1. The particle dependence of v 2 at moderate p T in Au+Au collisions SQM2003–Atlantic Beach, North CarolinaMarch 11–17, 2003 — Paul Sorensen — University of California–Los Angeles

2. Outline I.Analysis method overview. II.Theories related to our measurements. III.The minimum-bias v 2 (p T ) for K S and Λ to p T ~ 6.0 GeV/c. IV.The v 2 for K S and Λ from 0–5, 5–30, 30–70% of the collisions cross-sections. V.Discussion. Paul Sorensen Objective Measurements of the event–wise azimuthal anisotropy of charged particle production indicate that the elliptic anisotropy parameter (v 2 ) is large and nearly p T independent for 2.0 < p T < 8.0 GeV/c. I will present v 2 (p T ) for K S and Λ from three centrality intervals and for a minimum–bias data set reaching p T of nearly 6 GeV/c. 2 March 11–17, 2003SQM2003–Atlantic Beach, North Carolina

3. Paul Sorensen The products of the decays K S  π + π - (  i /   69%) and Λ  pπ - (  i /   64%) are detected in the TPC. Topology cuts are made on the vertices and the yield is extracted from the invariant mass distributions. 3 Analysis overview March 11–17, 2003SQM2003–Atlantic Beach, North Carolina

4. Centrality classes and the event plane Paul Sorensen The centrality is estimated from the number of charged tracks. The reaction-plane is estimated using the event-plane defined by the anisotropy in the azimuthal distribution of tracks. The event-plane is an imperfect estimator of the reaction-plane so the v 2 is corrected for the resolution estimated from a sub-events analysis. 4 Analysis overview

5. The azimuthal anisotropy parameters Paul Sorensen 5 Analysis overview

6. Azimuthal anisotropy from energy loss 6 In an energy loss (dE/dx) scenario, high p T partons lose energy as they traverse the hot nuclear matter. As such, high p T hadron production in central collisions may be suppressed relative to binary nucleon-nucleon collision scaling of peripheral collisions (R AA ). The dE/dx may also lead to the loss of away–side correlations from jet fragmentation. more opaque more opaque: fewer high p T particles In this picture, dE/dx can also lead to non- zero v 2 at high p T. less opaque The very large dE/dx limit: Emission is only seen from near the surface. Surface emission should lead to a p T and √s NN independent v 2 : E. V. Shuryak, Phys.Rev. C66 (2002) less opaque: more high p T particles Physics scenarios

7. A particle dependence from hadronization 7 (from parton transport) (Molnar & Voloshin: nucl-th/0302014) (Bass et al.: nucl-th/0301018) Physics Scenarios

8. A particle dependence from the p T scale This sketch illustrates the possible effects of pQCD overtaking non-pQCD effects (baryon junctions, hydro, etc.) at different p T scales for protons and pions. In this scenario, a particle type dependence will be seen in v 2 with proton v 2 higher than pion v 2 and the saturation of charged particle v 2 is caused by the superposition of the two. What will the particle dependence be for R AA ? p T scale 8 Physics scenarios

9. K S and Λ v 2 results at 130 GeV: “Azimuthal Anisotropy of K S and Lambda + Anti-lambda Production at Midrapidity from Au+Au Collisions at  s NN = 130 GeV” Published September 23, 2002, Phys. Rev. Lett. 132301-1. Preliminary  s NN = 200 GeV QM 2002 Transverse Momentum pT (GeV/c) Paul Sorensen 9Background March 11–17, 2003SQM2003–Atlantic Beach, North Carolina

10. The particle dependence of v 2 0.16 for K S 0.23 for Λ v 2 appears to saturate at approximately 0.16 for K S and 0.23 for Λ (v 2 Λ =v 2 Λ-bar). The mass dependence is hydro- like at low p T (a smaller mass gives a larger v 2 ). The p T onset of the saturation in v 2 is different for K S and Λ. The phenomenology seems better described in m T – m 0 than p T ; Why (kinetic energy)? What’s drives the different p T scales for K S and Λ v 2 ? 10

11. Centrality dependence of v 2 for K S and Λ Paul Sorensen The v 2 as a function of particle type and event centrality. The m T – m 0 plot makes it easier to study the deviations between particle type. The approximate maximum v 2 from surface emission for this centrality is well below v 2 for both particles but, the systematic errors must be considered. 11 STAR preliminary (Au+Au; 200 GeV; |y|<1.0)

12. Particle/centrality dependence of v 2 for K S and Λ Paul Sorensen Is the Λ v 2 to K S v 2 ratio smaller in central collisions? The errors–systematic and statistical–must be studied further and reduced, particularly for 0–5% central. 12 STAR preliminary (Au+Au; 200 GeV; |y|<1.0)

