Azimuthal Correlation Studies Via Correlation Functions and Cumulants

Azimuthal Correlation Studies Via Correlation Functions and Cumulants

N. N. AjitanandNuclear Chemistry, SUNY, Stony

Brook

N. N. Ajitanand, SUNY Stony Brook

Outline Outline

Motivation• Why Correlation studies ?

Correlation Techniques • Cumulant Method• Correlation Function Method

Correlation Results • Compatibility with Flow, Jets, etc. ?• What the Measurements tell us

SummarySummary


Why Study Correlations at RHICBRAHMS rapidity

distribution

Large Energy Density Substantial Flow (Hydro limit)Large Energy Density Substantial Flow (Hydro limit)Possible Access to EOSPossible Access to EOS

Substantial Energy Substantial Energy Density is Produced at RHICDensity is Produced at RHIC

time to thermalize the system (0 ~ 1 fm/c)

Bjorken~ 5 GeV/fm3

dy

dE

RT

Bj0

2

11

From ET DistributionsFrom ET Distributions


Striking difference between d+Au and Au+Au results.Cronin effect dominates in d+AuHigh-pT Jet Suppression dominate in Au+Au.

Au + Au Experiment d + Au Control Experiment

Preliminary DataFinal Data

Reminder - Single Particle Distributions Reminder - Single Particle Distributions


Correlation Studies Provide a Complimentary Probe for PossibleCorrelation Studies Provide a Complimentary Probe for PossibleQGPQGP formation formation…. (Very Important Signal)…. (Very Important Signal)

Jets are Sensitive to Jets are Sensitive to the QCD medium (dE/dx)the QCD medium (dE/dx)

Jets at RHIC

Jets: Primarily

from gluons at RHIC

hadrons

q

q

hadrons leadingparticle

leading particle

schematic view of jet production

Significant Jet Yield Significant Jet Yield Is Purported at RHICIs Purported at RHIC

Energy loss results in an anisotropy which can serve as an excellent probe of the medium

2dEl

dx


Important Tools for Important Tools for Correlation StudiesCorrelation Studies

• Anisotropy Relative to the Reaction

• Cumulants

• Correlation Functions


Measuring Azimuthal CorrelationsMeasuring Azimuthal Correlations

Reaction Plane MethodReaction Plane Method

Build distributionBuild distributionRelative to Rxn. planeRelative to Rxn. plane

2 21, tacos 2 )( ) n ( y

x

vp

p

Fourier analyze distribution to obtain anisotropy

Anisotropy = Flow if non-flow is demonstrably smallAnisotropy = Flow if non-flow is demonstrably small

Reaction plane methodReaction plane method

Reactio

n plane

x

y

2

i

Σ wi*sin(2i) tan(22) =

Σ wi*cos(2i)



CorrelationsCorrelations

1 21 2( ) )2 (in innm c

eve

1 2

1 2

( )2

( )

2

2

in

in

m

cv

v

if e

e

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

1 2 3 4 3 4 3 21 2 1 4( ) ( ) ( )( ) 4( )in in inin inne e e e e v


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


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 PreliminaryPHENIX Preliminary


Cumulant Analysis: Centrality DependenceCumulant Analysis: Centrality Dependence

Anisotropy driven by eccentricity : vAnisotropy driven by eccentricity : v22 scales with N scales with Npartpart

PHENIX Preliminary

2 2

2 2

<y > - <x >=

<y > + <x >

y

x

eccentricity

Glauber


Cumulant Analysis: Dependence on integral pT range

No significant dependence on No significant dependence on integral pintegral pTT of reference of reference

PHENIX Preliminary

pT ref

2 ( )P assor

pT


Scaling of the anisotropyScaling of the anisotropy

The differential anisotropy scales with the integral anisotropy

PHENIX Preliminary


Assorted Two-particle Azimuthal CorrelationFunctions

• 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

VirtuesVirtues


Leading Hadron Assorted CorrelationsLeading Hadron Assorted Correlations

Associated particle • MesonMeson• BaryonBaryon 1.0 2.5 GeV/cpT 1.0 2.5 GeV/cpT

pT

2 ( )P assor Leading Hadron

1.0 2.5 GeV/cpT 1.0 2.5 GeV/cpT

Re al

mix

NC

N

Correlation FunctionCorrelation Function


PHENIX Setup

Azimuthal Correlations Using Azimuthal Correlations Using DC+PC1+PC3+EMC TracksDC+PC1+PC3+EMC Tracks

