1 / 51

益井　宙 数理物質科学研究科物理学専攻５年次 本審査公開発表会 9 月 27 日 (2007)

This study aims to measure the centrality dependence of identified hadron elliptic flow in Au+Au collisions at √sNN = 200 GeV, in order to understand the relation between eccentricity and v2, extract freeze-out temperature and radial flow velocity, and test the validity of quark number scaling of v2.

raymon
Download Presentation

益井　宙 数理物質科学研究科物理学専攻５年次 本審査公開発表会 9 月 27 日 (2007)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Measurement of Centrality Dependence of Elliptic Flow for Identified Hadrons in Au+Au Collisions at sNN = 200 GeV 益井　宙 数理物質科学研究科物理学専攻５年次 本審査公開発表会 9月27日(2007)

  2. Outline • Introduction • Quark Gluon Plasma (QGP) • Why Elliptic Flow ? • Motivation • Analysis • Centrality, Tracking, Particle identification • Determination of event plane • Results and Discussions • Transverse momentum, Centrality dependence of v2 • Eccentricity scaling of v2, Blast-wave model, Quark number scaling of v2 • Conclusions

  3. Quark Gluon Plasma (QGP) F. Karsch, Lect. Notes Phys. 583, 209 (2002) • Ultimate goal of high energy heavy ion collision experiment • Create and study the properties of Quark Gluon Plasma (QGP) • Quark-hadron phase transition • Degeneracy factor (g) increase by O(g) • g(massless ) = 3 (Nf=2) • Lattice QCD calculation • Energy density jumps at Tc • Tc ~ 150 - 170 MeV • c ~ 1 GeV/fm3 • What is the probe for QGP ? Non-interacting Massless quarks and gluons 8 gluons, 2 spins. 2 spins, 2 charges, 3 colors, 2 quark flavors

  4. Experimental probes for QGP • Transverse collective flow • Introduced & found at 1970’s • Transverse collective emission of particles related to the reaction plane • 3 main types of flow • Radial flow • Directed flow (v1) • Elliptic flow (v2) • Quantitative study can be done with Fourier expansion series of azimuthal distribution for emitted particles S. Voloshin and Y. Zhang, Z. Phys. C70, 665 (1996) A. M. Poskanzer and S. A. Voloshin, PRC58, 1671 (1998)

  5. Why Elliptic flow ? Py Pz Z Y • Initial geometry overlap (eccentricity, )  Final momentum anisotropy (elliptic flow, v2) • The evolution of v2 depends on initial density profile, Equation of State, and system size • Sensitive probe to the early stage of heavy ion collisions X Px Reaction plane

  6. RHIC Relativistic Heavy Ion Collider Brookhaven National Laboratory • The first heavy ion collider in the world • 2 counter-circulating rings • 3.8 km circumference • Top energies: • 100 GeV/nucleon A+A • 250 GeV/nucleon p+p Run1 2000 Au+Au 130 GeV Run2 2001-2002 Au+Au, p+p 200 GeV Run3 2002-2003 d+Au, p+p 200 GeV Run4 2003-2004 Au+Au 200, 62.4 GeV Run5 2004-2005 Cu+Cu 200, 62.4, 22.5GeV, p+p 200 GeV Run6 2005-2006 p+p 200, 62.4 GeV Run7 2006-2007 Au+Au 200 GeV

  7. Collective Expansion E. Schnedermann et al, PRC48, 2462 (1993) • p+p • mT scaling • A+A • pT distribution is different for different particle species PHENIX: Au+Au: PRC 63, 034909 (2004); p+p: PRC74, 024904 (2006) • Blast-wave model describe the single particle spectra • Strong collective expansion at RHIC, T > 0.5c • How about collective azimuthal flow ? Thermal source Explosive source T,  T

