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

2. N. N. Ajitanand, SUNY Stony Brook 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 Summary

3. N. N. Ajitanand, SUNY Stony Brook Why Study Correlations at RHIC BRAHMS rapidity distribution Large Energy Density Substantial Flow (Hydro limit) Possible Access to EOS Substantial Energy Density is Produced at RHIC time to thermalize the system (  0 ~ 1 fm/c)  Bjorken  ~ 5 GeV/fm 3 From ET Distributions

4. N. N. Ajitanand, SUNY Stony Brook Striking difference between d+Au and Au+Au results. Cronin effect dominates in d+Au High-pT Jet Suppression dominate in Au+Au. Au + Au Experimentd + Au Control Experiment Preliminary DataFinal Data Reminder - Single Particle Distributions

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

6. N. N. Ajitanand, SUNY Stony Brook Important Tools for Correlation Studies Anisotropy Relative to the Reaction Cumulants Correlation Functions

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

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

9. N. N. Ajitanand, SUNY Stony Brook 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 v 2 extracted is robust and acceptance corrections are well implemented

10. N. N. Ajitanand, SUNY Stony Brook p T and η dependence of v 2  No apparent dependence of v2 on η over the PHENIX η coverage  Finite v 2 at high p T  jets are correlated with low p T particles Reaction Plane ! PHENIX Preliminary

11. N. N. Ajitanand, SUNY Stony Brook Cumulant Analysis: Centrality Dependence Anisotropy driven by eccentricity : v 2 scales with N part PHENIX Preliminary y x eccentricity Glauber

12. N. N. Ajitanand, SUNY Stony Brook Cumulant Analysis: Dependence on integral p T range  No significant dependence on integral p T of reference PHENIX Preliminary p T ref pTpT

13. N. N. Ajitanand, SUNY Stony Brook Scaling of the anisotropy The differential anisotropy scales with the integral anisotropy PHENIX Preliminary

14. N. N. Ajitanand, SUNY Stony Brook Assorted Two-particle Azimuthal Correlation Functions 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 Virtues

15. N. N. Ajitanand, SUNY Stony Brook Leading Hadron Assorted Correlations Associated particle Meson Baryon pT Leading Hadron Correlation Function

16. N. N. Ajitanand, SUNY Stony Brook PHENIX Setup Azimuthal Correlations Using DC+PC1+PC3+EMC Tracks Mesonidentification done using EMC TOF Baryon & Meson identification done using EMC TOF pT mesons baryons

17. N. N. Ajitanand, SUNY Stony Brook AssociatedMesons PHENIX Preliminary AssociatedBaryons Assorted Correlation Functions Noticeable differences in the asymmetries For associated baryons and mesons

18. N. N. Ajitanand, SUNY Stony Brook Assorted Correlation Functions associated PHENIX Preliminary 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. N. N. Ajitanand, SUNY Stony Brook De-convolution Ansatz Harmonic Contribution Fractional yield

20. N. N. Ajitanand, SUNY Stony Brook Test of de-convolution via Simulations jets and flow. Poisson sampling: –jets per event –particles per jet –flowing particles per event Jets produced with effective j T and k T –Avg. number of near and far-side jet particles equal Exponential pT distribution for particles Two source 3d simulation Simulation Model: Correlation functions generated in PHENIX acceptance

21. N. N. Ajitanand, SUNY Stony Brook Typical fit to 3d sim correlation Good overall representation of the correlation function is obtained

22. N. N. Ajitanand, SUNY Stony Brook Measuring Azimuthal Correlations Relative to the Reaction Plane Reaction plane x y 22 ii Σ w i *sin(2  i ) tan(2  2 ) = Σ w i *cos(2  i ) Build Correlation Function Relative to Rxn. plane Simulation Correlation Perp to Plane

23. N. N. Ajitanand, SUNY Stony Brook Correlations Perpendicular-to-RP Results From Simulations Correlations Parallel-to-RP Simultaneous Fit Recovers Jet and harmonic properties ~ 10%

24. N. N. Ajitanand, SUNY Stony Brook Reliable yield extraction is achieved

25. N. N. Ajitanand, SUNY Stony Brook Data Hadron-Hadron correlation (p T (trig)>3GeV/c) PHENIX preliminary See Shinichi’s Talk Flavor composition study in progress -- revealing

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

27. N. N. Ajitanand, SUNY Stony Brook Summary / Conclusion Differential azimuthal anisotropy has been measured in PHENIX using cumulants.  2 nd 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