Baryon & MesonMeson identification identification done using EMC TOFdone using EMC TOF

pT

2( )P assor

mesonsmesons

baryonsbaryons

2m


0.8

0.9

1.0

1.1

0 40 80 120 160

C

0.8

0.9

1.0

1.1

0 40 80 120 160 0 40 80 120 160 0 40 80 120 160 0 40 80 120 160

Cent: 0-5% 05-10% 10-20% 20-40% 40-60%

deg.)

AssociatedAssociatedMesonsMesons

/

2.5 4.0 GeV/c

1.0 2.5 GeV/cM B

LH

A

pT

pT

PHENIX Preliminary

AssociatedAssociatedBaryonsBaryons

Assorted Correlation Functions

Noticeable differences in the asymmetries Noticeable differences in the asymmetries For associated baryons and mesonsFor associated baryons and mesons


Assorted Correlation Functions

associated

associated

associated

associated

PHENIX Preliminary

• Similar Similar asymmetry trends asymmetry trends for associated for associated mesons & baryons mesons & baryons in d+Au in d+Au

• Dissimilar trendsDissimilar trendsfor associated for associated mesons and baryons mesons and baryons in Au+Au in Au+Au

De-convolution of Correlation Function NecessaryDe-convolution of Correlation Function Necessary


De-convolution AnsatzDe-convolution Ansatz

0( ) away aw

Je

Near N a

t

year F GausC a F a s HG u

Harmonic ContributionHarmonic ContributionFractional yield


Test of de-convolution via SimulationsTest of de-convolution via Simulations

• 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

Two source 3d simulation Simulation Model:Two source 3d simulation Simulation Model:

Correlation functions generated in PHENIX acceptanceCorrelation functions generated in PHENIX acceptance


Typical fit to 3d sim correlationTypical fit to 3d sim correlation

Good overall representation of the correlation functionGood overall representation of the correlation functionis obtainedis obtained



Relative to the Reaction PlaneRelative to the Reaction Plane

Reactio

n plane

x

y

2

i

Σ wi*sin(2i) tan(22) =

Σ wi*cos(2i)

Build Correlation Function Build Correlation Function Relative to Rxn. planeRelative to Rxn. plane

2dEl

dx

Simulation

Correlation Perp to PlaneCorrelation Perp to Plane


Correlations Perpendicular-to-RP

Results From SimulationsResults From Simulations

Correlations Parallel-to-RP

Simultaneous Fit Recovers Jet and harmonic properties ~ 10%Simultaneous Fit Recovers Jet and harmonic properties ~ 10%


Reliable yield extraction is achievedReliable yield extraction is achieved


DataData

Hadron-Hadron correlation (pHadron-Hadron correlation (pTT(trig)>3GeV/c)(trig)>3GeV/c)

PHENIX preliminary PHENIX preliminary

PHENIX preliminary

2dEl

dx

1 2 GeV/cpT 2 5 GeV/cpT

See Shinichi’s TalkSee Shinichi’s Talk

Flavor composition study in progress -- revealing


The high energy-density matter responsible for Jet QuenchingThe high energy-density matter responsible for Jet Quenching drives elliptic flowdrives elliptic flow

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

High Density High Density partonic material partonic material formed Earlyformed Early

Hard Scattered Hard Scattered PartonsPartonsTraverse partonic Traverse partonic materialmaterial Jet-quenching Jet-quenching (early) (early) v2 v2

q

q

leadingleadingparticleparticle

d + Au leadingleadingparticleparticle

This Scenario has Measurable ConsequencesWhich can be put into Evidence Quantitative estimates


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 FunctionsAssorted 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

Azimuthal Correlation Studies Via Correlation Functions and Cumulants

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