  8. Large v2 at RHIC PHENIX: PRL 91, 182301 (2003) • Large v2 at RHIC ! • v2 = 0.1  50 % more particles in in-plane than in out-of-plane • 50 % increase from SPS • Hydrodynamical model successfully describes v2 at pT < 2 GeV/c • Heavier particles have smaller v2 collective expansion • Perfect fluid ?! • Rapid thermalization  ~ 1 fm/c • Success of hydrodynamical model at RHIC Thermalization  v2   • Need to measure centrality dependence of v2 In previous measurements, statistics was not enough to study detailed centrality dependence • High statistics Run4 data sets ! (  20 more statistics ) v2

  9. Quark Recombination ? PHENIX: PRL 91, 182301 (2003) • Quark recombination scenario predicts the existence of universal scaling of v2 for light quarks • Hadron production via quark recombination is expected to be dominant for pT = 2 - 6 GeV/c at RHIC • Quark number scaling of v2 has been observed in minimum bias events for several identified particle species • What is the good probe to study quark number scaling of v2 ?   meson • Because • Small cross section (~ 9 mb) with non-strange hadrons = larger mean free path • Relatively longer life time ~ 45 fm/c compared to that of fireball O(10 fm/c) • Study the validity of the scaling for identified hadrons in a wide range of centrality D. Molnar and S. A. Voloshin, PRL91, 092301 (2003) Z. Lin and C. M. Ko, PRL89, 202302 (2002)

  10. Motivation • What have we learned from collective flow at RHIC ? • Strong collective (radial) flow • Success of Hydrodynamical model (with perfect fluid) for pT < 2 GeV/c • Deviation from Hydrodynamical model for pT > 2 GeV/c • Measure centrality dependence of identified hadron elliptic flow (, K, p, d and ) in sNN = 200 GeV Au+Au collisions • Goal: • Study the relation between eccentricity and v2 • Extract bulk freeze-out temperature and radial flow velocity from v2 • Test the validity of quark number scaling of v2 with identified hadrons for a wide range of centrality

  11. My contributions M1, M2 D1 D2 2001 - 2002 2003 2004 (Time-Of-Flight Detector): Timing calibration, offline software maintenance (Aerogel Cherenkov Counter): Offline software development, maintenance. Simulation for online LVL-2 trigger High pT charged hadron Elliptic Flow Directed Flow analysis by using Elliptic Event plane Fast track analsis for 62.4 GeV Au+Au PID hadron v2 Quark Matter 2002 Fall DNP 62.4 GeV: PRL94, 232302 (2005) D3 D4 2004 2005 2006 Au+Au & Cu+Cu: PRL98, 162301 (2007) Year-3 d+Au timing calibration Year-4 Au+Au 200 GeV & 62.4 GeV timing calibration Year-5 Cu+Cu 200 GeV timing calibration d & : nucl-ex/0703024 (Event Plane calibration): Offline software development. Calibration for Year-4 & Year-5 Event plane for several different subsystems. 200 GeV Year-4 Au+Au and Year-5 Cu+Cu, Elliptic Flow analysis Quark Matter 2004 RNP workshop CIPANP Quark Matter 2005 RHIC-AGS user’s meeting

  12. Analysis 0. PHENIX experiment 1. Event selection (centrality) 2. Track reconstruction 3. Particle identification 4. Event plane determination 5. v2 measurement

  13. PHENIX experiment • Global information (Trigger, centrality, collision vertex, etc) • Beam-Beam Counter (BBC), =2, ||=3-4 • Zero Degree Calorimeter (ZDC) and Shower Maximum Detector (SMD) =2, ||>5 • Central arm • =, ||<0.35 • Tracking, momentum • Drift Chamber (DC), R=2.2m • Pad Chamber (PC), R=2.5m (PC1), 4.9m (PC3) • Particle identification • Time-Of-Flight (TOF), R=5m, =/4 y x z

  14. Global Detectors • The role of BBC and ZDC+SMD • Minimum bias trigger, Collision z-vertex, Centrality, Event plane (BBC, SMD), Start timing for Time-Of-Flight Detector (BBC) 106mm beam beam 53mm 45o 120mm 220mm • BBC • Mesh-dynode PMT (1 inch • diameter) • 3 cm quartz Cherenkov radiator • 64 PMT elements on each BBC • ZDC (+SMD) • Sampling calorimeter (Tungsten, • Scintillator)  3 module • 2 int / module • SMD is located between 2nd and 3rd ZDC • 8  8 bins in (x,y) space

