Azimuthal Correlation Studies Via Correlation Functions and Cumulants

1. Azimuthal Correlation Studies Via Correlation Functions and Cumulants N. N. Ajitanand Nuclear Chemistry, SUNY, Stony Brook

2. Outline • Motivation • Why Correlation studies ? • Correlation Techniques • Cumulant Method • Correlation Function Method • Correlation Results • Compatibility with Flow, Jets, etc. ? • What the Measurements tell us • Summary

3. From ET Distributions time to thermalize the system (t0 ~ 1 fm/c) eBjorken~ 5 GeV/fm3 Why Study Correlations at RHIC BRAHMS rapidity distribution Substantial Energy Density is Produced at RHIC Large Energy Density Substantial Flow (Hydro limit) Possible Access to EOS

4. Reminder - Single Particle Distributions Au + Au Experiment d + Au Control Experiment Striking difference between d+Au and Au+Au results. Cronin effect dominates in d+Au High-pT Jet Suppression dominate in Au+Au. Final Data Preliminary Data

5. Significant Jet Yield Is Purported at RHIC schematic view of jet production leading particle hadrons q q Jets are Sensitive to the QCD medium (dE/dx) hadrons • Jets: • Primarily from gluons at RHIC leading particle Energy loss results in an anisotropy which can serve as an excellent probe of the medium Jets at RHIC Correlation Studies Provide a Complimentary Probe for Possible QGP formation…. (Very Important Signal)

6. Important Tools for Correlation Studies • Anisotropy Relative to the Reaction • Cumulants • Correlation Functions

7. y Reaction plane Reaction plane method i 2 x Build distribution Relative to Rxn. plane Σ wi*sin(2i) tan(22) = Fourier analyze distribution to obtain anisotropy Σ wi*cos(2i) Measuring Azimuthal Correlations Reaction Plane Method Anisotropy = Flow if non-flow is demonstrably small

8.  Correlations If Flow predominate Multiparticle correlations can be used to reduce non-flow contributions (N. Borghini et al, PRC. C63 (2001) 054906) Measuring Azimuthal Correlations

9. Application of Cumulant Method in PHENIX • Cumulant analysis: non-trivial PHENIX analysis • Simulations performed using a toy model MC generator with PHENIX acceptance as input • Results show that the v2 extracted is robust and acceptance corrections are well implemented

10. pT and η dependence of v2 • No apparent dependence of v2 on η over the PHENIX η coverage • Finite v2 at high pT • jets are correlated with low pT particles Reaction Plane ! PHENIX Preliminary PHENIX Preliminary PHENIX Preliminary

11. Glauber PHENIX Preliminary y eccentricity x Cumulant Analysis: Centrality Dependence Anisotropy driven by eccentricity : v2 scales with Npart

12. pT ref Cumulant Analysis: Dependence on integral pT range • No significant dependence on integral pT of reference PHENIX Preliminary pT

13. PHENIX Preliminary Scaling of the anisotropy The differential anisotropy scales with the integral anisotropy

14. Assorted Two-particle Azimuthal Correlation Functions Virtues • Asymmetry related to jet properties • Comparison of d+Au and Au+Au can reveal in-medium effects • Flavor dependence can probe details of jet fragmentation • etc

15. pT Leading Hadron Assorted Correlations Leading Hadron • Associated particle • Meson • Baryon Correlation Function

16. pT PHENIX Setup Azimuthal Correlations Using DC+PC1+PC3+EMC Tracks mesons baryons Baryon & Mesonidentification done using EMC TOF

17. Assorted Correlation Functions Associated Mesons PHENIX Preliminary Associated Baryons Noticeable differences in the asymmetries For associated baryons and mesons

18. associated associated PHENIX Preliminary associated associated Assorted Correlation Functions • Similar asymmetry trends for associated mesons & baryons in d+Au • Dissimilar trends • for associated mesons and baryons in Au+Au De-convolution of Correlation Function Necessary

19. De-convolution Ansatz Fractional yield Harmonic Contribution

20. Test of de-convolution via Simulations Two source 3d simulation Simulation Model: • jets and flow. • Poisson sampling: • jets per event • particles per jet • flowing particles per event • Jets produced with effective jT and kT • Avg. number of near and far-side jet particles equal • Exponential pT distribution for particles Correlation functions generated in PHENIX acceptance

21. Typical fit to 3d sim correlation Good overall representation of the correlation function is obtained

22. y Reaction plane i 2 x Simulation Build Correlation Function Relative to Rxn. plane Correlation Perp to Plane Σ wi*sin(2i) tan(22) = Σ wi*cos(2i) Measuring Azimuthal Correlations Relative to the Reaction Plane

23. Results From Simulations Correlations Parallel-to-RP Correlations Perpendicular-to-RP Simultaneous Fit Recovers Jet and harmonic properties ~ 10%

24. Reliable yield extraction is achieved

25. PHENIX preliminary PHENIX preliminary PHENIX preliminary Data Hadron-Hadron correlation (pT(trig)>3GeV/c) See Shinichi’s Talk Flavor composition study in progress -- revealing

26. High Density partonic material formed Early leading particle d + Au q q Pressure Gradients Develop in Partonic matter -> elliptic flow -> v2 leading particle Hard Scattered Partons Traverse partonic material  Jet-quenching (early)  v2 This Scenario has Measurable Consequences Which can be put into Evidence  Quantitative estimates Emerging Picture The high energy-density matter responsible for Jet Quenching drives elliptic flow

27. Summary / Conclusion Differential azimuthal anisotropy has been measured in PHENIX using cumulants. • 2nd order v2 measured as a function of pT and centrality • Scaling behavior demonstrated • Low and high pT reference study suggest that jets are correlated with RP Assorted Correlation Functions • Azimuthal Correlation functions obtained fro high pT leading hadrons in association with flavor identified partners. • d+Au: significant asymmetry observed for both flavors • Au + Au: Asymmetry significantly reduced for associated baryons • De-convolution method for extraction of jet and flow parameters demonstrated