1. Anisotropic flow at RHIC from SPS to RHIC
Raimond Snellings

2. Raimond Snellings; Moriond 2004
Introduction
Heavy-Ion Collisions
Study QCD at high temperature and density
Establish and characterize properties of deconfined matter and the phase transition
Requirement observables
Provide information about the early, possibly deconfined phase
Sensitive to the bulk properties
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3. “Early” stage: high-pt probes
Evidence of very dense system
RAA, IAA
Null experiment essential !
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4. Non-central heavy-ion collisions: coordinate system
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5. Calculating flow using multi particle correlations
Assumption all correlations between particles due to flow
Non flow correlation contribute order (1/N), problem if vn≈1/√N
Non flow correlation contribute order (1/N3), problem if vn≈1/N¾
N. Borghini, P.M. Dinh and J.-Y Ollitrault, Phys. Rev. C63 (2001)
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6. Raimond Snellings; Moriond 2004
v2(pt) for high pt particles (self normalizing tomography of dense matter)
M. Gyulassy, I. Vitev and X.N. Wang PRL 86 (2001) 2537
R17. Event Anisotropy as a Probe of Jet Quenching R.S and X.-N. Wang
R.S, A.M. Poskanzer, S.A. Voloshin, STAR note, arXiv:nucl-ex/
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7. Charged particle v2 at high-pt
STAR preliminary
PHENIX preliminary
N. N. Ajitanand: Nucl.Phys. A715 (2003)
K. Filimonov: Nucl. Phys. A715 (2003)
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8. Raimond Snellings; Moriond 2004
Elliptic flow at higher pt, extracted using multi-particle correlations
STAR Preliminary
v2{2}
v2{RP}
v2{4}
Significant v2 up to ~7 GeV/c in pt as expected from jet quenching. However at intermediate pt the magnitude is unexpectedly large
A. Tang (STAR) QM 2004
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9. Raimond Snellings; Moriond 2004
More detailed information: v2(pt) for identified particles at higher-pt
PHENIX
STAR
Preliminary
ShinIchi Esumi: Nucl. Phys. A715 (2003) 599
P. Sorensen
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10. Parton Coalescence/recombination?
D. Molnar, S.A. Voloshin: Phys.Rev.Lett. 91 (2003)
V. Greco, C.M. Ko and P. Levai: nucl-th/
C. Nonaka, R.J. Fries, S.A. Bass nucl-th/
J. Castillo (STAR preliminary) QM2004
M. Kaneta (PHENIX) QM2004
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11. Raimond Snellings; Moriond 2004
What about the bulk? y x
coordinate space
Coordinate space configuration anisotropic (almond shape) however, initial momentum distribution isotropic (spherically symmetric)
Only interactions among constituents generate a pressure gradient, which transforms the initial coordinate space anisotropy into a momentum space anisotropy (no analogy in pp)
Multiple interactions lead to thermalization -> limiting behavior ideal hydrodynamic flow py px
Momentum space
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12. Raimond Snellings; Moriond 2004
Time evolution
SCIENCE Vol: (2002)
Hydro calculation: P. Kolb, J. Sollfrank and U.Heinz
Elliptic Flow reduces spatial anisotropy -> self quenching
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13. Main contribution to elliptic flow develops early in the collision
Zhang, Gyulassy, Ko, Phys. Lett. B455 (1999) 45
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14. Integrated Elliptic Flow
PHOBOS: Phys. Rev. Lett. 89, (2002) 
PHENIX: Phys. Rev. Lett. 89, (2002)
STAR: Phys. Rev. Lett. 86, 402 (2001)
Hydrodynamic limit
STAR
PHOBOS
Compilation and Figure from M. Kaneta
RQMD
First time in Heavy-Ion Collisions a system created which at low pt is in quantitative agreement with hydrodynamic model predictions for v2 up to mid-central collisions
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15. Elliptic flow at lower energies
P. Kolb, J. Sollfrank, and U. Heinz, Phys. Rev. C. C (2000).
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16. Raimond Snellings; Moriond 2004
Identified particle v2
Fluid cells expand with collective velocity v, different mass particles get different Dp
Hydro: P. Huovinen, P. Kolb, U. Heinz
Typical pt dependence for different masses
Heavy particles more sensitive to velocity distribution (less effected by thermal smearing) therefore put better constrained on EOS
STAR
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17. Raimond Snellings; Moriond 2004
v2(pt,mass)
All particles reasonably described at low-pt with common set of parameters
PHENIX (squares) and STAR agree well
STAR, PHENIX preliminary
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18. Raimond Snellings; Moriond 2004
Everything flows?
J. Castillo (STAR) QM2004
What about charm?
M. Kaneta (PHENIX) QM2004
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pT [GeV/c]

19. Raimond Snellings; Moriond 2004
Conclusion
Consistent measurements of elliptic flow from PHENIX, PHOBOS and STAR
Elliptic flow for all measured particles at low-pt well described by boosted thermal particle distributions
Flow is large; indicative of strong partonic interactions at early stage of the collision
In ideal hydro; thermalization time < 1 fm/c to describe the flow
Up to pt = 7 GeV/c sizable elliptic flow, consistent with parton energy loss
Parton coalescence/recombination does a good job at intermediate pt; important tests the precise v2 of the f-meson and the W
GeV/c
Hydro
ReCo
R. Fries QM2004
pQCD
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20. Raimond Snellings; Moriond 2004
What have we learned from elliptic flow so far (according to theorists)?
