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Anisotropic Flow. Part II

Anisotropic Flow. Part II. Sergei A. Voloshin Wayne State University, Detroit, Michigan. Outline. Part I. Physics 1. Introduction. Definitions. 2. Directed flow - Physics of the “wiggle” - Blast wave parameterization

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Anisotropic Flow. Part II

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  1. Anisotropic Flow. Part II Sergei A. Voloshin Wayne State University, Detroit, Michigan page

  2. Outline Part I. Physics 1. Introduction. Definitions. 2. Directed flow - Physics of the “wiggle” - Blast wave parameterization - Coalescence I. Directed flow of light nuclei. Resonances. 3. Elliptic flow - General properties. “Early times” - Low Density and “Hydro” Limits - Phase transition - Blast wave. “Mass splitting - Coalescence II. Constituent quarks. - Elliptic flow at high pt’s. 4. Anisotropies and asymmetries - Femtoscopy of anisotropic source - High pt, 2-particle correlations - Global polarization. Parity violation. 5. Can we measure it? - correlations induced by flow - “Non-flow”. Flow fluctuations Part II. Methods and Results 1. Non-flow estimates - From the “resolution plot” - Azimuthal correlations in pp and AA 2. Multiparticle correlations - 4-particle cumulants. Methods. - Non-flow and flow fluctuations - Mixed harmonics. 3-particle correlations. - Distributions in q-vector - Detector effects 3. Main results - Reaching the hydro limit - Mass splitting - Constituent quark scaling - Elliptic flow at high pt - v1 and higher harmonics - other 4. Conclusion page

  3. End of the ideal world: “Non-flow”, flow fluctuations, … Not perfect azimuthal acceptance not flat Event Plane distribution. “Flattening of the reaction plane”. Approximate and exact solutions to the problem. Flow   “non-flow” “Non-flow” – azimuthal correlations of any other originexcept the correlation with respect to the reaction plane. It combines the possible contributions from resonance decay, inter and intra jet correlations, etc. An example: Effect of flow fluctuations Other possibilities fro flow fluctuations: fluctuation in theinitial geometry, in multiplicity at the same geometry, etc. Each one by itself presents little problem, but taken at the same time, it is the major problem we fight during the last years. page

  4. Non-flow estimates page

  5. Non-Flow estimates from the reaction plane resolution plot STAR. PRL 86 (2001) 402 Non-flow level page

  6. Non-flow. Depends on centrality? M < u u*> Multiplicity Correlations induced by transverse radialexpansion S.V. nucl-th/0312065 First and second harmonics of the distribution on the left n=1, T=110 MeV STAR nucl-ex/0409033 ! - the large values of transverseflow, > 0.25, would contradict “non-flow” estimates in elliptic flow measurements page

  7. Azimuthal correlation in pp collisions • Goals (from “flow” point of view): • Check if non-flow estimates/measurements reported for Au+Au are consistentwith measurements in pp. (One could expect the difference of the order of factor of <~2. Examples: Extra particles in jets  non-flow contribution increases B-to-B jet suppression – non-flow goes down) • Use pp data to estimate non-flow effects in Au+Au in the regions where othermethods do not work well (e.g. high ptregion; Kaon and Lambda flow, etc. ) page

  8. Scalar product method and pp vs. AA Non-flow looks exactly the same in pp and AA Results - directly “correctible”. Consider correlations of particles from some “bin”with all particles from a “pool” Notations: Flow in a particular pt/eta “bin” Average flow in the pt/eta region used to define RP (or “pool” of particles) Azimuthal correlations in pp ( ) Non-flow part in 2-part azimuthal correlation in AA Number of “independent NN collisions”, a la Npart/2. page

  9. pp vs. AA Most peripheral M<~10 0 pt 7 GeV STAR Preliminary 5% central M>~500 The plot above, showing the rise and fall of azimuthal correlations ( M<uu*>)can be explained only by flow: no any other known source of the azimuthal correlation is able to give such a dependence. The origin of such a dependence:~ M*  page

