Elliptic Flow and Constituent Quark Scaling

1. Elliptic Flow and Constituent Quark Scaling Marcus Bleicher1 & Xianglei Zhu2 1Institut für Theoretische Physik 2Frankfurt Institute for Advanced Studies Goethe Universität Frankfurt Germany Marcus Bleicher, Strange Quark Matter 2006

2. Thanks to the UrQMD group@ Frankfurt • Sascha Vogel (Resonances) • Stephane Haussler (Event-by-Event Fluctuations) • Hannah Petersen (Flow at FAIR) • Diana Schumacher (Di-Leptons) • Qingfeng Li (HBT) • Xianglei Zhu (Elliptic Flow and Charm) • and Horst Stoecker, Yan Lu, Paul Sorensen, Nu Xu Marcus Bleicher, Strange Quark Matter 2006

3. Parton Number Scaling of v2 • in leading order of v2, recombination predicts: Is this the only explanation? P. Soerensen, UCLA & STAR @ SQM2003 Bass, Nonaka, Mueller, Fries, 2003 Marcus Bleicher, Strange Quark Matter 2006

4. Contents • Introduction • Different methods for v2 • Constituent quark scaling • Summary Marcus Bleicher, Strange Quark Matter 2006

5. The tool: UrQMDv2.2 • Non-equilibrium transport model • Hadrons and resonances • String excitation and fragmentation • Cross sections are parameterized via AQM or calculated by detailed balance • pQCD hard scattering at high energies • Generates full space-time dynamics of hadrons and strings Marcus Bleicher, Strange Quark Matter 2006

6. Model check: Multiplicities • Rapidity distributions in line with data (Phobos) • Centrality dependence in line with data Marcus Bleicher, Strange Quark Matter 2006

7. Model check: pp-correlations Q. Li, M.B., H. Stoecker, nucl-th/0602032; Data: STAR • Correlations are well described except for most central reactions Marcus Bleicher, Strange Quark Matter 2006

8. Anisotropic flow Fourier expansion of the transverse angular distribution of the emitted particles: Reaction Plane v1 – directed flow v2 -- elliptic flow Marcus Bleicher, Strange Quark Matter 2006

9. Elliptic flow coordinate-space-anisotropymomentum-space-anisotropy y py px x • Elliptic flow is a self-quenching effect  shuts itself off after the early stage of the reaction • Radial flow (<pT>) is an integral quantity  developed over the whole reaction time Marcus Bleicher, Strange Quark Matter 2006

10. V2 at RHIC • Magnitude of v2 is large • Meson-baryon ordering • Constituent quark scaling • Decrease of v2 at high pT Are these unique QGP signatures? Marcus Bleicher, Strange Quark Matter 2006

11. Cumulant: Rapidity • Differential flow At large eta, the non-flow effects are less obvious. If the v2 fluctuations are also negligible to the cumulant method, the v2{2}, v2{4} and v2{6} should all agree with the exact v2. X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005 Marcus Bleicher, Strange Quark Matter 2006

12. Cumulants: Centrality In the most central bin: The fluctuations give larger v2{6} but smaller v2{4} In the very peripheral bins: The fluctuations give larger v2{6} and v2{4} Agree with the prediction of MCG model BUT: In the semi-central bins: the v2 fluctuations can be neglected. • Integral flow X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005 Marcus Bleicher, Strange Quark Matter 2006

13. Compare apples to apples • Differential flow • v2{2} is heavily affected by the non-flow effects especially at large pT. • The non-flow effects have been eliminated in v2{4} and v2{6}. • But v2{4} is still a little larger than the exact v2. Use Lee-Yang zero method X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005 LYZ-method in UrQMD: nucl-th/0601049 Marcus Bleicher, Strange Quark Matter 2006

14. Elliptic flow: Magnitude • Integral flow • V2 from UrQMD is about 50% smaller than the data • Space for parton rescattering? STAR data is from nucl-ex/0409033 X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005 Marcus Bleicher, Strange Quark Matter 2006

