azimuthal correlation studies via correlation functions and cumulants n. n. ajitanand nuclear...
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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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
Important Tools for Important Tools for Correlation StudiesCorrelation Studies
• Anisotropy Relative to the Reaction
• Cumulants
• Correlation Functions
N. N. Ajitanand, SUNY Stony Brook
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)
N. N. Ajitanand, SUNY Stony Brook
Measuring Azimuthal CorrelationsMeasuring Azimuthal Correlations
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
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
v2 extracted is robust and
acceptance corrections are
well implemented
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
Scaling of the anisotropyScaling of the anisotropy
The differential anisotropy scales with the integral anisotropy
PHENIX Preliminary
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
Measuring Azimuthal CorrelationsMeasuring Azimuthal Correlations
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
N. N. Ajitanand, SUNY Stony Brook
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%
N. N. Ajitanand, SUNY Stony Brook
Reliable yield extraction is achievedReliable yield extraction is achieved
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
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