1. Collective Dynamics at RHIC
Nu Xu
LBNL, Berkeley, USA
1) Introduction: QGP  partonic collectivity
2) Some results from SPS and RHIC
3) Summary and outlook
J. Fu, H. Huang, M. Kaneta, F. Liu, H.G. Ritter, K. Schweda, R. Snellings, Z. Xu, E. Yamamoto…

2. Introduction J/y, D ? W ? K* X F, L ? p, K D, p ? d, HBT ? ?Q2
1) Initial Condition
- baryon transfer
- ET production
- parton dof
2) System Evolves
- parton/hadron
expansion
3) Bulk Freeze-out
- hadron dof
- interactions stop ?
v2 saturates ? ? ? ? ?
time
bT saturates

3. Pressure, Flow, … Thermodynamic identity – entropy p – pressure
U – energy V – volume
t = kBT, thermal energy per dof
In nuclear collisions, interactions among constituents
and density distribution lead to:
pressure gradient  collective flow
number of degrees of freedom (dof)
Equation of State (EOS)
time integral – partonic + hadronic effects

4. Transverse flow observables
As a function of particle mass:
Directed flow (v1) – early
Elliptic flow (v2) – early
Radial flow – integrated over whole evolution
Note:
1) Effect of collectivity is additive – final effect is the sum of all
processes as long as interactions are there.
2) No thermalization is needed – pressure gradient only depends
on the density gradient and interactions.

5. Results from RHIC At RHIC ~ constant vs. centrality
STAR preliminary
At RHIC ~ constant vs. centrality
At AGS, ratios changes factor ~100 / SPS factor ~ 2 variation
 re-scatterings at hadronic stage reduced at RHIC
STAR: Phys. Rev. Lett. 86, 4778(01), 87, (01), 89, (02)

6. Proton flow at RHIC 197Au + 197Au at 130 GeV
STAR Preliminary
1) <pt> increases with centrality  flow
2) RQMD describes transverse motion well  hadronic re-scattering
3) It underestimates pbar yield due to large annihilation x-section  re-scattering at earlier stage?
Fiducial yields
Total yields
Systematic errors

7. Transverse momentum distribution
SPS:
NA44, Phys. Rev. Lett. 78, 2080(97)
Now let me mover to the radial flow part. The way we do it by measuring the transverse momentum distributions for different particles.
1) On the left, we see the transverse momentum distributions from two collision systems: S+S, and Pb+Pb. Both are at the CERN SPS energy, about 20 GeV per nucleon in the center of mass.
Pion, kaon, and proton distributions were measured. One sees that
a) the shape of the distribution becomes flatter for heavier particles. Proton is flatter than that of kaon’s, and kaon is flatter than that of pion’s. This behavior can be characterize by the fitting parameter T – also called slope parameter. The value of T is larger for heavier particles.
b) The exact value of the T also depends on the size of the colliding system.
For example, T is larger for Pb+Pb collisions than that of S+S collisions.
2) Similar behavior was also observed in collisions at RHIC energy. See right plot. Proton, kaon, and pion distributions are shown. The exponential slope parameters are also listed there.
Note: since the shape of the distribution is not exactly exponential, the value of slope T will depend on the fitting range.
Dependence on the particle mass and the
size of the colliding system  collective flow !

8. T vs. mass plot (SPS) sensitive to hadronization!
H. van Hecke, H. Sorge, N. Xu, Phys. Rev. Lett. 81, 5764(98).
Interactions with hadronic gas:
Large x-section limit:
pions, kaons, protons
Small x-section limit:
, J/
sensitive to hadronization!
1) Up to now, I only discussed the bulk properties of the heavy ion collisions with those particles like pion, kaons and protons. These particles in general have relative larger interaction cross sections with the hadronic gas, as they are major component of the hadron gas. There are other kind of particle, like phi, Omega baryons, and J/psi. Those particles do not interact with hadron gas strongly. In other words, they have relatively smaller cross sections.
The data – slope parameters as a function of particle mass.
2) Two band structure is clearly seen in the figure. One band, as we discussed before, show a mass dependence, for pions, kaons, protons, and deuterons. The behavior can be describes as tow components: random thermal motion T_th and collective motion beta. The fact that deuteron falls on the line further confirm the picture – there are space-momentum correlation which is necessary condition for collective flow.
The second band, shows no-mass-dependent. I lost phi, Omega, and J/psi. We know that these particles have relatively smaller cross sections with hadronic gas.
3) Since they do not interact with hadrons, then perhaps we can use them to probe the properties of the system at hadronization
the moment they are formed as hadrons. Taking the Schwinger’s picture, the formation probability can be written as this, where
kappa characterize the strength of the field – here is the QCD color field. Sometime, people also call it the string tension.
4) As one can see that the slope parameter for phi, Omega, and J/Psi are all about 240 MeV for heavy ion collisions at the SPS
energy.
At SPS, the observed collective transverse flow, b ~ 0.4c,
develops mostly at the hadronic stage. W and J/ do not flow!

9. Beam energy systematics
1) Smaller baryon chemical potential
mB = 45 MeV with Tch = 170 MeV
 Approaching net-baryon free !
2) Stronger transverse flow, bT= 0.55(c)
 More explosive expansion !

10. v2 for K0 and  Does v2 signal partonic flow?
1) Integrated v2 increases with particle mass ;
2) Hydro model results are consistent with
data. ‘QGP’ EoS used in calculations!
Does v2 signal partonic flow?
STAR Phys. Rev. Lett. 87, (01)
STAR, Phys. Rev. Lett. , accepted, (02)

11. Transverse collective flow
Heavier mass particles show stronger collective flow effects !
PHENIX: Phys. Rev. Lett (02) / STAR: f Phys. Rev. C65, (02) / STAR: L Phys. Rev. Lett. 89, (02)

12. Slope parameters vs. mass?
At high energy, high gluon density and strong interactions 
partonic flow
, D, J/y... sensitive to partonic collectivity ?
At RHIC, the observed collective transverse flow, b ~ 0.55c, sum of partonic and hadronic interactions ! W and J/ should flow!

13. Partonic Flow at RHIC? ? We need: 1) Non-zero values of v2 for W
YES NO
We need: ) Non-zero values of v2 for W
2) Increase of T for W, D, J/ …

14. Summary Not at the later hadronic stage,
1) SPS: most of the collective flow develops at
later hadronic stage
2) RHIC:
Copious scattering needed,
Not at the later hadronic stage,
Evidence of early patonic flow?!
3) To ‘see’ the partonic flow directly, spectra
and v2 for all hadrons, especially,
Ks f L X W D J/ ...

15. New Form of Matter ! Outlook Discover partonic collectivity – ‘QGP’
Diagnose bulk properties of ‘QGP’
Important:
Scan collision geometry b
Scan collision size A
Scan collision energy E