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Anisotropic Flow @ RHIC

Anisotropic Flow @ RHIC. Hiroshi Masui / Univ. of Tsukuba Feb./11/2007 RHIC 高エネルギー原子核反応の物理研究会、 RHIC 現象論松本合宿. Outline. Introduction Anisotropic flow, eccentricity Results Several scaling relations have been observed especially for elliptic flow Eccentricity scaling

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Anisotropic Flow @ RHIC

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  1. Anisotropic Flow@ RHIC Hiroshi Masui / Univ. of Tsukuba Feb./11/2007 RHIC高エネルギー原子核反応の物理研究会、RHIC現象論松本合宿

  2. Outline • Introduction • Anisotropic flow, eccentricity • Results • Several scaling relations have been observed especially for elliptic flow • Eccentricity scaling • Scaling of higher order anisotropy • mT and NCQ scaling of elliptic flow • Summary H. Masui / Univ. of Tsukuba

  3. Definition& Terminology H. Masui / Univ. of Tsukuba

  4. Anisotropic Flow Z • What ? • Azimuthally anisotropic emission of particles with respect to the reaction plane • Why ? • The probe for early time • Driven by • initial eccentricity of overlap zone • Re-interactions among the particles (pressure gradient) • Initial eccentricity --> Final momentum anisotropy Reaction plane Y X Pz Py Px H. Masui / Univ. of Tsukuba

  5. Observables • Particle azimuthal distributions by Fourier expansion • Odd harmonics (v1, v3, …) vanish at mid-rapidity in symmetric collision • v2 = “Elliptic Flow” S. Voloshin and Y. Zhang, Z. Phys. C70, 665 (1996) A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C58, 1671 (1998) H. Masui / Univ. of Tsukuba

  6. Methods Two main types of methods H. Masui / Univ. of Tsukuba

  7. Event plane method • Brackets denote average over all events and all particles, kn is “event plane resolution” • w (weight) is chosen to maximize the event plane resolution (ex. pT, multiplicity etc) • The best weight is vn itself  H. Masui / Univ. of Tsukuba

  8. Event plane @ PHENIX • Event plane determination @ Beam-Beam Counter (BBC), || ~ 3 - 4 • Large rapidity gap between measured particles ( ~ 0) and event plane  Reduce non-flow effects • di-jet contribution is negligible (nucl-ex/0609009) H. Masui / Univ. of Tsukuba

  9. Multi-particle correlation 2-particle correlation • Non-flow effects contribute order • 1/N in 2-particle correlation • 1/N3 in 4-particle correlation 4-particle correlation H. Masui / Univ. of Tsukuba

  10. Terminology • std : standard eccentricity • Spatial anisotropy in coordinate space • part : Participant eccentricity • Effect from the fluctuations in the positions of participant nucleons • v2{EP2} : v2 with respect to the 2nd harmonic Event Plane • v2{BBC} : v2{EP2} by BBC in PHENIX • v2{FTPC} : v2{EP2} by Forward-TPC in STAR • v2{EP}(AA-pp) : Modified event plane method • v2{n} : v2 from n-th particle cumulants • v4{n} : v4 from n-th particle cumulants H. Masui / Univ. of Tsukuba

  11. Eccentricity : definition • Participant eccentricity in a given event is defined by the axes (x’, y’) • … denote average over all participant nucleons and events in the same impact parameter • {…} denote the average over all participants in one collision event H. Masui / Univ. of Tsukuba

  12. Eccentricity vs centrality • Fluctuations lead significant increase of eccentricity at most central and peripheral H. Masui / Univ. of Tsukuba

  13. Results (i)non-identified hadrons H. Masui / Univ. of Tsukuba

  14. Integrated v2 • ~ 50 % increase from SPS to RHIC • Hadron cascade underestimate the magnitude of v2 at RHIC • Due to the small transverse pressure in early times QM2005, H. Masui RQMD FOPI : Phys. Lett. B612, 713 (2005). E895 : Phys. Rev. Lett. 83, 1295 (1999) CERES : Nucl. Phys. A698, 253c (2002). NA49 : Phys. Rev. C68, 034903 (2003) STAR : Nucl. Phys. A715, 45c, (2003). PHENIX : Preliminary. PHOBOS : nucl-ex/0610037 (2006) H. Masui / Univ. of Tsukuba

  15. Eccentricity scaling (i) • Assume  = k  v2 • A Glauber model estimate of  gives • k = 3.1  0.2 • v2 scales with  and the scaled v2 values are independent of the system size Scale invariance of ideal hydrodynamics nucl-ex/0608033 H. Masui / Univ. of Tsukuba

  16. Eccentricity scaling (ii) Statistical errors only • Scaling of v2/part in Cu+Cu and Au+Au • Participant eccentricity is relevant geometric quantity for generating elliptic flow Au+Au 200 GeV Cu+Cu 200 GeV PRL: nucl-ex/0610037 PHOBOS CollaborationPRL: nucl-ex/0610037 PRC C72, 051901R (2005) H. Masui / Univ. of Tsukuba

  17. Eccentricity scaling (iii) QM2006, S. A. Voloshin QM2006, R. Nouicer • Linear increase from SPS to RHIC • Eccentricity scaling of v2 reach hydro limit at most central H. Masui / Univ. of Tsukuba

  18. Differential v2, v2(pT) :PHENIX vs STAR (Au+Au) • Non-flow effects are under control • v2{4}  v2{BBC} ~ v2{FTPC} < v2{2} • Similar acceptance : BBC, FTPC STAR : Phys. Rev. Lett. 93, 252301 (2004) PHENIX : Preliminary QM2006, S. A. Voloshin H. Masui / Univ. of Tsukuba

