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益井　宙 数理物質科学研究科物理学専攻５年次 TAC セミナー 4 月 24 日 (2007)

Measurement of Centrality Dependence of Elliptic Flow for Identified Hadrons in  s NN = 200 GeV Au+Au Collisions. 益井　宙 数理物質科学研究科物理学専攻５年次 TAC セミナー 4 月 24 日 (2007). Outline. Introduction Why Elliptic Flow ? Motivation Analysis PHENIX subsystem Event plane method

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益井　宙 数理物質科学研究科物理学専攻５年次 TAC セミナー 4 月 24 日 (2007)

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  1. Measurement of Centrality Dependence of Elliptic Flow for Identified Hadrons in sNN = 200 GeV Au+Au Collisions 益井　宙 数理物質科学研究科物理学専攻５年次 TACセミナー 4月24日(2007)

  2. Outline • Introduction • Why Elliptic Flow ? • Motivation • Analysis • PHENIX subsystem • Event plane method • Results and Discussions • Conclusion

  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 ? Z Py Pz • Why do we use elliptic flow as the probe of QGP ? 1. Clear origin • Initial geometry overlap (eccentricity) • re-interaction among particles + density distribution • Pressure gradient is the driving force of elliptic flow 2. Sensitive to the phase transition  equation of state (EOS) 3. Signal is self-quenching with time  early signal 4. Sensitive to the local thermal equilibrium ( vs R, :mean free path R: characteristic length scale of the system) • Free streaming  v2 = 0 Px Reaction plane Y X

  6. How early ? B. Zhang et al, PLB455, 45 (1999) P. Kolb et al, PRC62, 054909 (2000) • Reach asymptotic value well before the hadronization ! • Parton cascade (left) ~ 2 fm/c • Ideal hydrodynamics (right) ~ 5 fm/c Pb+Pb b=7 fm Au+Au sNN = 200 GeV b=7.5 fm

  7. SPS vs RHIC SPS (sNN = 17 GeV) RHIC (sNN = 200 GeV) • SPS: hydrodynamical model 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)

  8. Radial flow E. Schnedermann et al, PRC48, 2462 (1993) • mT scaling in p+p • Larger kick for heavier particles in A+A • heavier particles can be pushed higher pT • Strong radial flow lead larger proton v2 PHENIX: Au+Au: PRC 63, 034909 (2004); p+p: PRC74, 024904 (2006)

  9. 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)

  10. Quark number scaling of v2(pT) • Quark recombination scenario predict existence of universal quark v2 for light quarks • Scaling works well for pT range where recombination is dominant • Is this scenario really unique explanation of v2 behavior for intermediate pT ? STAR:PRL 92, 052302 (2004) ; PHENIX:PRL 91, 182301 (2003) Quark number scaling of v2 D. Molnar and S. A. Voloshin, PRL91, 092301 (2003) Z. Lin and C. M. Ko, PRL89, 202302 (2002)

  11. Mass or quark numbers ? •  meson is the good probe to test quark number scaling of v2 because: • Early freeze-out than other hadrons • Small hadronic cross section • Relatively longer lived life time ~ 40 fm/c • Mass ~ proton • Important to understand contributions from hadronic phase • Use deuterons to study radial flow effect • Heavier hadrons are more sensitive to radial flow • Deuteron v2 can be used as a “benchmark” of quark (hadron) recombination/coalescence scenario

  12. Motivation • Measure centrality dependence of identified hadron elliptic flow (, K, p, d and ) in sNN = 200 GeV Au+Au collisions • Goal: • Test the validity of quark number scaling of v2 with  and d • Shed light on the thermodynamic properties, especially for freeze-out temperature and radial flow velocity from centrality dependence of , K, and p v2

  13. 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

  14. Analysis

  15. 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 (running)

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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 ~ 5 GeV/c, d :1 - 4 GeV/c • EMC • /K ~ 1.5 GeV/c

  21. 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

  22. 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)

  23. 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

  24. Event plane resolution & Extract v2 Central Low multiplicity Small v2 Peripheral ** Valid only equal multiplicity event  Event plane resolution of each sub-event is same

  25. Results &Discussions

  26. /K/p v2: Basic checks • 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)

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

  28. Glauber Model simulation • Woods-saxon density profile • R = 6.38 fm, a = 0.53 fm, 0 = 0.17 fm-3 • Nuclear thickness function • NN = 42 mb • Calculate number of participating nucleons • In p+p, Npart = 2

  29. Eccentricity scaling • Eccentricity scaling of v2 • Remove geometry effect on v2 • increase and saturate with Npart • proportional to Npart1/3 =

