1. Many Thanks to Organizers!
Collective Expansion in Relativistic Heavy Ion Collisions -- Search for the partonic EOS at RHIC
Nu Xu
Lawrence Berkeley National Laboratory
Many Thanks to Organizers!
J. Castillo, X. Dong, H. Huang, H.G. Ritter, K. Schweda, P. Sorensen, Z. Xu

2. Outline Introduction Energy loss - QCD at work Bulk properties - ∂PQCD
- hadron spectra
- elliptic flow v2
Summary and Outlook

3. Phase diagram of strongly interacting matter
CERN-SPS, RHIC, LHC: high temperature, low baryon density
AGS, GSI (SIS200): moderate temperature, high baryon density

4. Study of Nuclear Collisions Like…
P.C. Sereno et al. Science, Nov. 13, 1298(1998).
(Spinosaurid)
High pT -
QCD probes
Bulk
Properties

5. High-energy Nuclear Collisions
time
S. Bass
Hadronization
and Freeze-out
Initial conditions
Initial condition in high-energy nuclear collisions
Cold-QCD-matter, small-x, high-parton density
- parton structures in nucleon / nucleus
Parton matter - QGP
- The hot-QCD
Initial high Q2
interactions
Hard scattering production - QCD prediction
Interactions with medium - deconfinement/thermalization
Initial parton density
Experimental approaches:
Energy loss - ‘jet-quenching’
Elliptic flow - v2, radial flow
Heavy flavor production, combination of 1) and 2)

6. High-energy Nuclear Collisions
jets
J/y, D W f X L
p, K, K*
D, p
d, HBT
Initial Condition
- initial scatterings
- baryon transfer
- ET production
- parton dof
System Evolves
- parton interaction
- parton/hadron
expansion
Bulk Freeze-out
- hadron dof
- interactions stop
partonic scatterings?
early thermalization? Q2 TC
Tch
Tfo
elliptic flow v2
time
radial flow bT

7. Physics Goals at RHIC
Identify and study the properties of matter with partonic degrees of freedom.
Penetrating probes Bulk probes
- direct photons, leptons spectra, v1, v2 …
- “jets” and heavy flavor partonic collectivity
- fluctuations
jets observed high pT hadrons (at RHIC, pT(min) > 3 GeV/c)
collectivity - collective motion of observed hadrons, not necessarily reached
thermalization among them.
Hydrodynamic
Flow
Collectivity
Local
Thermalization
= 

8. Collision Geometry z x beam Non-central Collisions
Au + Au sNN = 200 GeV x
Non-central Collisions
beam
Number of participants: number of incoming nucleons in the overlap region
Number of binary collisions: number of inelastic nucleon-nucleon collisions
Charged particle multiplicity  collision centrality
Reaction plane: x-z plane

9. Au + Au Collisions at RHIC
Central Event
STAR
(real-time Level 3)

10. Charged Hadron Density
19.6 GeV GeV GeV
Charged hadron pseudo-rapidity 
PHOBOS Collaboration
1) High number of Nch indicates
initial high density;
2) Mid-y, Nch  Npart  nuclear
collisions are not incoherent;
3) Saturation model works
Initial high parton density at RHIC
PRL 85, 3100 (00); 91, (03); 88, 22302(02); 91, (03)

11. Energy Loss in A+A Collisions
leading particle suppressed
back-to-back jets disappear
p+p Au + Au
Nuclear Modification Factor:

12. Hadron Suppression at RHIC
Hadron suppression in more central Au+Au collisions!

13. Jets Observation at RHIC
p+p collisions at RHIC
Jet like events observed
Au+Au collisions at RHIC
Jets?

14. Suppression and Correlation
In central Au+Au collisions: hadrons are suppressed and back-to-back ‘jets’
are disappeared. Different from p+p and d+Au collisions.
Energy density at RHIC:  > 5 GeV/fm3 ~ 300
Parton energy loss: Bjorken
(“Jet quenching”) Gyulassy & Wang 1992 …

15. Energy Loss and Equilibrium
Leading hadrons
Medium
In Au +Au collision at RHIC:
Suppression at the intermediate pT region - energy loss
The energy loss leads to progressive equilibrium in Au+Au collisions
STAR: nucl-ex/

16. Parton Energy Loss
(1) Measured spectra show evidence of suppression
up to pT ~ 6 GeV/c;
(2) Jet-like behavior observed in correlations:
- hard scatterings in AA collisions
- disappearance of back-to-back correlations
“Partonic” Energy loss process leads to progressive equilibrium in the medium
Next step: fix the partonic Equation of State, bulk properties

17. tds = dU + pdV Pressure, Flow, …
s– entropy; p – pressure; U – energy; V – volume
t = kBT, thermal energy per dof
In high-energy nuclear collisions, interaction among constituents and density distribution will lead to:
pressure gradient  collective flow
 number of degrees of freedom (dof)
Equation of State (EOS)
No thermalization is needed – pressure gradient only depends on the density gradient and interactions.
 Space-time-momentum correlations!

18. Transverse Flow Observables
As a function of particle mass:
Directed flow (v1) – early
Elliptic flow (v2) – early
Radial flow – integrated over whole evolution
Note on collectivity:
Effect of collectivity is accumulative – final effect is the
sum of all processes.
2) Thermalization is not needed to develop collectivity - pressure
gradient depends on density gradient and interactions.

