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Collective Dynamics at RHIC Aihong Tang. Outline: How perfect? Is the “ perfect liquid ” a unique explanation? How do we probe the initial condition ? When, and how is the collectivity achieved? Can we test the thermalization?

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## Collective Dynamics at RHIC Aihong Tang

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**Collective**Dynamics at RHIC Aihong Tang Aihong Tang QuarkMatter 06, Shanghai**Outline:**• How perfect? • Is the “perfect liquid” a unique explanation? • How do we probe the initial condition? • When, and how is the collectivity achieved? • Can we test the thermalization? • How do we divide soft physics and hard physics? • Scaling of soft physics • How does the hadronic interaction contribute to the collective motion? • Phase transition and Critical End Point Aihong Tang QuarkMatter 06, Shanghai**How Perfect ?**D. Teaney, PRC 68 034913 (2003) v2/ approaches the limit of ideal hydrodynamics Viscosity reduces v2 Viscosity needs to be small in order to explain data Almost nothing can be more liquid-like than it ! STAR, PRC 66 034904 (2002) Aihong Tang QuarkMatter 06, Shanghai**Is “perfect liquid” a unique explanation ?**CGC Glauber CGC > Glauber A. Adil, et al. nucl-th/0605012 (2006) • Is it Glauber + perfect liquid or, • CGC + viscous matter? • It is important to understandthe initial condition ! Aihong Tang QuarkMatter 06, Shanghai T. Hirano, RHIC & AGS Users Mtg 06**How do we probe the initial condition ?**Flow direction of spectators P. Sorensen’s talk, 18Nov. Sat. Parallel 2.4 D. Hofman, Phobos highlight talk, this QM Flow direction of spectators A. Adil, M. Gyulassy and T.Hirano. Phys. Rev. D 73 074006 (2006) At higher pt CGC predicts greater rapidity twist away from the beam axis than the bulk. v2 fluctuation is directly related to the fluctuation of initial conditions. Considerable amount of v2 fluctuation (36%-40%) in data is observed. Aihong Tang QuarkMatter 06, Shanghai Probe the initial condition by following its footprints in flow observables !**When, and how is the collectivity achieved?**STAR preliminary Y. Bai’s talk, this QuarkMatter PHENIX, nucl-ex/0608033 (2006) D.Teaney, J.Lauret and E. Shuryak, nucl-th/0110037 • and are less affected by hadronic interactions and they show sizable flow ! • Hadronic interactions at a later stage do not produce enough v2 Collectivity is achieved fast and early (from pre-hadronic phase). Y. Lu et al. Journal of Phys. G 32 1121 (2006) F. Liu’s talk, 19 Nov. Sun Parallel3.4 Aihong Tang QuarkMatter 06, Shanghai**Can we test the thermalization ?**Y. Bai’s talk, 18Nov. Sat. Parallel 2.4 Taken the systematical error into account, the ratio of v4/v22 does not contradict to theoretical calculations. Aihong Tang QuarkMatter 06, Shanghai**What is soft, what is hard ?**Au+Au 200 GeV P. Kolb and R. Rapp, Phys. Rev. C 67 044903 (2003) P.F. Kolb and U. Heinz, nucl-th/0305084 Hydro breaks down around 1.5~2 GeV/c for ,k and p, but works well up to pt ~ 4 GeV/c for . Whether a pt range is for “Soft physics” or “Hard physics” depends on particle species. Aihong Tang QuarkMatter 06, Shanghai**What is soft, what is hard ?