1. Energy dependence of anisotropic flow
Raimond Snellings

2. RHIC: the first 3 years RHIC Scientists Serve Up “Perfect” Liquid
New state of matter more remarkable than predicted -- raising many new questions
April 18, 2005
5 July 2006

3. Outline The perfect liquid at RHIC
How do we approach the perfect liquid?
What can we expect at the LHC?
What can we learn from higher harmonics?
5 July 2006

4. Anisotropic Flow
Anisotropic flow ≡ azimuthal correlation with the reaction plane
the cleanest signal of final-state reinteractions
Unavoidable consequence of thermalization
Natural description in hydrodynamic language, however when we talk about flow we do not necessary imply (ideal) hydrodynamic behavior
Flow in cascade models: depends on constituent cross sections and densities, partonic and/or hadronic
Non-flow ≡ contribution to vn from azimuthal correlations between particles not due to their correlation with the reaction plane (HBT, resonances, jets, etc)
5 July 2006

5. Measuring Anisotropic Flow
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
Measuring the cumulants of different order provides constraints on both fluctuations and non-flow. Can be conveniently calculated using generating functions, extended to vn{∞} using Lee-Yang zeros, reliable vn>1/N
N. Borghini, P.M. Dinh and J.-Y Ollitrault, Phys. Rev. C63 (2001)
5 July 2006

6. The perfect liquid
5 July 2006

7. The “nearly perfect” liquid
HYDRO: Kolb, Sollfrank, Heinz, PRC 62 (2000)
STAR PRL 86, 402 (2001)
P.F. Kolb et al., PLB 500 (2001)
v2{4} 130 GeV
Zhixu Liu
Magnitude and transverse momentum dependence of v2
A strongly interacting, more thermalized system which is for more central collisions behaves consistent with ideal fluid behavior!
5 July 2006

8. Viscosity and parton cascade
D. Molnar and P. Huovinen, PRL94:012302,2005
D. Teaney PRC68:034913,2003
Viscosity needs to be small
Parton cascades need huge opacities
Partially solved by coalescence
Microscopic picture responsible for large v2 still not understood (E. Shuryak sQGP is being understood)
5 July 2006

9. Strong Collective Motion, v2(m,pt)
Particles flow with a common velocity
The most compact representation of the strong radial flow and its azimuthal variation
Best described by QGP EoS!?
5 July 2006

10. The QCD EoS and Cs
F. Karsch and E. Laermann, arXiv:hep-lat/
Test the effect of four different EoS; qp is lattice inspired, Q has first order phase transition, H is hadron gas with no phase transition and T a smooth parameterization between hadron and QGP phase
Pasi Huovinen, arXiv:nucl-th/
5 July 2006

11. v2(m,pt) and the softest point
Pasi Huovinen, arXiv:nucl-th/
EoS Q and EoS T (both have significant softening) do provide the best description of the magnitude of the mass scaling in v2(pt)
The lattice inspired EoS (EoS qp) in ideal hydro does as poorly as a hadron gas EoS! (opposite to conclusion Kämpfer)
Elliptic flow as function of pt and mass very sensitive to EoS (particular the heavier particles)
Before we can draw conclusions about the EoS much more work needed in theory (test different EoS, influence viscosity, hadronic phase)
5 July 2006

12. Energy dependence Energy dependence missed by ideal hydro
NA49, Phys. Rev. C(68), (2003)
Kolb, Sollfrank, Heinz, PRC 62 (2000)
Heiselberg and Levi PRC 59
D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/ ; Phys. Rev. Lett 86, 4783 (2001).
Energy dependence missed by ideal hydro
Hydro + cascade describes v2 from SPS to RHIC
At higher energies ideal hydro contribution dominates
Hydro + cascade follows “low density limit”??
5 July 2006

13. v2, eccentricity and fluctuations
M. Miller and RS, arXiv:nucl-ex/
5 July 2006

14. v2, eccentricity and fluctuations
M. Miller and RS, arXiv:nucl-ex/
“standard” v2{2} overestimates v2 by 10%, higher order cumulant underestimate v2 by 10% at intermediate centralities
Measuring the cumulants of different order provides constraints on both fluctuations! and on non-flow contributions!
5 July 2006

15. PHOBOS eccentricity fluctuations
S. Manly, QM2005
Large effect for small systems over whole centrality range
5 July 2006