  30. 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 

  31. 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

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

  33. Hadron coalescence • Check the coalescence or recombination lead scaling relation of v2 • Hadron coalescence : d  p + n • Assume neutron v2 = proton v2 • Ratio of scaled v2(d) to v2(p) is ~ 1 • Hadron coalescence of d  Scaling relations betwee d and p

  34. Quark number scaling of v2 • Close to 1 at intermediate pT • Scaled v2 show remaining difference among different particle species at low pT • Are there any variables to scale v2 from low to intermediate pT ?  Transverse kinetic energy scaling (mT scaling) of v2

  35. Transverse kinetic energy scaling PHENIX: nucl-ex/0608033 • KET scaling holds up to ~ 1 GeV • Pressure gradient  collective kinetic energy • 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

  36. Centrality dependence: /K/p • KET scaling • 10 - 20 % systematics. Better than pT scaling

  37. Scaled v2 for  meson • Deuterons and  meson scale together • KET scaling better !

  38. Centrality dependence: d,  • KET + quark number scaling also works for d and 

  39. Summary (1) • Centrality dependence of v2 • Increase with increasing centrality for all particles species • Consistent with centrality dependence of initial spatial anisotropy ( v2   ) • v2/ increase, saturate with centrality ( Npart1/3 ) • Dynamical collectivity increase with system size • Quark number scaling of v2 • Transverse kinetic energy (KET) + quark number scaling • KET is the relevant scaling quantity to explain the v2(pT) from low to mid pT range  Collective pressure drives partonic flow

  40. “Thermometer” of QGP ? time A. Kiyomichi: PhD thesis • Thermal model fit + single pT spectra gives temperature at “kinetic freeze-out” • Elliptic flow saturate very early times (~ a few fm/c) • Does Elliptic flow have sensitivity to the early temperature on QGP phase ? • Use Elliptic flow as the “Thermometer” of QGP !

  41. Thermal model • Assumptions • Hadronization just after local thermal equilibrium • No chemical, kinetic freeze-out • No dynamical evolution • Constant temperature • Density gradient distributions • = Boost magnitude & direction • Determine the boost anisotropy • Spatial anisotropy is fixed by initial overlap density • Free parameters • Temperature: T • Magnitude of boost velocity: T reaction plane

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

  43. Thermal model fit • Minimize 2 by fitting , K and p simultaneously • Lower temperature means longer QGP phase • Results • pT spectra and v2 cannot be fitted with same parameter sets • pT spectra: T = 117 (MeV) • Overestimate v2 • v2: T = 204 (MeV) • Flatter slope of pT spectra  A hint of early saturation of v2 Left - Fit pT spectra - Draw fitting results for v2 • Right • - Fit v2 • Draw fitting results for • pT spectra

  44. 2 contour of (T, T) • pT spectra fit • Anti-correlation • Larger (smaller) T, smaller (larger) T • Flatter pT spectra for larger T and T • v2 fit • Positive correlation • Larger (smaller) T, larger (smaller) T • Smaller v2 for larger T • Larger v2 for larger T (at large T)

  45. Conclusions • Measure elliptic flow (v2) parameter of identified hadrons for a broad range of centrality and pT • Centrality dependence of v2 • Consistent with centrality dependence of initial spatial anisotropy  Elliptic flow drives Initial geometry • Transverse Kinetic energy (KET) + Quark Number scaling • Holds for all particles species in measured centrality bins  Partonic flow by collective pressure • Thermal model fit • pT spectra and v2 cannot be fitted with same parameter sets • Larger temperature from v2 fit compared to pT spectra fit  A possible hint of early saturation of v2

  46. To do • Study radial flow effect on v2 • Thermal model fit • Show only 20 - 30 % centrality bin • Fit pT spectra and v2 for other centrality bin, study centrality dependence of (T, T) systematics • Use high statistics pT spectra from year-4 results • Use year-2 result in this presentation • Comparison of results with different assumptions

  47. Back up

  48. Sign of v2 Py v2 > 0 v2 < 0 • Sign of v2 is important • Initial geometry + density gradient lead positive v2 • But sign of v2 cannot be determined by 2nd harmonic EP • Direction of true reaction plane  1st harmonic event plane Px reaction plane or

  49. Event plane correlations • Positive correlations of 2nd harmonic EP between • BBC’s, and CNT (Central arm) - BBC • Same direction of flow at CNT and BBC

  50. 1st harmonic event plane v2 > 0 v2 < 0 • Correlation between 1st harmonic and 2nd harmonic EP • Spectator neutron at ZDC-SMD gives direction of true reaction plane 1SMD   1SMD /2 /2 0 0 -/2 -/2 - - - -   0 0 22BBC 22BBC

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