19. Results from BRAHMS, PHENIX, and STAR experiments
Hadron Spectra From RHIC mid-rapidity, p+p and Au+Au collisions at 200 GeV 5%
10-20%
20-40%
40-60%
60-80%
(ss)
centrality
(usd)
(ssd)
(sss)
Results from BRAHMS, PHENIX, and STAR experiments

20. Compare with Model Results
Model results fit to , K, p spectra well, but over predicted <pT> for multi-strange hadrons - Do they freeze-out earlier?
Phys. Rev. C (04); Phys. Rev. Lett. 92, (04); 92, (04); P. Kolb et al., Phys. Rev. C (03)

21. Thermal fits: Tfo vs. < bT >
200GeV Au + Au collisions
1) p, K, and p change
smoothly from peripheral
to central collisions.
2) At the most central
collisions, <T> reaches
0.6c.
3) Multi-strange particles ,
 are found at higher Tfo
(T~Tch) and lower <T>
 Sensitive to early partonic stage!
 How about v2?
STAR: NPA715, 458c(03); PRL 92, (04); 92, (04).
Chemical Freeze-out: inelastic interactions stop
Kinetic Freeze-out: elastic interactions stop

22. Anisotropy Parameter v2
coordinate-space-anisotropy  momentum-space-anisotropy y py x px
Now I will discuss the event anisotropy. The idea behind the measurement is the following:
For non-central collisions, as shown here, the overlapped region looks like a ellipsoid. Sometimes this is called elliptical flow. The space anisotropy is defined as … After collisions, the space anisotropy is converted into momentum anisotropy. Experimentally we use the v2 parameter to characterize it.
As I said, the conversion from space to momentum anisotropy is through collisions – may be partons at early time, and may be hadrons. So we think this variable should be sensitive to the initial conditions and the equation of state.
We will hear more on this later during the conference.
Initial/final conditions, EoS, degrees of freedom

23. v2 at Low pT
P. Huovinen, private communications, 2004
- At low pT, hydrodynamic model fits well for minimum bias events indicating early thermalization in Au+Au collisions at RHIC!
- More theory work needed to understand details: such as centrality dependence of v2; consistency between spectra and v2 …

24. v2 at All pT v2, the spectra of multi- strange hadrons, and the
PHENIX: PRL91, (03) STAR: PRL92, (04)
Models: R. Fries et al, PRC68, (03), Hwa, nucl-th/
v2, the spectra of multi-
strange hadrons, and the
scaling of the number of
constituent quarks
 Partonic collectivity
has been attained at
RHIC!
 Deconfinement, model
dependently, has been
attained at RHIC!
Next question is the
thermalization of light
flavors at RHIC:
- v2 of charm hadrons
- J/ distributions !!

25. Nuclear Modification Factor
1) Baryon vs. meson effect!
2) Hadronization via coalescence
3) Parton thermalization (model)
- (K0, ): PRL92, (04); NPA715, 466c(03);
- R. Fries et al, PRC68, (03)

26. Bulk Freeze-out Systematics
The additional increase in bT is
likely due to partonic pressure
at RHIC.
1) v2 self-quenching, hydrodynamic model works at low pT
2) Multi-strange hadron freeze-out earlier, Tfo~ Tch
3) Multi-strang hadron show strong v2

27. Partonic Collectivity at RHIC
1) Copiously produced hadrons freeze-out:
Tfo = 100 MeV, T = 0.6 (c) > T(SPS)
2)* Multi-strange hadrons freeze-out:
Tfo = MeV (~ Tch), T = 0.4 (c)
3)** Multi-strange v2:
Multi-strange hadrons  and  flow!
4)*** Constituent Quark scaling:
Seems to work for v2 and RAA (RCP)
Partonic (u,d,s) collectivity at RHIC!

28. Summary & Outlook Charged multiplicity - high initial density
(2) Parton energy loss - QCD at work
(3) Collectivity - pressure gradient ∂PQCD
 Deconfinement and Partonic collectivity
Open issues - partonic (u,d,s) thermalization
- heavy flavor v2 and spectra
- di-lepton and thermal photon spectra

29. Equation of State
With given degrees of freedom, the EOS - the system response to the changes of the thermal condition - is fixed by its p and T or .
Energy density  GeV/fm3
Equation of state:
EOS I : relativistic ideal gas: p = /3
EOS H: resonance gas: p ~ /6
EOS Q: Maxwell construction:
Tcrit= 165 MeV, B1/4 = 0.23 GeV
lat=1.15 GeV/fm3
P. Kolb et al., Phys. Rev. C62, (2000).

30. Phase diagram of strongly interacting matter
LHC
RHIC
GSI
CERN-SPS, RHIC, LHC: high temperature, low baryon density
AGS, GSI (SIS200): moderate temperature, high baryon density

31. RHIC @ Brookhaven National Laboratory
PHOBOS
BRAHMS
PHENIX h
STAR

32. LHC
B: The beauty of the Swiss rivers and mountains, especially the river, the Geneva lake! Oh, but the girl that cathe one’s breath.

33. ALICE: dedicated HI experiment
CMS: pp experiment with HI program

34. International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Key features: Intense, high-quality secondary beams of rare isotopes and antiprotons
2012: first beam
$$$$: ~ 109 Euro
SIS 100 Tm
SIS 200 (250) Tm
23 (29) AGeV U
60 (75) GeV p
Antiproton storage ring:
Hadron Spectroscopy
Ion and Laser Induced Plasmas:
High Energy Density in Matter
Structure of Nuclei
far from Stability
Polarized anti-proton
proton collisions,
nucleon structure
Compressed Baryonic Matter