1. 2nd International Workshop on the Critical Point and Onset of Deconfinement, 2005 Bergen, Norway Fluctuations at RHIC Claude A Pruneau STAR Collaboration Physics & Astronomy Department Wayne State University Detroit, Michigan, USA

2. Talk Outline Net Charge Fluctuations Transverse Momentum Fluctuations K/  Fluctuations (proof of principle) Questions: Smoking gun for QGP, phase transition ? Can we learn about the collision dynamics ?

3. Prediction by Koch, Jeon, et al., Asakawa et al., Heiselberg et al., of reduced net charge fluctuation variance following the production of a QGP. QQ D QGP Thermal + Fast Hadronization £  0.25£1£1 Resonance/Hadron Gas ~0.7~2.8 Poisson / uncorrelated 14 Net Charge Fluctuations - a signature for the QGP ?

4. Predictions Consider different scenarios: Neutral resonances decay to charged particles Increases N ch Do not contribute to Jeon/Koch, PRL83(99)5435 QGP QGP - Coalescence Scenario ( A. Bialas, PLB 532 (2002) 249) Gluons “attached” to quarks and forming constituent quarks. Small contribution to the entropy.

5. Brief Historical Review Choice of Observable Many different approaches proposed/used “D” - S. Jeon and V. Koch, Phys. Rev. Lett. 85, 2076 “  Q ” - H. Heiselberg, Phys. Rep. 351, 161 “  Q ” - M. Gazdzicki and S. Mrowczynski, Z. Phys. C 54, 127 “ +-,dyn ” - C.P., S. Gavin, S. Voloshin - PRC 66, 44904 (2002). Relationships between observables S. Mrowczynski, nucl-th/0112007. “Equivalence not perfect - advocate usage a common language by all experiments. Published Measurements Au + Au s NN 1/2 = 130 GeV PHENIX, PRL 89 (2002) 082301. STAR, PRC68, 044905 (2003). Pb + Pb CERES @ QM04 NA49

6. Independent Particle (Poisson) Limit Definition: Measurement: Properties and robustness of this observable discussed in: 1.“Methods for the study of particle production fluctuations”, C.P., S.G., S.V. - PRC 66, 44904 (2002). 2.S. Mrowczynski, PRC C66, 024904 (2002). 3.“On the Net-Charge Fluctuations in Relativistic Heavy-Ion Interactions”, J. Nystrand, E. Stenlund, and H. Tydesjo, PRC 68, 034902 (2003). Dynamical Net Charge Fluctuations Physical Motivation:

7. Independent of volume fluctuations Independent Particle Production Collision Dynamics Independent of collision centrality Robust Observable (Independent of efficiency) Charge Conservation Perfect N + =N - correlation Dynamical Fluctuations Properties

8. Data Sets - STAR Au + Au s NN 1/2 = 20, 62, 130, 200 GeV Collision Centrality Determination based on all charged particle multiplicity |  |<0.5. Centrality slices 0-5%, 5-10%, 10-20 %, … Use Glauber model/MC to estimate the corresponding number of participants. Events analyzed for |z vertex |<MAX. DCA < 3 cm. Track quality N hit >15; N fit /N hit >0.5. Fluctuations studied in finite rapidity ranges, and azimuthal slices, for 0.2 < p t < 5.0 GeV/c.

9. Net Charge Dynamical Fluctuations Beam Energy Dependence Study STAR TPC - |  |<0.5; 0.2 < pt < 5.0 GeV/c Finite Fluctuations @ all energies. Increased dilution with increasing N part Some energy dependence | +-,dyn | larger at 20 than 62, 130 and 200 GeV. Au +Au

10. Effects of Kinematic Cut Simulation based on 630k HIJING events @ 62 GeV |  | 0., 0.1, 0.2, 0.3 GeV/c

11. Comparisons with Models 1000000/620000 Hijing events, 700000 RQMD events

12. QGP Signature? 1/N Scaling? PHOBOS - PRC65, 061901R Au + Au sqrt(s NN )=130 and 200 GeV. Poisson Limit Coalescence Resonance Gas Koch/Jeon QGP ~ -3. Au +Au 62 GeV

13. Fluctuations vs Beam Energy H. Sako (CERES) @ QM 04. Not corrected for finite efficiency STAR -Preliminary

14. Dynamical Fluctuations vs Energy STAR |  |<0.5 PHENIX |  |<0.35,  =  /2 CERES 2.0<  <2.9 UrQMD RQMD

15. NA49 Results

16. Summary so far… No smoking gun for D ~ 1 +-,dyn dependence on beam energy is not clear. dN/d  +-,dyn exhibits finite dependence on beam energy and collision centrality - mostly accounted for by the change in dN/d . More detailed comparison between experiments requires more work… What about reaction dynamic effects?

17. Transverse Momentum Fluctuations P t Dynamic Fluctuations observed to be finite at RHIC. PHENIX STAR Non-monotonic change in p t correlations with incident energy/centrality might indicate the onset of QGP. STAR - Au + Au s NN 1/2 = 20, 62, 130, 200 GeV. |  |<1, 0.15 < p t < 2.0 GeV/c

18. Measurement of P t Fluctuations To quantify dynamical p t fluctuations We define the quantity. It is a covariance and an integral of 2-body correlations. It equals zero in the absence of dynamical fluctuations Defined to be positive for correlation and negative for anti- correlation.