16. v2/e revisited
S. Voloshin CIPANP-’06
By using participant eccentricity Cu+Cu and Au+Au at two energies follow the v2/e scaling
Although fluctuations in epart are reduced to compared to e”standard” using e{2} and v2{4}/e{4} could be an improvement
Why does it work that well?
5 July 2006

17. Rapidity dependence No boost invariance!
Hirano: Nucl Phys A
No boost invariance!
5 July 2006

18. Rapidity dependence dN/dh scales versus h-ybeam v2/e ~ 1/S dN/dy
PHOBOS nucl-ex/
PHOBOS PRL 94, (2005)
dN/dh scales versus h-ybeam
v2/e ~ 1/S dN/dy
Rapidity dependence no surprise?
5 July 2006

19. Rapidity dependence of eccentricity
Is the e/S independent of rapidity?
5 July 2006

20. LHC energies
E. Simili
Using dN/dy scaling of multiplicity and v2/eps extrapolation
Values a bit above hydro predictions (from T. Hirano)
5 July 2006

21. Energy dependence
T. Hirano
D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/ ; Phys. Rev. Lett 86, 4783 (2001).
The higher the beam energy the more dominant the QGP (here ideal hydro) contribution becomes
5 July 2006

22. Viscosity/entropy versus T
Hirano and Gyulassy arXiv:nucl-th/
Csernai, Kapusta and McLerran arXiv:nucl-th/
Important to quantitatively calculate the effect of viscosity on v2
Would reduce further the elliptic flow
5 July 2006

23. Higher Harmonics
Peter Kolb, PRC 68,
Higher harmonics are expected to be present, for smooth azimuthal distributions the higher harmonics will be small vn ~ v2n/2
v4 - a small, but sensitive observable for heavy ion collisions (Peter Kolb, PRC 68, )
v4 - magnitude sensitive to ideal hydro behavior (Borghini and Ollitrault, arXiv:nucl-th/ )
Ideal hydro v4/v22 = 0.5
STAR, Phys. Rev. Lett.(92), (2004)
5 July 2006

24. What do we learn from v4?
Ratio v4/v22 is sensitive to degree of thermalization (Borghini and Ollitrault nucl-th/ )
v4(pt)/v2(pt)2 is 1/2 for ideal hydro (more accurate for increasing values of pt)
Observed integrated ratio is larger than unity
Do we have intuitive test if the ratio is related to the degree of thermalization?
ratio v4/v22 expected to decrease as the collisions become more central
ratio v4/v22 expected to increase as function of transverse momenta
rapidity & energy dependence
5 July 2006

25. v2 and v4 at 200 GeV STAR preliminary Y. Bai, AGS users meeting 2006
5 July 2006

26. 200 GeV v4{EP2}/v2{4}2 STAR Preliminary
Y. Bai, AGS users meeting 2006
STAR Preliminary
v4/v22 decreases with pt below 1 GeV/c after which is starts to increase again (expected)
Magnitude and centrality dependence do not follow intuitive expectations
5 July 2006

27. 62 GeV v4{EP2}/v2{4}2 STAR Preliminary
Y. Bai, AGS users meeting 2006
Centrality and pt dependence similar to 200 GeV magnitude of v4/v22 even somewhat lower!
Energy dependence does not follow intuitive expectations
5 July 2006

28. Rapidity dependence STAR Preliminary
A. Tang
Ratio increases towards midrapidity contrary to expectations
5 July 2006

29. Conclusions
Strong collective motion at RHIC energies, consistent with perfect liquid behavior
No microscopic picture available
Constraining the EoS requires more detailed calculations
Energy dependence
No obvious horns, kinks or steps
Collapse of the proton v2 at SPS (next talk)
Measurements of v2{2}, v2{4}, v2{6} allow for estimates of the fluctuations and non flow as function of energy (detailed measurement still needs to be done, strong argument for energy scan)
v2 measurement at LHC will provide critical test of our understanding of the almost perfect liquid, testing the “hydro limit”
Au+Au and Cu+Cu follow v2/e scaling when using epart
Why does it work that well?
v4 is promising new observable to test hydrodynamic behavior
Detailed high statistics measurement available
Are the non-flow and fluctuation contributions to v4 under control?
Challenge to theory!
5 July 2006