Azimuthal Correlation Studies Via Correlation Functions and Cumulants

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

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

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

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

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

Measuring Azimuthal Correlations Reaction Plane Method Reaction plane method y e n a l np o ti ac i Re Σ wi*sin(2 i) tan(2 2) = Σ wi*cos(2 i) 2 x Build distribution Relative to Rxn. plane Fourier analyze distribution to obtain anisotropy Anisotropy = Flow if non-flow is demonstrably small N. N. Ajitanand, SUNY Stony Brook

Measuring Azimuthal Correlations If Flow predominate Multiparticle correlations can be used to reduce non-flow contributions (N. Borghini et al, PRC. C 63 (2001) 054906) 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 N. N. Ajitanand, SUNY Stony Brook

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

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

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

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

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 N. N. Ajitanand, SUNY Stony Brook

Leading Hadron Assorted Correlations Leading Hadron p. T Associated particle • Meson • Baryon Correlation Function N. N. Ajitanand, SUNY Stony Brook

PHENIX Setup p. T Azimuthal Correlations Using DC+PC 1+PC 3+EMC Tracks mesons baryons Baryon & Meson identification done using EMC TOF N. N. Ajitanand, SUNY Stony Brook

Assorted Correlation Functions Associated Mesons PHENIX Preliminary Associated Baryons Noticeable differences in the asymmetries For associated baryons and mesons N. N. Ajitanand, SUNY Stony Brook

Assorted Correlation Functions • Similar asymmetry trends for associated mesons & baryons in d+Au associated • Dissimilar trends PHENIX Preliminary associated for associated mesons and baryons in Au+Au De-convolution of Correlation Function Necessary N. N. Ajitanand, SUNY Stony Brook

De-convolution Ansatz Fractional yield Harmonic Contribution N. N. Ajitanand, SUNY Stony Brook

Test of de-convolution via Simulations Two source 3 d simulation Simulation Model: • 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 p. T distribution for particles Correlation functions generated in PHENIX acceptance N. N. Ajitanand, SUNY Stony Brook

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

Measuring Azimuthal Correlations Relative to the Reaction Plane y e n a l np o ti ac i Re Σ wi*sin(2 i) tan(2 2) = Σ wi*cos(2 i) 2 x Build Correlation Function Relative to Rxn. plane Simulation Correlation Perp to Plane N. N. Ajitanand, SUNY Stony Brook

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

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

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

High Density partonic material formed Early leading particle d + Au q q leading particle Pressure Gradients Develop in Partonic matter -> elliptic flow -> v 2 Hard Scattered Partons Traverse partonic material Jet-quenching (early) v 2 This Scenario has Measurable Consequences Which can be put into Evidence Quantitative estimates The high energy-density matter responsible for Jet Quenching drives elliptic flow N. N. Ajitanand, SUNY Stony Brook

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