19. G. Westfall et al., STAR to be submitted to PRC. P t Correlation Integral Calculate > and Vs acceptance Vs centrality - 9 standard STAR centrality bins in N ch, |  | < 0.5 Results reported here for all centralities for |  | < 1.0 (full STAR acceptance) for 0.15 < p t < 2.0 GeV/c Correlations are positive Decrease with centrality ~ 1/N dependence Somee incident energy dependence HIJING underpredicts the measured correlations

20. Scale by dN/d  to remove 1/N correlation dilution and allow comparison with  pt and  pt Scaling Properties (1) HIJING does not agree with the data. - Magnitude - Centrality Dependence Clear Scaling Violation

21. Scaling Properties (2) Take square root of, d ivide by > to obtain dimensionless quantity + remove effects of > variation incident energy and centrality HIJING still does not agree with the data. CERES - SPS - Adamova et al., Nucl. Phys. A727, 97 (2003)

22. ( ) 1/2 / > 1.1%

23. Dynamical Effects Resonance Decays Radial and Elliptical Flow Diffusion/Thermalization Jet Production/Quenching …

24. Resonance Contributions - An Example  +-,dyn Probability - f 3 Assume multinomial production of  +,  -, and   with probabilities f 1, f 2, and f 3. Generating functions:  ~ 0.17 k o s  ~ 0.12 ~ 0.08 effective with DCA < 3cm. Resonances   0.3 STAR, PRL92 (2004) 092301

25. Collectivity S. Voloshin, nucl-th/0312065 Uses “blast wave” Model

26. Sensitivity to Velocity Profile S. Voloshin, nucl-th/0312065 Single Particle Spectrum Two Particle Correlation

27. Comparison with Data Scale, d ivide by >2 and number of participants. Compare to Blastwave calculation by S. Voloshin

28. Effect of radial flow on Net Charge Correlations Toy model Multinomial production of  +,  -, and  0. Isotropic source Maxwell Boltzman Dist. T = 0.18 GeV Radial Flow v r as shown.

29. Toy Model (Continued) Binomial production of  +,  -, and X 0. Isotropic source Maxwell Boltzman Dist. T = 0.18 GeV No Radial Flow m x as shown.

30. Hijing/Rqmd Prediction of Angular Dependence Au + Au @ s NN 1/2 = 62 GeV RQMD HIJING Version 1.38

31. +-,dyn vs |  | range RQMD STAR @ 200 GeV

32. Azimuthal Dependence Au+Au @ s NN 1/2 = 62 GeV 0-5% 10-20% 30-40% 70-80% Indications of resonance + flow effects Interpretation requires detailed model comparisons Resonance Gas - Toy Model T=0.18 GeV;  +,  -, , K 0 s, v r as shown

33. K/  Fluctuation Measurement Consider two approaches: 1.Fluctuations of the Kaon to Pion yields ratios 2.Measure integral correlations Particle identification from dE/dx in TPC M. Anderson et al. NIMA499 (2003)

34. K/  Fluctuations ExperimentRatio type  data  mixed  dyn NA49 K/  23.27%23.1%2.8%±0.5 STAR K/  17.78%17.23%4.6%±0.025 STAR K+/+K+/+ 24.29%24.10%3.06%±0.066 STAR K-/-K-/- 24.81%24.55%3.61%±0.055 Suprya Das, STAR Preliminary

35. K/  Dynamical Fluctuations k ,dyn k ,dyn (|  |<0.5) HIJING 1.38 - Au + Au 200 GeV M Preliminary

36. Summary Net Charge fluctuations No smoking gun for reduced fluctuations as predicted by Koch et al. Bulk of observed correlations due to resonance decays. A new tool to evaluate the role of resonances and radial flow. Observed centrality dependence of +-,dyn vs . P t fluctuations No smoking gun for large fluctuations. No beam energy dependence. A tool to study the velocity profile (see Sergei Voloshin’s talk). K/  Yield fluctuations Results by STAR on their way...

37. Energy Dependence s NN 1/2 +-,dyn +-,q-lim +-,q-lim / +-,dyn 20 GeV-0.00351 ± 0.00026-0.0016~46% 62 GeV-0.00290 ± 0.00018 130 GeV-0.00217 ± 0.00014-0.00095~40% 200 GeV-0.00242 ± 0.00007-0.00086~35% Charge Conservation Limit: +-,q-lim = -4/N CH,4  Au + Au 0-5 % most central collisions

38. Comparison with HIJING/RQMD

39. Thermalization Solves Boltzmann equation with Langevin noise  phase-space correlations  dynamic fluctuations S. Gavin, Nucl. Dyn. Conf. Jamaica

40. Summary of Charge Fluctuation Measures based on a slide from J. Mitchell’s QM04 talk.

41. Basic Observable - Mixed Events Au+Au at 200 GeV is zero for mixed events

42. Estimate Contribution from Short Range Correlations To get an estimate for the contribution from short range correlations, we calculate excluding pairs with q inv < 100 MeV To do this calculation, we assume all particles are pions model dependent CERES carried out somewhat different calculation to estimate the contribution from SRC When pairs with q inv < 100 MeV are removed, a strong, artificial anti-correlation is introduced CERES compensated for this effect by introducing randomly chosen particles We compensate by subtracting mixed events with the same cut on pairs with q inv < 100 MeV

43. Results for SRC Estimation Correlation Function, q inv > 100 MeV Au+Au 62 GeV

44. Ratios for pairs with q inv > 100 MeV to for all pairs Au+Au 62 GeV = 0.80  0.06 = 0.90  0.01 = 0.90  0.04

45. Estimate of Contribution from SRC to