 4-velocity, Lorentz factor

K.J. Eskola, et al., nucl-th/9705015L. Ch, ISBN-

----------------------------------------------- - Initial conditions (?) - EOS (?) - Freeze-out conditions (?)

Hydrodynamics solutions

Bag Model Equation of StateTwo Flavor Quarks (up, down)

Degeneracy factors:quarks Q = (3 color)x(2 flavor)x(2 helicity)=12gluons G = (8 color)x(2 helicity) = 16

Bag Constant: (E/V)vac = +BFree quarks and gluons:

)()2(3

1

12)(

)2(3

1

12)(

)2(

33

3

33

3

3

33

3

kkQ

B

kG

kkQ

kG

kkQ

nnkkd

e

kkdnnkkdBp

e

kkdnnkkdB

V

E

Bag Model EOS

Free quark and gluons in a bag:3 (p+B) = – B (B bag constant)

1) At finite baryon density B=2kF2/32 and zero T

3(p+B) = -B = 3kF4/22

Fermi pressure keeps the bubble from collapsing

2) At finite T and vanishing baryon density B=03(p+B) = -B = 372(kBT)4/30

Thermal pressure keeps the bubble from collapsing

EOS of Nucleon DOF @T=0

Mix Hadrons and the QGP

QCD on LatticeQCD on Lattice

Lattice calculations predict TC ~ 170 MeV

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!

Z. Fordor et al, JHEP 0203:014(02) Z. Fodor et al, hep-lat/0204001C.R. Allton et al, hep-lat/0204010F. Karsch, Nucl. Phys. A698, 199c(02).

Sample QGP EOSLatent 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

x

z

y

Initial Geometry Important

Eccentricity = 22

22

xy

xy

Time Evolution of the Asymmetry

Elliptic Flow v2 and Early Dynamics

22

22

xy

xy)(tan,2cos 1

2x

y

p

pv

Coordinate space: initial asymmetry

Momentum space: final asymmetry

py

px

x

y

dN/d 1 + 2v2 cos2

Pressure induced flow +Surface emission pattern +Final state rescattering –

V2 and the Early Stage EOS

Elliptic Flow: ultra-cold Fermi-GasElliptic Flow: ultra-cold Fermi-Gas

• Li-atoms released from an optical trap exhibit elliptic flow analogous to what is observed in ultra-relativistic heavy-ion collisions

Elliptic flow is a general feature of strongly interacting systems!

y

Dynamical Origin of Elliptic Flow

STAR PreliminaryAu+Au 200 GeV

V2 in the high pT region: should large parton energy loss lead to surface emission pattern ?! Particle Dependence of v2 ?

Collective Pressure

High pressure gradientLarge expansion velocity

Small expansion velocity

pT dependent !

Surface Geometrical Phase Space

Surface Emission PatternHigh particle density

Low particle density

pT independent ! orpT dependence may comefrom surface thickness (pT)

x

Three pT Regions

STAR

PHENIX

LOW INTERMEDIATE HIGH

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?

PRL 92 (2004) 052302; PRL 91 (2003) 182301

Elliptic Flow v2

Large radial flow reduces Large radial flow reduces vv22 for protonsfor protons

•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!

High pTprotons

Low pTprotons

xy

pT

Blast wave peak depends on

Multi-strange hadrons, , and , are expected to have smaller hadronic x-sections.

and v2 values are large: apparently independent hadronic x-section.

Consistant with the creation of v2 before hadron formation.

STAR Preliminary; PRL 91 (2003) 182301

Multi-strange Baryon v2

meson flow

meson (s-sbar) state! Jinhui ChenGuoliang MaSINAP

Constituent Quark Degree of Freedom

KS – two quark coalescence– 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 !

Hadronization Scheme for Bulk Partonic Matter:

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 FluidExperimental 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

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

RCPThree PT Regions:

-- Fragmentation

-- multi-parton dynamics (recombination or coalescence or …)

-- Hydrodynamics (constituent quarks ? parton dynamics from gluons to constituent quarks? )

The END