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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

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Azimuthal correlation studies via correlation functions and cumulants l.jpg

Azimuthal Correlation Studies Via Correlation Functions and Cumulants

N. N. Ajitanand

Nuclear Chemistry, SUNY, Stony Brook

Slide2 l.jpg

Outline Cumulants

  • Motivation

    • Why Correlation studies ?

  • Correlation Techniques

    • Cumulant Method

    • Correlation Function Method

  • Correlation Results

    • Compatibility with Flow, Jets, etc. ?

    • What the Measurements tell us

  • Summary

  • Why study correlations at rhic l.jpg

    From ET Distributions Cumulants

    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

    Slide4 l.jpg

    Reminder - Single Particle Distributions Cumulants

    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

    Jets at rhic l.jpg

    Significant Jet Yield Cumulants

    Is Purported at RHIC

    schematic view of jet production






    Jets are Sensitive to

    the QCD medium (dE/dx)


    • 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)

    Slide6 l.jpg

    Important Tools for Cumulants

    Correlation Studies

    • Anisotropy Relative to the Reaction

    • Cumulants

    • Correlation Functions

    Measuring azimuthal correlations l.jpg

    y Cumulants

    Reaction plane

    Reaction plane method




    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

    Slide8 l.jpg

     Correlations Cumulants

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

    Measuring Azimuthal Correlations

    Application of cumulant method in phenix l.jpg
    Application of Cumulant Method in PHENIX Cumulants

    • 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

    P t and dependence of v 2 l.jpg
    p CumulantsT 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

    Cumulant analysis centrality dependence l.jpg

    Glauber Cumulants

    PHENIX Preliminary




    Cumulant Analysis: Centrality Dependence

    Anisotropy driven by eccentricity : v2 scales with Npart

    Cumulant analysis dependence on integral p t range l.jpg

    p CumulantsT ref

    Cumulant Analysis: Dependence on integral pT range

    • No significant dependence on integral pT of reference

    PHENIX Preliminary


    Scaling of the anisotropy l.jpg

    PHENIX Preliminary Cumulants

    Scaling of the anisotropy

    The differential anisotropy scales with the integral anisotropy

    Slide14 l.jpg

    Assorted Two-particle Azimuthal Correlation Cumulants



    • 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

    Slide15 l.jpg

    pT Cumulants

    Leading Hadron Assorted Correlations

    Leading Hadron

    • Associated particle

    • Meson

    • Baryon

    Correlation Function

    Phenix setup l.jpg

    pT Cumulants

    PHENIX Setup

    Azimuthal Correlations Using DC+PC1+PC3+EMC Tracks



    Baryon & Mesonidentification done using EMC TOF

    Slide17 l.jpg

    Assorted Correlation Functions Cumulants



    PHENIX Preliminary



    Noticeable differences in the asymmetries

    For associated baryons and mesons

    Slide18 l.jpg

    associated Cumulants


    PHENIX Preliminary



    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

    Slide19 l.jpg

    De-convolution Ansatz Cumulants

    Fractional yield

    Harmonic Contribution

    Test of de convolution via simulations l.jpg
    Test of de-convolution via Simulations Cumulants

    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

    Slide21 l.jpg

    Typical fit to 3d sim correlation Cumulants

    Good overall representation of the correlation function

    is obtained

    Measuring azimuthal correlations22 l.jpg

    y Cumulants

    Reaction plane





    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

    Slide23 l.jpg

    Results From Simulations Cumulants





    Simultaneous Fit Recovers Jet and harmonic properties ~ 10%

    Slide25 l.jpg

    PHENIX preliminary Cumulants

    PHENIX preliminary

    PHENIX preliminary


    Hadron-Hadron correlation (pT(trig)>3GeV/c)

    See Shinichi’s Talk

    Flavor composition study in progress -- revealing

    Slide26 l.jpg

    High Density partonic material formed Early Cumulants



    d + Au



    Pressure Gradients Develop in Partonic matter -> elliptic flow -> v2



    Hard Scattered Partons

    Traverse partonic material

     Jet-quenching (early)  v2

    This Scenario has

    Measurable Consequences

    Which can be put into


     Quantitative estimates

    Emerging Picture

    The high energy-density matter responsible for Jet Quenching

    drives elliptic flow

    Summary conclusion l.jpg
    Summary / Conclusion Cumulants

    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