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

H. Masui / Univ. of Tsukuba 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 Feb/11/2007 H. Masui / Univ. of Tsukuba

Definition & Terminology Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Anisotropic Flow 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 Z Reaction plane Y X Py Pz Px Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba 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) Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Methods Two main types of methods Event plane method Multi-particle correlation Advantage & disadvantage Assume all correlations are flow (ii) Easy to implement for identified hadrons (iii) Need to determine event plane (i) Reduce non-flow contribution by higher order correlation (ii) No event plane (iii) Larger statistical error Stat. / Sys. error and non-flow effects Typically, order of stat. error is same as k=1 in right eq. Di-jet contributions can be removed by rapidity gap Stat. (sys.) error increase (decrease) for higher order correlation References J.-Y. Ollitrault, Phys. Rev. D48, 1132 (1993) A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C58, 1671 (1998) 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) Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba 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 Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba 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) Feb/11/2007 H. Masui / Univ. of Tsukuba

Multi-particle correlation Non-flow effects contribute order 1/N in 2-particle correlation 1/N3 in 4-particle correlation Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba 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 Feb/11/2007 H. Masui / Univ. of Tsukuba

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 Feb/11/2007 H. Masui / Univ. of Tsukuba

Eccentricity vs centrality Fluctuations lead significant increase of eccentricity at most central and peripheral Feb/11/2007 H. Masui / Univ. of Tsukuba

Results (i) non-identified hadrons Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Integrated v2 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) ~ 50 % increase from SPS to RHIC Hadron cascade underestimate the magnitude of v2 at RHIC Due to the small transverse pressure in early times Feb/11/2007 H. Masui / Univ. of Tsukuba

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 Feb/11/2007 H. Masui / Univ. of Tsukuba

Eccentricity scaling (ii) Statistical errors only Au+Au 200 GeV Cu+Cu 200 GeV PRL: nucl-ex/0610037 PRC C72, 051901R (2005) PHOBOS Collaboration PRL: nucl-ex/0610037 Scaling of v2/part in Cu+Cu and Au+Au Participant eccentricity is relevant geometric quantity for generating elliptic flow Feb/11/2007 H. Masui / Univ. of Tsukuba

Eccentricity scaling (iii) QM2006, S. A. Voloshin QM2006, R. Nouicer Systematic error on dN/dy ~ 10 %, similar on v2 and S Linear increase from SPS to RHIC Eccentricity scaling of v2 reach hydro limit at most central Feb/11/2007 H. Masui / Univ. of Tsukuba

Differential v2, v2(pT) : PHENIX vs STAR (Au+Au) STAR : Phys. Rev. Lett. 93, 252301 (2004) PHENIX : Preliminary QM2006, S. A. Voloshin | η |<0.9 (Main TPC) -3.9 < η < -2.9 (FTPC East) 2.9 < η < 3.9 (FTPC West) 0.15 < pT < 2.0 GeV/c Non-flow effects are under control v2{4}  v2{BBC} ~ v2{FTPC} < v2{2} Similar acceptance : BBC, FTPC Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba v2(pT) in Cu+Cu STAR preliminary (QM06, S. A. Voloshin) PHENIX v2{2} v2{FTPC} PHENIX : nucl-ex/0608033 Larger non-flow effects in smaller system Dominant non-flow is ~ O(1/N) Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Higher order QM06, Y. Bai STAR preliminary || < 1.3 QM05, H. Masui 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) Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba v4/(v2)2 vs pT Star Preliminary Experimentally, v4/(v2)2 ~ 1.2 - 1.5 Ideal hydro prediction v4/(v2)2 = 0.5 Maximum non-flow contribution Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba 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 Feb/11/2007 H. Masui / Univ. of Tsukuba

Results (ii) identified hadrons Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba “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 Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba 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) Feb/11/2007 H. Masui / Univ. of Tsukuba

Multi-strange hadrons Why ?  and  are less affected by hadronic interactions Hadronic interactions at a later stage do not produce enough v2 J. H. Chen et., al, Phys. Rev. C74, 064902 (2006) Y. Liu et., al, J. Phys. G32, 1121 (2006) Feb/11/2007 H. Masui / Univ. of Tsukuba

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 Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Universal scaling of v2 Substantial elliptic flow signals are observed for a variety of particles species at RHIC Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Universal scaling of v2 At mid-rapidity Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba 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 Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Back up Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba 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 … Feb/11/2007 H. Masui / Univ. of Tsukuba

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 Feb/11/2007 H. Masui / Univ. of Tsukuba

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 Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba 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 Feb/11/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba 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 Feb/11/2007 H. Masui / Univ. of Tsukuba