  15. Centrality • Geometry of heavy ion collision • Impact parameter • Number of participant nucleons • Multiplicity, energy of spectator neutrons • Number of Participant (Npart) • Calculate Npart by Glauber Model • Glauber Model • Thickness function • Woods-saxon density distribution ZDC Spectator Participant BBC Spectator

  16. Tracking • Drift Chamber •  : incident angle, K : effective field integral, p : momentum • Momentum determination • Momentum resolution : p/p = 0.7 %  1 % p • Pad chamber • 3 dimensional hit point (straight line) • Reconstruct pz (PC1) • Associate DC tracks to outer detectors (PC3, TOF) Y X

  17. Particle identification: /K/p/d • TOF (Flight time  Mass square) • Timing resolution: TOF ~ 120 ps, EMC ~ 500 ps • Particle separation • TOF • /K ~ 3 GeV/c • Can be extended up to pT ~ 4 GeV/c by using asymmetric cuts • K/p ~ 4 GeV/c, d :1 - 4 GeV/c • EMC • /K ~ 1.5 GeV/c

  18. Particle identification:  • K+K- • Branching ratio = 49 % • Reconstruct  meson by invariant mass • 1 < pT < 4 GeV/c • Kaon from TOF detector, use also EMCal to increase the statistics at low pT • Combinatorial background is estimated by event mixing technique • Background distribution is normalized in M = 1.2 - 1.3 GeV/c2 • Signal extraction • Breit-wigner + constant

  19. Event plane @ PHENIX • Event plane determined at BBC (|| = 3 - 4) • Cover full azimuth (Half of full azimuth in Central arm) • Measure particles with respect to the event plane at BBC • Large rapidity gap (|| ~ 3) reduce non-flow effects* * contribute the flow signal NOT originated from reaction plane PHOBOS: PRL91, 052303 (2003)

  20. Flattening correction • Reconstructed EP usually not exactly flat • Detector acceptance • Detector response • Beam position offset • Etc … • Overall “shift” correction • Remove almost all bias (black  blue) • Flattening correction • remove remaining non-flat contributions (blue -> red) • Requirement •  should be small • Isotropic distribution -> vanishing of k-th Forier moment of the new distribution () shift Flattening

  21. Event plane resolution & Extract v2 Central Low multiplicity Small v2 Peripheral • Assumptions : (for a given centrality, ) • All particles are independent in the same event • Multiplicity is large (>>1) • No fluctuation of v2 ** Valid only equal multiplicity event  Event plane resolution of each sub-event is same

  22. Results &Discussions(1) Eccentricity scaling(2) Blast-wave fit(3) Quark number scaling

  23. v2(pT) for , K, and p • Increase statistics from Run2 (20) • Run2 ~ 30 M event, Run4 ~ 600 M event • sin(2[-BBC]) = 0 as we expect • No charge dependence • Consistent with Run2 results • Consistent with K0s and ’s from STAR experiment Systematic error Event plane: ~ 6 % at mid-central, ~20 % at central and peripheral Track matching cuts, PID cuts, energy loss cuts ~ 3 % pT > 3 GeV/c Random background, ~1 - 10 % (centrality dependent) Mis-identification for Kaon, ~2 - 12 % (centrality dependent)

  24. Centrality dependence: /K/p • v2(pT) increase with centrality • Qualitatively consistent with the centrality dependence of initial geometry overlap

  25. Charge dependence • 3 % difference of v2 for p and pbar, not observed for  and K • Feed down decay from  ? • v2 for net proton ? MC simulation