13. Au+Au collision geometry; Scaling by eccentricity ε Paul Sorensen 13

14. Centrality dependence of v 2 /ε for K S and Λ Paul Sorensen v 2 /ε is increasing monotonically from peripheral to central collisions for both particles. The accuracy of our estimates of ε need to be considered. 14 STAR preliminary (Au+Au; 200 GeV; |y|<1.0)

15. v 2 /ε; central/peripheral (species and m T dependence) While the increase in v 2 /ε with √s happens at low p T, the increase in v 2 /ε with centrality happens primarily at high p T. v 2 /ε is independent of centrality for hydrodynamics with a constant speed of sound. v 2 /ε demonstrates how effective the system is at converting geometric to momentum anisotropy. Central collisions are more effective than peri. in creating anisotropy in high p T. 15 charged hadron v 2 : Kirill Filimonov QM2002 C. Adler et.al. Phys. Rev. C66, 034904

16. From v 2 to R AA Preliminary  s NN = 200 GeV 16 Paul Sorensen R AA is an observable that may be intimately related to v 2. See Hui Longs talk for the particle dependence of R AA. For the first time the particle dependence of v 2 has been measured for high and low p T (and vs. centrality). Charged hadron R AA March 11–17, 2003SQM2003–Atlantic Beach, North Carolina

17. 17 The p T scale of K S and Λ production What physics could be behind the p T scales of the saturation in v 2 and the suppression in R AA ? How does the particle type influence the p T scale? p T meson ≈2·p T parton ? p T baryon ≈3·p T parton ? The saturation of v 2 and the drop of R AA seem to be correlated.

18. Summary v 2 and R AA for K S and Λ show a strong particle type dependence: – Compared to K S, Λ production shows a larger azimuthal anisotropy but a smaller suppression for 2.0 < p T < 4.0 GeV/c. v 2 /ε rises monotonically from peripheral to central collisions: – Suggestion of saturation is seen in all centralities. – Central collisions are more effective than peripheral at converting spatial anisotropy to momentum anisotropy in high p T K S and Λ and production. For central collisions R AA for Λ is larger than for K S and coincides with our estimate of N bin scaling expectations for 1.8 < p T < 3.5 GeV/c. While an extreme energy loss scenario predicts a maximum v 2 of ~15%, Λ v 2 reaches as high as ~24% and K S v 2 reaches as high as ~16%. Paul Sorensen 18 March 11–17, 2003SQM2003–Atlantic Beach, North Carolina

19. Outlook In a dE/dx scenario–where opacity from partonic dE/dx leads to a finite, p T independent v 2, an R AA below one, and an absence of back-to-back, jet-like correlations–the larger Λ v 2 (for 2 < p T < 4) contradicts the smaller Λ suppression manifested in R AA. What are the origins of the particle type dependence; –A particle type dependence in the p T scale of a non-pQCD (hydro, baryon- junctions, etc.) to pQCD transition? → Below 4 GeV/c Λ’s are not from jets? –A mass dependence (from hydro, cronin or fragmentation)? –A 2 vs. 3-quark dependence (coalescence after a partonic v 2 is established? For moderate to high p T, the hadronization process may be a crucial component to understanding heavy ion collisions (see, for example, the following slides on coalescence). willAs we continue the systematic study of identified particles (φ, Ξ, Ω, etc.) STAR will resolve many of these open issues. See for example Hui Long’s work presented at this meeting. Paul Sorensen 19

20. In this picture v 2 of a hadrons at p T is the partonic v 2 at p T /n scaled by the # of quarks (n). 20 STAR preliminary (Au+Au; 200 GeV; |y|<1.0) In this scenario we must assume that some v 2 is built up during a partonic stage. We can then infer the value of the quark v 2 in the relevant p T region (~8%). A comparison of v 2 for K S and Λ to qualitative predictions from coalescence

21. This parton coalescence rescaling seems to work for each of our centrality intervals Paul Sorensen 21

22. Supplementary Slides -Lambda vs. Anti-lambda v 2 - -Reaction plane distribution- -N bin and N part scaling- -v 2 for 130 GeV identified particles- -Modified blast wave fits- -And much more- Paul Sorensen STAR for the STAR Collaboration 22

23. Paul Sorensen 23 March 11–17, 2003SQM2003–Atlantic Beach, North Carolina

24. v 2 /ε vs. charged particle density ( 1 / S dN / dy ) Paul Sorensen S is the area of the overlap region; dN/dy is the rapidity density. The most central events approach the hydro limit (a mean free path much smaller than the collision overlap region). v 2 /ε is increasing with charged particle density. What is the detailed √s and centrality behavior? 24 charged hadron v 2 √s ratio: Kirill Filimonov QM2002 C. Adler et.al. Phys. Rev. C66, 034904

25. v 2 /ε; mid-central to peripheral Paul Sorensen 25 charged hadron v 2 : Kirill Filimonov QM2002 C. Adler et.al. Phys. Rev. C66, 034904