U. Heinz: Resulting in a well-developed quark-gluon plasma with almost ideal fluid-dynamical collective behavior and a lifetime of several fm/c (arXiv:hep-ph/ ).
E. Shuryak: Probably the most direct signature of QGP plasma formation, observed at RHIC (arXiv:nucl-th/ ).
L. McLerran: one needs very strong interactions amongst the quark and gluons at very early times in the collision (arXiv:hep-ph/ ).
M. Gyulassy: The most powerful probe of the QGP equation of state: the mass dependence of v2; One of the three lines of evidence for the QGP at RHIC (arXiv:nucl-th/ ).
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21. Raimond Snellings; Moriond 2004
Backup
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22. Raimond Snellings; Moriond 2004
v2(pt) SPS-RHIC
Integrated v2 depends on slope and <pt>
<pt> pions 17 GeV ≈ 400 MeV/c, 130 GeV charged particles <pt> ≈ 500 MeV/c
NA49: Phys. Rev. C68 (2003) ; CERES: Phys. Rev. Lett. 92 (2004)
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23. Elliptic flow; excitation function
NA49
STAR
NA49
Phys.Rev. C68 (2003)
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24. Integrated v2 from cumulants
About 20% reduction from v2{2} to v2{4}
v2{4} ≈ v2{6}
A. Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/
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25. Raimond Snellings; Moriond 2004
Higher moments
<v2n> ≠ <v2>n
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26. The possible fluctuation contribution
“standard” v2{2} overestimates v2 by 10%, higher order cumulant underestimate v2 by 10% at intermediate centralities
M. Miller and RS, arXiv:nucl-ex/
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27. Compare fluctuations to data
M. Miller and RS, arXiv:nucl-ex/
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28. Why is v2 so large at higher-pt?
Measured v2 values seem to be larger than the maximum values in the case of extreme quenching -> surface emission
E. Shuryak: nucl-th/
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29. Raimond Snellings; Moriond 2004
Hydro + Jet Quenching?
T. Hirano and Y. Nara: nucl-th/
X.-N. Wang: nucl-th/
Coupling of hydro and parton energy loss gives a reasonable description of the data and also has a mass dependence at higher-pt
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30. How has elliptic flow defined our view of physics at RHIC?
Charged particle elliptic flow at low pt; one of the first papers from RHIC
First time quantitative agreement with hydrodynamics -> suggestive of early thermalization, strongly interacting parton phase
Identified particle elliptic flow at low pt
QGP equation of state (phase transition) provides accurate description
Charged particle elliptic flow at higher pt
First indications of jet quenching (later RAA)
Strongly dissipative system -> limiting surface emission (later back to back suppression). Suggested by Shuryak for high-pt v2, earlier already by Huovinen for whole pt range -> Not the whole answer at low pt shown by mass dependence of v2(pt) for p, K, p.
Identified particle elliptic flow at higher pt
Surface emission, not whole answer at higher pt either shown by mass dependence of v2 of pion, Kaon, proton and Lambda
pion, Kaon, proton and Lambda v2 give indication for parton coalescence. First suggested at QM2002 by Voloshin (later also used for RAA intermediate pt mass dependence)
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31. Raimond Snellings; Moriond 2004
v2 at LHC energy
S. Radomski
(PPR) ALICE simulations and reconstruction, show that we will be in a beautiful position to do this physics at LHC
P. Kolb, J. Sollfrank, and U. Heinz, Phys. Rev. C. C (2000).
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32. Flow (radial, directed and elliptic)x y z
Only type of transverse flow in central collision (b=0) is transverse flow.
Integrates pressure history over complete expansion phase
Elliptic flow, caused by anisotropic initial overlap region (b > 0).
More weight towards early stage of expansion.
Directed flow, sensitive to earliest collision stage (pre-equilibrium, b > 0)
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33. v1 predictions (QGP invoked)
L.P. Csernai, D. Rohrich: Phys. Lett. B 458 (1999) 454
J. Brachmann et al., Phys. Rev. C (2000)
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34. v1 predictions (more general, QGP interpretation not necessary)
R.S., H. Sorge, S.A. Voloshin, F.Q. Wang, N. Xu: Phys. Rev. Lett (2000)
M. Bleicher, H. Stocker: Phys. Lett. B 526 (2002) 309 (UrQMD)
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35. Directed flow at the SPS (NA49)
NA49: Phys.Rev. C68 (2003)
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36. First measurement of v1 at RHIC
Confirms v2 is in-plane at RHIC
Suggestive of limiting fragmentation picture
Consistent with theory predictions
The data with current statistics shows no sign of a wiggle (also does not exclude the magnitude of the wiggle as predicted
A. Tang, M. Oldenburg, A. Poskanzer, J. Putschke, RS, S. Voloshin
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37. Is there boost invariance? PHOBOS v2(h)
PHOBOS: Phys. Rev. Lett. 89, (2002) 
Preliminary v2200
Final v2130
200
130
average over
all centrality
(Npart ~200)
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38. Event Characterization
How do we distinguish peripheral collisions from central collisions? b
5% Central
STAR
Ncoll
Npart
Impact Parameter (b)
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