  26. Glauber Model simulation • Glauber MC simulation • NN = 42 mb • Woods-saxon density profile • R = 6.38 fm, a = 0.53 fm, 0 = 0.17 fm-3 • Calculate number of participating nucleons and number of collisions • In p+p, Npart = 2, Ncoll = 1 • Centrality is determined by the measured cross section • Eccentricity • “Standard” eccentricity: std • Calculated with fixed axes (x, y) • “Participant ” eccentricity: var • Use variable axes, which is defined by the positions of participant nucleons event-by-event • Bracket denote the average over all events and all participating nucleons

  27. Eccentricity scaling (1) • Scaling with std breaks between in peripheral Au+Au and in central Cu+Cu • Need to take into account the event-by-event position fluctuation of participant nucleons  Participant eccentricity

  28. Eccentricity scaling (2) • Non-zero  at b = 0,   1 at most peripheral • (Cu) > (Au) due to larger fluctuations in smaller system • Scaling works in Au+Au and Cu+Cu with var • Participant eccentricity is the relevant geometric quantity to explain the v2/ among the different systems

  29. Results &Discussions(1) Eccentricity scaling (2) Blast-wave fit(3) Quark number scaling

  30. Blast-wave model A. Kiyomichi: PhD thesis • Blast-wave model • Thermal equilibrium + collective transverse expansion • Freeze-out temperature (T) and radial flow velocity (T) • Transverse momentum spectra have been well described • Strong collective expansion : T > 0.5c • How about v2 ? v2 is expected to saturate in the early stage O(a few fm/c)  Different sensitivity to the bulk properties compared to the single particle spectra • Need to extend the standard Blast-wave framework in non-central collisions (0)

  31. Extended Blast-wave model • Extend standard Blast-wave parameterization in order to fit v2(pT) in non-central collisions • Assumptions • Use density distributions from initial geometry overlap instead of uniform density • Velocity profile • Use Density gradient distributions • Eccentricity () is fixed by initial overlap density • Velocity anisotropy (2) is fixed by the velocity profile • 2 free parameters • Temperature: T • Magnitude of transverse boost velocity: T reaction plane

  32. Density & gradient distributions • Calculate Npart(x, y) and Ncoll(x, y) from Woods-saxon density profile • Direction of density gradient  direction of boost • Length = magnitude of boost

  33. Fitting results • Minimize 2 by fitting K and p simultaneously • Exclude  from fitting due to resonance decay contributions and bad 2 • Fitting , K and p gives essentially same results • Results • Fitting results from spectra are consistent with standard Blast-wave model • Ncoll density gives better 2 • Radial flow velocity is almost unchanged • Temperature is larger for v2 compared to spectra • pT spectra: T = 109 (MeV) • v2: T = 330 (MeV)  A hint of early saturation of v2 Left: Npart density profile Right: Ncoll density profile

  34. 2 contours • Scan minimum 2 in (T, T) space • Red and blue circles show 3  2 contours • Solid minimum position for both v2 and spectra • T ~ 3 - 4 MeV, T ~ 0.005 - 0.01 • T : almost unchanged • T : 100 - 200 MeV larger for v2 v2 v2 spectra spectra

  35. Sensitivity to Eccentricity • Include effective dynamical effect in our extended Blast-wave model • Study sensitivity of fitting parameters to eccentricity • Assume 1D expansion in x direction (reaction plane) • Velocity distribution is re-calculated for a given density distribution Initial density In-plane 1D expansion R0 : RMS of initial density distribution

  36. Results • Radial velocity and T from spectra are not changed with  • Temperature from v2 fit strongly decrease with  • 2/NDF < 1 up to  ~ 0.05 with systematic error • T(v2) ~ Tch (150 MeV) > T(spectra) at the eccentricity extracted by HBT analysis  early freeze-out of v2 ?

