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
e Bj 
1 1 dET
 R 2 t 0 dy
time to thermalize the
system (t0 ~ 1 fm/c)
eBjorken ~ 5 GeV/fm3
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-pT 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:

leading particle
Primarily from
gluons at RHIC
dE
dx
l2
Jets are Sensitive to
the QCD medium (dE/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
i
Σ wi*sin(2i)
tan(22) =
Σ wi*cos(2i)
2
x
Fourier analyze distribution
to obtain anisotropy
v2  cos 2(   2 ) ,   tan (
1
py
)
px
Anisotropy = Flow if non-flow is demonstrably small
N. N. Ajitanand, SUNY Stony Brook
Measuring Azimuthal Correlations
 Correlations

ein(1 2 )
if v22
v2 
m
 vn2  ein(1 2 )
ein (1  2 )
ein (1  2 )
c
c
m
If Flow predominate Multiparticle correlations can be used to
reduce non-flow contributions (N. Borghini et al, PRC. C63 (2001) 054906)
ein (1 2 3 4 )  ein (1 2 ) ein (3  4 )  ein (1 4 ) ein (3  2 )  vn4
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
PHENIX Preliminary
PHENIX Preliminary
PHENIX Preliminary
 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 !
N. N. Ajitanand, SUNY Stony Brook
Cumulant Analysis: Centrality Dependence
Glauber
e
PHENIX Preliminary
y
eccentricity
x
<y2 > - <x 2 >
e= 2
<y > + <x 2 >
Anisotropy driven by eccentricity : v2 scales with Npart
N. N. Ajitanand, SUNY Stony Brook
Cumulant Analysis: Dependence on integral pT range
PHENIX Preliminary
P2 ( assor )
pT ref
pT
 No significant dependence on
integral pT 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
P2 ( assor )
Leading Hadron
1.0  pT  2.5 GeV/c
pT
Associated particle
• Meson
1.0  pT  2.5 GeV/c
• Baryon 
N Re al   
Correlation Function C    
N mix   
N. N. Ajitanand, SUNY Stony Brook
PHENIX Setup
P2 ( assor )
pT
Azimuthal Correlations Using
DC+PC1+PC3+EMC Tracks
mesons
baryons
Baryon & Meson identification
done using EMC TOF
m2
N. N. Ajitanand, SUNY Stony Brook
Assorted Correlation Functions
2.5  pTLH  4.0 GeV/c
1.0  pTAM / B  2.5 GeV/c
10-20%
05-10%
Cent: 0-5%
40-60%
20-40%
1.1
1.0
Associated
Mesons
C
0.9
PHENIX Preliminary
0.8
1.1
1.0
Associated
Baryons
0.9
0.8
0
40
80
120
160 0
40
80
120
160 0
40
80
120
160 0
40
80
120
160 0
40
80
120
160
deg.)
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
associated

• Dissimilar trends
PHENIX Preliminary
associated
associated
for associated
mesons and baryons
in Au+Au
De-convolution of Correlation Function Necessary
N. N. Ajitanand, SUNY Stony Brook
De-convolution Ansatz


C ( )  a0  FNear  GausNear  Faway  Gausaway  H 


Jet


Fractional yield
Harmonic Contribution
N. N. Ajitanand, SUNY Stony Brook
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
N. N. Ajitanand, SUNY Stony Brook
Typical fit to 3d 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
i
Σ wi*sin(2i)
tan(22) =
Σ wi*cos(2i)
2
x
dE
dx
l2
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 (pT(trig)>3GeV/c)
1  pT  2 GeV/c
2  pT  5 GeV/c
PHENIX preliminary
dE
dx
l2
PHENIX preliminary
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 -> v2
Hard Scattered Partons
Traverse partonic material
 Jet-quenching (early)
 v2
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.
 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
N. N. Ajitanand, SUNY Stony Brook