  19. v2(pT) in Cu+Cu STAR preliminary (QM06, S. A. Voloshin) • Larger non-flow effects in smaller system • Dominant non-flow is ~ O(1/N) PHENIX v2{2} v2{FTPC} PHENIX : nucl-ex/0608033 H. Masui / Univ. of Tsukuba

  20. Higher order QM06, Y. Bai STAR preliminary || < 1.3 • Non-zero v4 at RHIC • v4 ~ (v2)2 (Ollitrault) • v4/(v2)2 is a probe of ideal hydro behavior • N. Borghini and J.-Y. Ollitrault, Phys. Lett. B642, 227 (2006) QM05, H. Masui H. Masui / Univ. of Tsukuba

  21. v4/(v2)2 vs pT • Experimentally, v4/(v2)2 ~ 1.2 - 1.5 • Ideal hydro prediction v4/(v2)2 = 0.5 • Maximum non-flow contribution Star Preliminary H. Masui / Univ. of Tsukuba

  22. Summary (i) • The magnitude of v2 is as large as that from perfect fluid hydrodynamics at RHIC • 50 % increase from SPS • Hadron cascade cannot reprduce the magnitude of v2 • Eccentricity scaling • Consistent description of Au+Au and Cu+Cu v2 systematics by participant eccentricity • Different conclusion from different experiments • Non-flow effects are under control via • Large rapidity gap (PHENIX, STAR) • Multi-particle correlation (STAR) • Higher order, v4 • Non-zero v4 is observed • v4/(v2)2 ~ 1 > 0.5 but systematic error is huge at high pT H. Masui / Univ. of Tsukuba

  23. Results (ii)identified hadrons H. Masui / Univ. of Tsukuba

  24. “mT scaling” of v2 • v2{BBC} for identified hadrons • At low pT, mT scaling of v2 • Radial flow leads mass ordering of v2 • Meson-Baryon grouping at intermediate pT • Quark coalescence, recombination H. Masui / Univ. of Tsukuba

  25. NCQ scaling of v2 • NCQ scaling indicate the collective flow evolves in quark level • Number of Constituent Quark scaling by quark coalescence / recombination model • Assumption • Exponential pT spectra • Narrow momentum spread (-function) • Common v2 for light quarks (u, d, s) R. J. Fries, et., al, Phys. Rev. C68, 044902 (2003) V. Greco, et., al, Phys. Rev. C68, 034904 (2003) H. Masui / Univ. of Tsukuba

  26. Multi-strange hadrons J. H. Chen et., al, Phys. Rev. C74, 064902 (2006) • Why ? •  and  are less affected by hadronic interactions • Hadronic interactions at a later stage do not produce enough v2 Y. Liu et., al, J. Phys. G32, 1121 (2006) H. Masui / Univ. of Tsukuba

  27. Multi-strange hadrons QM06, A. Taranenko •  meson v2 is more consistent with meson v2 than baryon v2 • Show sizable v2 • Collectivity at pre-hadronic stage, s-quark flow STAR preliminary 200 GeV Au+Au SQM06, M. Oldenburg H. Masui / Univ. of Tsukuba

  28. Universal scaling of v2 • Substantial elliptic flow signals are observed for a variety of particles species at RHIC H. Masui / Univ. of Tsukuba

  29. Universal scaling of v2 At mid-rapidity H. Masui / Univ. of Tsukuba

  30. Summary (ii) • Mass ordering at low pT • Predicted by hydrodynamics (radial flow effect) • At intermediate pT, NCQ scaling holds a variety of particles species • Indication of light quark (u, d, s) collectivity at pre-hadronic stage • Universal v2 motivated by perfect fulid hydrodynamics is observed for both mesons and baryons over a broad range of kinetic energy, centrality via NCQ scaling H. Masui / Univ. of Tsukuba

  31. Back up H. Masui / Univ. of Tsukuba

  32. Flow measurements • 2 main types of methods • “Event plane” method • J.-Y. Ollitrault, Phys. Rev. D48, 1132 (1993) • A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C58, 1671 (1998) • Multi-particle correlation method • N. Borghini, P. M. Dinh, J.-Y. Ollitrault, Phys. Rev. C63 054906 (2000); Phys. Rev. C64, 054901 (2001) • R. S. Bhalerao, N. Borghini, J.-Y. Ollitrault, Nucl. Phys. A727, 373 (2003); Phys. Lett. B580, 157 (2004) • Different sensitivity to “non-flow” effects • Correlations unrelated to the reaction plane, ex. jets, resonance decays etc … H. Masui / Univ. of Tsukuba

  33. Non-flow effects from Jets (i) • Nucl-ex/0609009 • “Trigger” pT : 2.5 < pT < 4 GeV/c • “Associated” pT : 1 < pT < 2 GeV/c • Background Au+Au events from HIJING • Checked to reproduce the charged hadron multiplicity in  from PHOBOS • v2 is implemented according to the PHENIX v2 measurement (nucl-ex/0608033) • Di-jet pairs are generated from PYTHIA H. Masui / Univ. of Tsukuba

  34. Non-flow effects from Jets (ii) • Fake v2 for leading particles • Fake v2 is negligible in BBC acceptance (3 <  < 4) • NOTE • Results are not corrected event plane resolution H. Masui / Univ. of Tsukuba

  35. Non-flow effect on v4 • Consider 3-particle correlation • Maximum non-flow contribute if (i, k) correlate non-flow and (j, k) correlate flow Non-flow flow H. Masui / Univ. of Tsukuba

  36. Clear  signal •   K+K- • Typical S/N ~ 0.3 • Centrality 20 – 60 % • S/N is good • Event plane resolution is good • Separation of v2 between meson and baryon is good • Magnitude of v2 do not vary very much Before subtraction Signal + Background Background After subtraction H. Masui / Univ. of Tsukuba

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