Anisotropic Flow @ RHIC Hiroshi Masui / Univ. of Tsukuba Mar/03/2007 Heavy Ion Cafe

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 Initial spatial anisotropy (eccentricity, ) Low pT Re-scattering (pressure gradient) Intermediate pT Quark coalescence/recombination High pT Jet quenching Z Reaction plane Y X Py Pz Px Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Observables Particle azimuthal distributions by Fourier expansion v1 = “Directed Flow” 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) Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Flow analysis @ PHENIX PHOBOS: PRL91, 052303 (2003) Event plane method Determined at forward and backward beam counter (BBC, || = 3.0 - 3.9) Correlate paticles at mid-rapidity (|| < 0.35) and BBC event plane Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Event plane method  “Event plane” Estimate of true reaction plane Brackets denote average over all events and all particles in a selected rapidity window, 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 Mar/03/2007 H. Masui / Univ. of Tsukuba

Flattening correction Acceptance anisotropy should be removed Re-centering correction black -> blue Flattening correction remove remaining non-flat contributions (blue -> red)  should be small Isotropic distribution -> vanishing of k-th Forier moment of the new distribution () Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Large v2 at RHIC 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 Mar/03/2007 H. Masui / Univ. of Tsukuba

Event plane = reaction plane ? We cannot determine the direction of 2nd moment BBC event plane w.r.t. the reaction plane  sign of v2 is unknown 1st moment event plane give us the reference direction y Py or x Px Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Validity check (1) 2nd moment BBC event plane Same direction Cannot distinguish in-plane or out-of-plane Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Validity check (2) 2nd moment Central Arm Event plane Same direction to BBC Event plane Still, sign is unknown Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Validity check (3) 1st moment BBC and SMD Event plane Back-to-back direction for both BBC and SMD Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Validity check (4) BBC(1st) - SMD(1st) correlation Opposite direction to same side SMD Opposite v1 for BBC and SMD Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Validity check (5) BBC(2nd) - SMD(1st) correlation Positive correlation  v2 is in-plane ! Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Outline Large v2 at RHIC v2 is in-plane ! Initial geometry origin ?! v2 is expected to be driven by initial eccentricity pressure (density) gradient Explore the origin of v2 : Several scaling properties of v2 Eccentricity scaling Transverse kinetic energy (KET) scaling + NCQ (Number of Constituent Quark) scaling Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Eccentricity Estimate eccentricity by Glauber Model std (part) gives minimum (maximum) eccentricity Since part include auto-correlation True  lies between std and part ? Mar/03/2007 H. Masui / Univ. of Tsukuba

Eccentricity scaling (1) Scaling of v2/part in Cu+Cu and Au+Au Participant eccentricity is relevant geometric quantity for generating elliptic flow PRL: nucl-ex/0610037 PRC C72, 051901R (2005) standard participant Cu+Cu 200 GeV Statistical errors only Au+Au 200 GeV PHOBOS Collaboration PRL: nucl-ex/0610037 Mar/03/2007 H. Masui / Univ. of Tsukuba

Eccentricity scaling (2) QM2006, S. A. Voloshin v2{ZDC} scales std Insensitive the fluctuations in the participant eccentricity Linear increase of v2/ from SPS to RHIC Incomplete thermalization ? Saturation ? Mar/03/2007 H. Masui / Univ. of Tsukuba

Eccentricity scaling (3) PHENIX uses integrated v2 as the estimate of eccentricity Assume  = k  v2, k = 3.1  0.2 from Glauber model Cancel systematic error from event plane v2 scales with  and the scaled v2 values are independent of the system size Centrality independent shape of v2(pT)/v2 pT does not change so much nucl-ex/0608033 Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba KET scaling Baryon nucl-ex/0608033 Meson PRC69, 034909 (2004) Pressure gradient  Collective kinetic energy Radial flow with common velocity T ~ 0.5c Gain more energy for heavier particles  mass ordering of v2 KET scaling holds up to KET ~ 1 GeV Clear meson and baryon splitting at intermediate pT Mar/03/2007 H. Masui / Univ. of Tsukuba

Centrality dependence KET scaling holds for measured centrality range up to KET ~ 1 GeV Centrality dependence ? Mar/03/2007 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) Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba  meson  meson v2 Important test at intermediate pT m ~ mp Mass (radial flow) effect, or constituent quarks  scales like a meson s-quark flow, not mass effect Smaller radial flow velocity also support the partonic flow at pre-hadronic stage QM06, A. Taranenko SQM06, N. Xu Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Universal scaling of v2 QM06, A. Taranenko Substantial elliptic flow signals are observed for a variety of particles species at RHIC Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Universal scaling of v2 QM06, A. Taranenko At mid-rapidity Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Summary Eccentricity scaling RHIC v2 is driven by eccentricity In-plane v2, and eccentricity scaling Participant eccentricity is relevant geometric quantity for generating elliptic flow KET scaling KET scaling of v2 holds up to KET ~ 1 GeV Consistent with the flowing matter with common velocity At intermediate pT, NCQ scaling holds a variety of particles species Indication of light quark (u, d, s) collectivity at pre-hadronic stage Universal scaling of v2 (Eccentricity + KET + NCQ) works for a variety of particle species and for a side range of centrality Need to investigate the validity range of scaling Mar/03/2007 H. Masui / Univ. of Tsukuba

H. Masui / Univ. of Tsukuba Back up Mar/03/2007 H. Masui / Univ. of Tsukuba

BBC - SMD EP correlation Positive correlation, v2 > 0 at BBC Expected cos(2) is given by Mar/03/2007 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 Mar/03/2007 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) Mar/03/2007 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 Mar/03/2007 H. Masui / Univ. of Tsukuba