  10. Final results: pp & AuAu AuAu (flow + non-flow) pp(non-flow) STAR: PRL 93(2004)252301 At high pt in central collisions, azimuthal correlation in AuAu could be dominated by nonflow. It does not mean that v2 is zero! In VERY peripheral collisions, azimuthal correlation in AuAu are dominated by non-flow. Analysis has to be continued: charge combination dependence, identified particles… page

  11. Many-particle correlations page

  12. Non-flow and multiparticle correlations pt weight “ON” 12/15/2000 flow*nflow + nflow*flow (1,3)(2,4)+(1,4)(2,3) Assuming page

  13. Non-flow and multiparticle correlations flow*nflow + nflow*flow (1,3)(2,4)+(1,4)(2,3) STAR Application: Generating functions (Borghini, Ding, Ollitrault) + many other ways page

  14. Non-flow or Fluctuations? Correct if v is constantin the event sample Should be used even in a case of =0 Non-flow Flow fluctuations In this approximation,v is between v{4} and (v{2}+v{4})/2. • Several reasons for vto fluctuate in a centrality bin: • Variation in impact parameter (taken out in STAR 130 GeV PRC flow paper) • Real flow fluctuations (due to fluctuations in initial conditions or in system • evolution) page

  15. Getting v2(b) • Procedure: • Assume some form for v2(b) • Use any event generator to relatemultiplicity and impact parameter • calculate powers of v • compare to what is measured by v2{4} Note: the curves in the plot are NOT fit to the points how/where the points are shown page

  16. Fluctuation in eccentricity  v2{2} vs v2{4} x,y – coordinates of “wounded” nucleons Calculations: R. Snellings and M. Miller v2 ~  fluctuations in flow page

  17. v2{4}/v2{2} : Compare to data R. Snellings The flow fluctuations calculatedwith participating nucleons is too strong compared to the data ! page

  18. Mixed harmonics: how it works Similar for v4 via Y Poskanzer, S.V. PRC 58 (1998)1671 What to do when the reaction plane is known: X The difference between x component and y component correlations: … and when it is not exactly known: 3-particle correlation: Borghini, Dinh, Ollitrault PRC 66(2002)014905 Main non-flow contribution left is due toresonance/jets that flow themselves page

  19. q-distribution • Two more: • q-distributions: • Q vector products Used in the very first E877 analysis Distribution in the magnitude of the flow vector Non-flow contribution Correlations due to flow page

  20. v2 from q-distributions STAR, PRC 66 (2002) 034904 -- The results are very close to those from 4-particle correlation analysis. -- Difficult to trace the contribution of flow fluctuations. page

  21. A few comments on some of the results page

  22. Anisotropic flow from AGS to RHIC QM’95 ( organized by Art! ): Y. Zhang (E877) – technique, first measurements at AGS (free of non-flow!) D. Miśkowiec (E877) – first attempt for HBT with respect to the reaction plane J.-Y. Ollitrault – drew attention to non-flow effects and how to deal with them M. Gyulassy (concluding remarks) : “The discovery of collective sidewards flow in Au+Au at the AGS is a major highlight of this year. … It is of fundamental importancebecause it provides a direct probe of the equation of state at extremely high densities….” STAR. PRL 86 (2001) 402 The highest citation indexof any (?) experimental paperon heavy ion collisions E. Shuryak:“… probably the most direct signature of QGP plasma formation, observed at RHIC.” (nucl-th/0112042) U. Heinz: “… resulting in a well developed quark-gluon plasma with almost ideal fluid-dynamical collective behavior and a lifetime of several fm/c” (hep-ph/0109006). page

  23. Elliptic flow as function of … • It is measured vs: • collision energy • transverse momentum • centrality • particle ID • Integrated values of v2 noticeably increase with energy • The slope of v2(pt) increase slowly • Most of the increase in integrated v2 comes from the increase in mean pt. PHOBOS page