  37. Results &Discussions(1) Eccentricity scaling (2) Blast-wave fit(3) Quark number scaling

  38. Quark number scaling of v2 • Ratio of (Data) to (Fit) • Close to 1 at intermediate pT  Quark number scaling • Scaled v2 show remaining mass hierarchy among different particle species at low pT • v2() > v2(K) > v2(p) • Can we explain v2(pT) for different particles from low to intermediate pT ? v2 for constituent quarks • Assumptions: • Thermal pT distribution, momentum conservation • Universal v2 for light quarks, v2 << 1 pT for constituent quarks

  39. Transverse kinetic energy scaling PHENIX: nucl-ex/0608033 • Assume v2 is determined by the transverse kinetic energy • Pressure gradient  Collective kinetic energy • KET scaling holds up to KET ~ 1 GeV • Clear splitting for mesons and baryons • Possible hint of quark d.o.f become apparent at higher KET • Quark number scaling for v2(KET) ! baryon meson

  40. Centrality dependence: /K/p • Quark number scaling with KET holds for all centrality within systematic errors, except for KET/nq < 0.3 GeV • Radial flow after hadronization ?

  41. Extract d &  v2 N. Borghini and J.-Y. Ollitrault PRC70, 064905 (2004) d • Simultaneous fitting of relative yield and v2 • Fitting mass distributions by signal + background • S/B depends on mass • Parameterize S/(S+B) and B/(S+B) vs mass • Fitting v2obs vs mass with 2 free parameters v2S and v2B 

  42. Deuteron &  v2 • Deuteron () v2 is smaller than others for pT < 2 (1.5) GeV/c • For pT > 2 (1.5) GeV/c, v2 is as large as other hadrons

  43. Centrality dependence: d,  • Sizeable v2 for both d and  • Centrality dependence ?

  44. Scaled v2 for  meson • Quark scaling of v2 also works for d and  mesons • Suggest that partonic collectivity is established at pre-hadronic stage

  45. Centrality dependence: d,  • KET + quark number scaling also works for d and  mesons in central to peripheral collisions

  46. Conclusions • Measure elliptic flow (v2) parameter of identified hadrons for a broad range of centrality and pT • Large data sets in Run4 allow us to study detailed centrality dependence of v2 for different particle species • Increase v2 with increasing centrality • Same mass ordering for measured centrality range • Eccentricity scaling of v2 • Scaling works for both Au+Au and Cu+Cu with participant eccentricity  Participant eccentricity is the relevant geometric quantity • Extended Blast-wave model • Larger temperature from v2 fit compared to pT spectra fit • Better fitting results with Ncoll density profile • T(v2) ~ Tch(150 MeV) at the eccentricity extracted by HBT analysis  Suggest early freeze-out for v2 • Transverse Kinetic energy (KET) + Quark Number scaling • Holds for all particles species in measured centrality bins within systematic errors • Finite v2 & quark number scaling of v2 with KET for  meson  Partonic flow by collective pressure

  47. Back up

  48. v2(pT): SPS vs RHIC SPS (sNN = 17 GeV) RHIC (sNN = 200 GeV) • Hydrodynamical model (Perfect fluid: no viscosity, no heat conductivity) • SPS: overestimate v2 • RHIC: good agreement for pT < 2 GeV/c  Rapid (0 ~ 1 fm/c) thermalization at RHIC • Hydrodynamical model • Keep mass ordering • Increase linearly Data • Meson v2 start to saturate • v2(p) > v2( or K) Are there any mechanisms to explain this behavior of v2 ? Hydrodynamical model: 1st order phase transition, Tc=165 MeV, Tf=120 MeV, 0 = 0.8 fm/c PHENIX: PRL 91, 182301 (2003) NA49: nucl-ex/0606026 (2007)

  49. Quark recombination Recombination Fragmentation Carry only a fraction (z < 1) of the initial quark momentum Hadrons from coalescence have larger momentum than the quark momentum • There can be a region where quark recombination process becomes dominant when parton phase space density quickly drops with increasing pT • At RHIC, it is expected quark recombination is dominant for intermediate pT region, pT ~ 2 - 6 GeV/c R. C. Hwa and C. B. Yang, PRC66, 025205 (2002); V. Greco et al, PRL90, 202302 (2003); R. J. Fries et al, PRL90, 202303 (2003)

  50. Simultaneous /K/p fit

More Related