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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

Azimuthal Correlation Studies Via Correlation Functions and Cumulants

N. N. Ajitanand

Nuclear Chemistry, SUNY, Stony Brook

slide2

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
why study correlations at rhic

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

slide4

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

jets at rhic

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)

slide6

Important Tools for

Correlation Studies

  • Anisotropy Relative to the Reaction
  • Cumulants
  • Correlation Functions
measuring azimuthal correlations

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

slide8

 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

application of cumulant method in phenix
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

p t and dependence of v 2
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

cumulant analysis centrality dependence

Glauber

PHENIX Preliminary

y

eccentricity

x

Cumulant Analysis: Centrality Dependence

Anisotropy driven by eccentricity : v2 scales with Npart

cumulant analysis dependence on integral p t range

pT ref

Cumulant Analysis: Dependence on integral pT range
  • No significant dependence on integral pT of reference

PHENIX Preliminary

pT

scaling of the anisotropy

PHENIX Preliminary

Scaling of the anisotropy

The differential anisotropy scales with the integral anisotropy

slide14

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
slide15

pT

Leading Hadron Assorted Correlations

Leading Hadron

  • Associated particle
  • Meson
  • Baryon

Correlation Function

phenix setup

pT

PHENIX Setup

Azimuthal Correlations Using DC+PC1+PC3+EMC Tracks

mesons

baryons

Baryon & Mesonidentification done using EMC TOF

slide17

Assorted Correlation Functions

Associated

Mesons

PHENIX Preliminary

Associated

Baryons

Noticeable differences in the asymmetries

For associated baryons and mesons

slide18

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

slide19

De-convolution Ansatz

Fractional yield

Harmonic Contribution

test of de convolution via simulations
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

slide21

Typical fit to 3d sim correlation

Good overall representation of the correlation function

is obtained

measuring azimuthal correlations22

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

slide23

Results From Simulations

Correlations

Parallel-to-RP

Correlations

Perpendicular-to-RP

Simultaneous Fit Recovers Jet and harmonic properties ~ 10%

slide25

PHENIX preliminary

PHENIX preliminary

PHENIX preliminary

Data

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

See Shinichi’s Talk

Flavor composition study in progress -- revealing

slide26

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

summary conclusion
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
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