  24. Energy dependence PHENIX nucl-ex/0410003 page

  25. Where we are – checking with “oldstuff”    ?     S.V. RHIC Winter Workshop, Berkeley, January 1999 http://www-rnc.lbl.gov/~nxu/oldstuff/workshop/rww99.html Unexpected – constituent quark scaling page

  26. Quark Scaling page

  27. Constituent quark model + coalescence Only in the intermediate region (rare processes) coalescence can be described by:  coalescence fragmentation S.V., QM2002 D. Molnar, S.V., PRL 2003 Low pt quarks High pt quarks In the low pt region density is large and most quarks coalesce: N hadron ~ N quark In the high pt region fragmentation eventually wins: Taking into account that in coalescence and in fragmentation , there could be a region in quark pt where only few quarks coalesce, but give hadronsin the hadron pt region where most hadrons are produced via coalescence. • Side-notes: • a) more particles produced via coalescence vs parton fragmentation  larger mean pt… •  higher baryon/meson ratio •  lower multiplicity per “participant” • -> D. Molnar, QM2004, in progress • > Bass, Fries, Mueller. Nonaka; Levai, Ko; … • > Eremin, S.V. page

  28. Constituent quark scaling STAR PRL 92(2004)052302 • Constituent quark scaling holds very well. Deviations are where expected. • Elliptic flow saturates at pt~ 1 GeV, just at constituent quark scale. An accident? Gas of free(?) constituent quarks – deconfinement ! page

  29. AuAu@62 GeV AuAu@62 GeV STAR Preliminary page

  30. Are they thermalized? S. Pratt, S. Pal , nucl-th/0409038 • Two pictures correspond to the same v2 of quarks, but • v2(B) = 3/2 v2(M) (no thermalization ?) • v2(B) = v2(M) (freeze-out at constant phase space density) • My conclusion: constituent quark scaling - Deconfinement! • No thermalization (at least in this region of pt) • (Freeze-out at constant density in the configuration space) • The same mechanism at sqrt(s_NN) 200 and 62 GeV. • If thermalized, disappear at LHC?? page

  31. Comparison with Hydro page

  32. v2(pt): Comparison with hydro • Hydrodynamic model • describes the data rather well • But should it? (non-flow, min-bias, etc.) STAR, PRL 87, 182301 (2001) page

  33. Recent preprint P. Houvinen, nucl-th/0505036 page

  34. v2(pt) @ 200 and 62 GeV pion Y. Bai (STAR), DNP ‘04 min. bias 0 ~ 80% star preliminary 0 ~ 80 % star preliminary Pt STAR expects good identified particle v2 measurements up to relatively high pt. Need detailed/tuned hydro calculations for different centralities and identified particles. page

  35. Hydro vs LDL How LDL results would look like if calculated forconstituent quark? page

  36. MPC (D. Molnar and M. Gyulassy)AMPT+”string melting”(Zi-Wei Lin, C.M.Ko) Elastic scattering, Baseline (HIJING) parameters: gg= 3 mb, tr= 1 mb; 1 gluon  1 charged particle; dNglue/dy=210. opacity = tr dN/dy =210 mb v2 HIJING x 80 HIJING x 35 HIJING x 13 HIJING x 1 hydro , sBC Constituent quark plasma: tr up 2 - 3 (?) times, dN/dy up > 2 times,  Could be close to the data… “String melting”: a) # of quarks in the system = # of quarks in the hadrons b) “quark” formation time page

  37. Integrated v2 at different energies (0-40% central) (0-40% central) We still have to analyze carefully the centrality dependence page

  38. Hydro limits • uncertainty in the centrality definition • sqrt(s)=130 GeV data: 0.075 < pt < 2.0 GeV/c • sqrt(s)=200 GeV data: 0.15 < pt < 2.0; the data scaled down by factor of 1.06 to account for change in (raw) mean pt. • AGS and SPS – no low pt cut • STAR and SPS 160 – 4th order cumulants Hydro: P.F. Kolb, et al • Questions to address: • is it saturating? • add rapidity dependence? - what happens at SPS energies? Any ‘wiggle’? page