15. Energy dependence • Qualitative description OK • Importance of potentials at low energies • Lack of pressure shows up at lower SPS energies H. Petersen, X. Zhu, M.B. Marcus Bleicher, Strange Quark Matter 2006

16. When is v2 created? • The earlier a particle is emitted the larger is the elliptic flow • The higher the pT of a particle the larger is the elliptic flow • High pT particles are more sensitive to the initial v2 Y. Lu, M.B., et al., nucl-th/0602009 Marcus Bleicher, Strange Quark Matter 2006

17. Initial ‘string matter’ • String matter dominates the early stages • lack of early pressure ‘string matter‘ = QGP? • Strong color field or color glas or a hydrodynamical initial state fix the initial pressure problem H. Petersen, X. Zhu, M.B. Marcus Bleicher, Strange Quark Matter 2006

18. Back to the story line: Messengers from the mixed phase: Multi-strange hadrons • freeze-out early • all v2 should be from QGP • Thus, if W, X and f have sufficient v2 • Proof of partonic collectivity (maybe QGP) Marcus Bleicher, Strange Quark Matter 2006

19. Where will be the charm? Indications of early freeze-out • Two different groups: (a) p,K,p (b) f, W • Multi-strange particle freeze-out earlier than bulk K. Schweda, STAR  Sensitivity to early (partonic) stage Marcus Bleicher, Strange Quark Matter 2006

20. Early freeze-out: models • Flow ordering  different hadronic cross sections UrQMD, RHIC A. Dumitru, S. Bass, M.B., H. Stoecker, Phys.Lett.B460:411-416,1999 Marcus Bleicher, Strange Quark Matter 2006

21. Do multi-strange hadrons flow? • Data indicates approximate 3:2 scaling with constituent quarks • Baryons are generally below mesons • Decrease of v2 at high pTIs this rough scaling a signal for recombination? P. Sorensen, SQM 2006 Marcus Bleicher, Strange Quark Matter 2006

22. V2(pT) for various hadrons Maybe its just the additive Quark model? min. bias UrQMD Y. Lu, M.B., et al., nucl-th/0602009 Open – MesonsFull -- Baryons 1) Clear separation of meson and baryon v2 2) Low pT, v2(meson)>v2(baryon) 3) High pT, v2(m)<v2(b) 4) v2’s of multi-strange hadrons comparable to light hadrons Marcus Bleicher, Strange Quark Matter 2006

23. NCQ-scaling • there might be an ordering of v2/n:W<X<L<N UrQMD Y. Lu, M.B., et al., nucl-th/0602009 AQM cross sections: Np: 26 mbLp: 23 mbXp: 20 mbWp: 16 mb pp: 18 mbKp: 14 mb NCQ-scaling of v2 is roughly reproduced in UrQMD! Marcus Bleicher, Strange Quark Matter 2006

24. B-M Asymmetry Inclusion of gluons in recombination was predicted to lead to a larger meson v2/n than baryon v2/n: B.Müller, et al. nucl-th/0503003 Marcus Bleicher, Strange Quark Matter 2006

25. Summary • At RHIC (transport models w/ strings and hadrons): • Part of v2 might also come from hadronic stage • non-flow correlations are correct • Mass ordering is correct • (B-M) Asymmetry has correct shape • Constituent quark scaling (w/o ReCo! but AQM) • However, transport models w/o QGP produce too few pressure in the early stage above 30 GeV Marcus Bleicher, Strange Quark Matter 2006

26. Back up slides Marcus Bleicher, Strange Quark Matter 2006

27. Model check: Expansion Transverse Expansion of the bulk is described Model uncertainties on level of 30-50% Bratkovskaya, M.B. et al., Phys.Rev.C69:054907,2004 Uncertainties depend on:PYTHIA implementation and properties of high mass resonances Marcus Bleicher, Strange Quark Matter 2006

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