flow and collective phenomena in nucleus-nucleus collisions huan z huang department of physics and...
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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
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
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
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
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).
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 –
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
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
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 ?
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? )