  39. “Cold” deconfinement, color percolation? Percolation point by H. Satz, QM2002 There is a need for the “next generation”of this plot: better estimates of epsilon,adding more data (in particular 62 GeV) It is a real pity that NA49 measurements have so large systematic uncertainty. Need detector with better azimuthal acceptance (could be just a simple extra detector used to determine the RP) . FT RHIC? CERN SPS energies b ~ 4 fm RHIC: b ~ 7 fm page

  40. Charged particle v2 at high-pt phenix preliminary nucl-ex/0305013 STAR: PRL 93(2004)252301 v2(pt) has maximum at about 3 GeV/cAbove 6 GeV we do not have a reliable answer (yet) what the real flow contribution is page

  41. Charm flow (via electron measurements) STAR SQM04 But is it surprising?: v2stays the same? page

  42. New possibilities • Anisotropies and asymmetries • HBT with respect to the reaction plane • Non-identical particle correlations with respect to the reaction plane • High pt 2-particle correlation wrt reaction plane • Global polarization in AA • Parity violation page

  43. Hanbury Brown – Twiss interferometry of an anisotropic source y x Can we see the evolution? Let us measure the geometry of anisotropic source! Proposed: S.V. & W. Cleland, PRC 53 (1996) 896; PRC 54(1996) 3212 Further technique developments: U. Wiedemann, U. Heinz, M. Liza First attempt to measure : D. Miskowiec, E877, QM ’95 First and subsequent real measurements: M. Lisa et al., E895, STAR page

  44. Hanbury Brown – Twiss interferometry of an anisotropic source STAR PRL 93(2004)012301 STAR PRC 71(2005)044906 Blast wave model: T=100 MeV,r0=0.6 R=11.7 fm, Dt=2.2 fm/c ra=0.037, s2=0.037 Same parameters fit R(f) and v2(pT,m) page

  45. azHBT S.V. LBNL 1998 annual report # R20http://ie.lbl.gov/nsd1999/rnc/RNC.htm RQMD v 2.3, AuAu @ RHIC In this picture at high energies /high pt, the relative differencebetween out-of-plane size and in-plane size only increases. page

  46. azHBT-2 Note “out-of-phase” Rside modulations for k=0 case. Should we try very low kT at RHIC? IPES initial conditions, U. Heinz, P. Kolb PL B542 (2002) 216 page

  47. Do different particles freeze-out at the same place? page

  48. Non-identical 2-particle correlations S.V., R. Lednicky, S. Panitkin, Nu Xu, PRL 79 (1997) 4766 page

  49. 2-particle correlations wrt RP J. Bielcikova, P. Wurm, K. Filimonov S. Esumi, S.V., PRC, 2003 x – azimuthal angle, transverse momentum, rapidity, etc. Approach: - “remove” flow contribution- parameterize the shape of what is left - study RP orientation dependence of the parameters CERES, PRL 92(2004)032901 Selection of one (or both) of particles in- or out- of the reaction plane “distorts” the RP determination “a” == “trigger particle” STAR, PRL 93 (2004) 252301 page

  50. Parity, CP- violation, global polarization… D. Kharzeev, hep-ph/0406125 : Emission of positive (negative) pions could be asymmetric along the system angular momentum Liang, Wang, nucl-th:0410079 . PRL S.V. nucl-th:0410089 Large orbital momentum of the system can be transformed into particle spin momentum  global polarization Kharzeev, Pisarski, Tytgat, PRL 81 (1998) 512 Kharzeev, Pisarski, PRD 61 (2000) 111901 Observing parity (CP) violation with anisotropic flow techniques Parity violation S.V. PRC 62 (2000) 044901 S.V. PRC 70 (2004) 057901 Global polarization “Oriented” DCC Asakawa, Minakata, Müller, nucl-th/0212070 Negative elliptic flow of neutral pions page

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