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Energy dependence of anisotropic flow

Energy dependence of anisotropic flow. Raimond Snellings. 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. Outline. The perfect liquid at RHIC

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Energy dependence of anisotropic flow

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  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 Raimond.Snellings@nikhef.nl

  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? Raimond.Snellings@nikhef.nl

  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) Raimond.Snellings@nikhef.nl

  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) 054906 Raimond.Snellings@nikhef.nl

  6. The perfect liquid Raimond.Snellings@nikhef.nl

  7. v2{4} 130 GeV Zhixu Liu The “nearly perfect” liquid HYDRO: Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909 • 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! STAR PRL 86, 402 (2001) P.F. Kolb et al., PLB 500 (2001) 0012137 Raimond.Snellings@nikhef.nl

  8. Viscosity and parton cascade • 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) D. Molnar and P. Huovinen, PRL94:012302,2005 D. Teaney PRC68:034913,2003 Raimond.Snellings@nikhef.nl

  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!? Raimond.Snellings@nikhef.nl

  10. F. Karsch and E. Laermann, arXiv:hep-lat/0305025 The QCD EoS and Cs • 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/0505036 Raimond.Snellings@nikhef.nl

  11. v2(m,pt) and the softest point Pasi Huovinen, arXiv:nucl-th/0505036 • 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) • 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) Raimond.Snellings@nikhef.nl

  12. Energy dependence NA49, Phys. Rev. C(68), 034903 (2003) • 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”?? Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909 Heiselberg and Levi PRC 59 D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001). Raimond.Snellings@nikhef.nl

  13. v2, eccentricity and fluctuations M. Miller and RS, arXiv:nucl-ex/0312008 Raimond.Snellings@nikhef.nl

  14. v2, eccentricity and fluctuations M. Miller and RS, arXiv:nucl-ex/0312008 “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! Raimond.Snellings@nikhef.nl

  15. PHOBOS eccentricity fluctuations • Large effect for small systems over whole centrality range S. Manly, QM2005 Raimond.Snellings@nikhef.nl

  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? Raimond.Snellings@nikhef.nl

  17. Rapidity dependence • No boost invariance! Hirano: Nucl Phys A715 821 824 2003 Raimond.Snellings@nikhef.nl

  18. Rapidity dependence • dN/dh scales versus h-ybeam • v2/e ~ 1/S dN/dy • Rapidity dependence no surprise? PHOBOS nucl-ex/0509034 PHOBOS PRL 94, 122303 (2005) Raimond.Snellings@nikhef.nl

  19. Rapidity dependence of eccentricity • Is the e/S independent of rapidity? Raimond.Snellings@nikhef.nl

  20. LHC energies • Using dN/dy scaling of multiplicity and v2/eps extrapolation • Values a bit above hydro predictions (from T. Hirano) E. Simili Raimond.Snellings@nikhef.nl

  21. Energy dependence • The higher the beam energy the more dominant the QGP (here ideal hydro) contribution becomes T. Hirano D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001). Raimond.Snellings@nikhef.nl

  22. Viscosity/entropy versus T • Important to quantitatively calculate the effect of viscosity on v2 • Would reduce further the elliptic flow Hirano and Gyulassy arXiv:nucl-th/0506049 Csernai, Kapusta and McLerran arXiv:nucl-th/0604032 Raimond.Snellings@nikhef.nl

  23. Higher Harmonics Peter Kolb, PRC 68, 031902 • 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, 031902) • v4 - magnitude sensitive to ideal hydro behavior (Borghini and Ollitrault, arXiv:nucl-th/0506045) • Ideal hydro v4/v22 = 0.5 STAR, Phys. Rev. Lett.(92), 062301 (2004) Raimond.Snellings@nikhef.nl

  24. What do we learn from v4? • Ratio v4/v22 is sensitive to degree of thermalization (Borghini and Ollitrault nucl-th/0506045) • 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 Raimond.Snellings@nikhef.nl

  25. STAR preliminary v2 and v4 at 200 GeV Y. Bai, AGS users meeting 2006 Raimond.Snellings@nikhef.nl

  26. 200 GeV v4{EP2}/v2{4}2 • 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 Y. Bai, AGS users meeting 2006 STAR Preliminary Raimond.Snellings@nikhef.nl

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

  28. STAR Preliminary Rapidity dependence • Ratio increases towards midrapidity contrary to expectations A. Tang Raimond.Snellings@nikhef.nl

  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! Raimond.Snellings@nikhef.nl

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