26. v 2 (p T ) particle dependence Paul Sorensen At low m T -m 0 the Λ and K S follow a hydro like mass dependence. For m T -m 0 ≥ 1.0 GeV/c Λ v 2 continues to increase while K S v 2 begins to saturate; so that the ratio deviates from hydro model expectations. 26 STAR preliminary (Au+Au; 200 GeV; |y|<1.0)

27. Monte Carlo Glauber Calculation  s NN = 200 GeV %  geo 0-5352 ( 6 7 )990.0 ( 69 77 )2.85 (0.17) 5-10298 ( 10 10 )783.7 ( 71 74 )2.65 (0.17) 10-20232 ( 11 10 )563.2 ( 64 59 )2.43 (0.17) 20-30165 ( 13 12 )355.0 ( 53 49 )2.14 (0.17) 30-40114 ( 13 12 )213.9 ( 41 36 )1.86 (0.16) 40-6061 ( 10 10 )91.8 ( 22 23 )1.44 (0.14) 60-8019.8 ( 5 6 )20.0 ( 7 9 )0.96 (0.10) Woods-Saxon nuclear geometry parameters:  0 =.16935 nucl./fm 3 r 0 = 6.38  0.06 fmc 0 = 0.535  0.027 fm Cross-sections:  NN = 42  1 mb  geo = 7.2  0.4 b 27

28. v 2 vs m t – m 0 for 130 GeV identified particles C. Adler et al. Phys. Rev. Lett. 87, 182301 (2001). 28

29. Modified blast wave fits A simultaneous fit to both particles at all p T fails. A simultaneous fit to both particles for p T less than 1.0 GeV/c gives results similar to those reported by STAR for 130 GeV identified particle v 2 *. * C. Adler et al. Phys. Rev. Lett. 87, 182301 (2001). 29

30. How do we maintain an azimuthal anisotropy in the number of particles produced at a given p T while the azimuthal anisotropy of disappears? 0.8 1.2 1.6 30

31. Surface width=1.6 fm 1.0 Surface Binary Scaling R AA p T (GeV/c) STAR Preliminary Au+Au 200 GeV Woods-Saxon distribution. A binary collision occurs if d min   (  /  ). Pythia is used to handle particle production for each binary collision with sqrt(s) > 4 GeV, otherwise, particles are produced through resonance,eg NN   N. Au+Au at  s NN =200 GeV Centrality<5% Nbin_v=1016,Npart=347 5%<Centrality<10% Nbin_v=816,Npart=293 10%<Centrality<20% Nbin_v=592,Npart=226 30%<Centrality<40% Nbin_v=237,Npart=107 Surface N-binary Scaling for High p T (Model Calculations by An Tai) 31

32. v 2 for m T – m 0 between 1.5 – 4.0 GeV/c 2 Paul Sorensen The relative probability to produce mesons or baryons depends on the density of the quarks. Hadronization Schemes: Parton-hadron duality Independent fragmentation Whatever works? The hadronization scheme may be important for understanding the particle dependence of R AA and v 2. Coalescence is qualitatively consistent with the particle dependence of v 2 and R AA. 32

33. The spectra for K S and Λ + Λ Paul Sorensen 33 STAR preliminary (Au+Au; 200 GeV; |y|<1.0)

34. Paul Sorensen R AA for K S and Λ For p T from 1.8-3.5 GeV/c Λ+ Λ production coincides with N bin scaling while K S and h +/- production is suppressed in this region (R AA Λ =R AA Λ-bar). At p T ~ 5.5 GeV/c K S, Λ+Λ and h +/- production are suppressed by a similar amount. The p T scales for K S and Λ R AA are different. 34

35. 35 STAR preliminary (Au+Au; 200 GeV; |y|<1.0)

36. 36 The p T scale of K S and Λ production What physics is behind the p T scales of the saturation in v 2 and the suppression in R AA ? How does the type influence the p T scale? p T meson ≈2·p T parton ? p T baryon ≈3·p T parton ? The saturation of v 2 and the drop of R AA seem to be correlated.

37. 37 The p T scale of v 2 & R AA for K S, Λ & h +/- What physics is behind the p T scales of the saturation in v 2 and the suppression in R AA ? How does the particle type influence the p T scale? The v 2 saturation and the the decrease in R AA appear to be loosely correlated for both K S and Λ.

38. 200 GeV 130 GeV Lambda v 2 (130 GeV) : 0.58 K S v 2 (130 GeV) : 0.68 Lambda v 2 (200 GeV) : 0.80 K S v 2 (200 GeV) : 0.80 N hits > 15 N hits / N max > 0.52 |eta| < 1.5 0.1 < pT < 2.0 GeV/c DCA < 2.0 cm z–vertex < 25 cm Track–wise and event–wise cuts Maximum resolution correction factor from random sub-events Event plane resolution correction factor 38

39. RFF B RFF CFFF C FFF B Paul Sorensen 39