**STAR preliminary S. Blyth’s talk, 19Nov. Sun. Parallel 3.1 Coalescense/recombination model works at different pt range for different particle species. Understanding the division between soft and hard physics is a key to understand particle ratios (and other physics) at intermediate pt Aihong Tang QuarkMatter 06, Shanghai**Scaling of soft physics**M. Lamont, SQM06. Curve : K. Redlich =1 =2/3 =1/3 Evidence from HBT and Strangeness production shows that length plays an important role in soft physics. D. Das & Z. Chajeck Aihong Tang QuarkMatter 06, Shanghai**Scaling of soft physics**PHOBOS, nucl-ex/0610037 S. Voloshin’s talk, 18Nov. Sat. Parallel 2.4 Volume STAR preliminary Length If plotted as a function of length, good linearity is observed for a few key observables from soft sector. Length is directly related to the average number of interactions for a particle on its way out ! For fixed b = 6 fm D.Teaney, J.Lauret and E. Shuryak, nucl-th/0110037 Aihong Tang QuarkMatter 06, Shanghai**How does the hadronic interaction contribute to the**collective motion? Y. Lu et al. Journal of Phys. G 32 1121 (2006) F. Liu’s talk, 19 Nov. Sun Parallel3.4 Hadron-string transport models can qualitatively reproduce the mass splitting at low pt and the NCQ scaling at intermediate pt while it fails by 40% to exhaust the absolute value. Aihong Tang QuarkMatter 06, Shanghai**v1 from different collision systems**G. Wang’s talk, 19Nov. Sun. Parallel 3.4 v1 is found being independent of collision systems. Aihong Tang QuarkMatter 06, Shanghai**Longitudinal scaling**STAR preliminary G. Wang’s talk, 19Nov. Sun. Parallel 3.4 PHOBOS Phys. Rev. Lett. 97 012301 (2006) Limiting fragmentation holds for different energies, collision systems and harmonics. STAR preliminary Y. Bai’s talk, 18Nov. Sat. Parallel 2.4 Aihong Tang QuarkMatter 06, Shanghai PHOBOS nucl-ex/0610037 (2006)**Does the proton flow collapse?**NA 49, Phys. Rev. C 68 034903 (2003) “Anti-Flow” observed 1st Order Phase Transition ? Brachmann, Soff, Dumitru, Stocker, Maruhn, Greiner Bravina, Rischke , PRC 61 (2000) 024909. L.P. Csernai, D. Roehrich PLB 458, 454 (1999) M.Bleicher and H.Stocker, PLB 526,309(2002) H. Stoecker, Nucl. Phys. A750 121 (2005) Aihong Tang QuarkMatter 06, Shanghai**Does the proton flow collapse?**flow antiflow Brachmann, Soff, Dumitru, Stocker, Maruhn, Greiner Bravina, Rischke , PRC 61 (2000) 024909. L.P. Csernai, D. Roehrich PLB 458, 454 (1999) M.Bleicher and H.Stocker, PLB 526,309(2002) Aihong Tang QuarkMatter 06, Shanghai**Does the proton flow collapse?**AuAu 62 GeV STAR Phys. Rev. C 73 034903 (2006) “Anti-Flow” --- an inconclusive topic but has good potential Aihong Tang QuarkMatter 06, Shanghai**Are we close to the Critical End Point ?**Recent lattice calculation suggests that the CEP has a small chemical potential, which places it in the range of observability in the energy scans at RHIC Hydrodynamical calculation with CEP shows that CEP acts as an attractor of isentropic trajectories R. Gavai and S. Gupta hep-lat/0509151 (2006) M. Stephanov, hep-ph/0402115 (2006) Look forward to low energy scan program at RHIC C. Nonaka and M. Asakawa, Phys. Rev. C. 71 044904 (2005) Aihong Tang QuarkMatter 06, Shanghai**Summary:**• Rich results from RHIC support a Hydrodynamic expansion of a thermalized fluid in which the collectivity is achieved fast and at the very early time. • Understanding the initial condition plays a key role in understanding what happens thereafter. Anisotropic flow may help us constraint initial conditions. • The PID dependence of division between soft physics and hard physics will help us understanding not only the physics in the soft sector, but also the physics at intermediate pt. • A few key observables from soft physics are found scaling with length, which is directly related to the average number of interaction for a particle before the freeze-out. • Limiting fragmentation holds for different collisions energies, systems and flow harmonics. • Theoretical work suggests that we might be close to the Critical End Point -- look forward to the future energy scan program at RHIC. Aihong Tang QuarkMatter 06, Shanghai

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